PT78772B - Real-time hierarchal pyramid signal processing apparatus - Google Patents

Abstract

A pipeline structure (Figure 3) is used for one or both of the following processes: (a) for the analysing, occurring at delayed real time, of the frequency spectrum of an information component (having one or more dimensions) of a given time signal (G0), the maximum frequency of interest of which is no greater than f0 and (b) for synthesising, in delayed real time, such a temporal signal (G0) from its frequency analysis spectrum (L0...G OMEGA ). Such a pipeline structure is particularly suitable for image processing of the two-dimensional space frequencies of television images which are defined by a temporal video signal (Figure 3). …<IMAGE>…

Description

DESCRIPTION OF THE INVENTION

This invention relates to a signal processing apparatus for analyzing and / or synthesizing signals. More specifically, the signal processing apparatus of this invention employs a pipe-line recorder architecture for analyzing, in real time delay, the frequency spectrum of an information component (with one or more dimensions) of a given time signal having a higher frequency of interest, not greater than f, and / or for synthesizing, in a deferred real time, a time signal from the respective analyzed frequency spectrum. Although not limited to this, this invention is particularly convenient for de-real-time image processing of two-dimensional spatial frequencies of television images defined by a time video signal.

Many works have been done in an attempt to establish a working model of the human visual system. It has been determined that the human visual system appears to calculate a prime space-frequency decomposition of the light images by the view of the spatial frequency information in a number of contiguous bands covering the frequency space. Each band has approximately the width of an octave and the center frequency of each band differs from the center frequency of its neighbor band by a factor approximately equal to two. Research indicates that there are approximately six bands or "channels" that cover the 0.5 to 60 cycles / degree of the space-frequency range of the human vi system. The importance of these findings lies in the fact that spatial frequency information farthest from that a value equal to two of other spatial frequency information will be treated independently by the human visual system.

It was also determined that the space-frequency treatment that occurs in the visual system is located in space. In this way, the signals within each space-frequency channel are calculated in small subregions of the image. These subregions overlap each other and are approximately two cycles wide at a particular frequency.

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If a sine wave grating image is uti. As a standard of testing, the threshold of the

contrast-sensitivity for grating sinusoidal wave image weakens rapidly with

* grating sine wave of the image. That is, high special frequencies need high contrast to be

¹ BAC (20% ~ 30 cycles / degree) but lower spatial frequencies require relatively low contrast to be seen (0.2% 2 to 3 cycles / degree).

It has been determined that the human visual ability to determine a contrast variation of a grating sine wave of image that is above the threshold is also better for the lower spatial frequencies than for the higher spatial frequencies. Specifically, a human mean target requires, in order to correctly discriminate a contrast variation of 75% of the time, approximately a 12% variation in contrast to 3 cycles / degree, but requires a 30% variation for a grating wave with 30 cycles / degree.

Dr. Peter Burt, who specializes in the properties discussed above, of the human visual system has created an algorithm (hereinafter referred to as "Burt's Pyramid") that he developed to compute a non-real time base to analyze frequencies dimensional images of an image between a plurality of separate spatial frequency bands. Ca of the space band (with the exception of the lower frequency band) is preferably one octave wide. Thus, if the highest spatial frequency of ng / image is not higher than _Q , the higher frequency band will cover the octave from fg / 2 to fg (having a center frequency of 3 fg / 4); the higher frequency neighboring band will cover the octave from fg / 4 to fg / 2 (having a center frequency of 3fg / 8) etc.

Reference is made to the list of articles in which the author or co-author is Dr. Burt, who describes in detail various aspects of the Pyramid of Burt:

"Segmentation and calculation of the properties of a region of

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-4gens, by means of an auxiliary hierarchical calculation "by Peter 3.

Burt et al, IEEE Transactions on Systems, Man and Cyberne ¹ tics, Vol. SMC-11, NS. 12, 802-809, December 1981.

- "The Laplacian Pyramid as a Compact Image Code", by Peter 3. Burt and others at IEEE Transactions on Communications,

Vol. COM-31, NS. 4, 532-540, April 1983.

- "Quick Algorithms for Calculation of Image Properties" by Peter 3. Burt in Computer Vision Graphics, and Imaos Processinci, 21, 368-382 (1983).

- "Tree and pyramid structures to encode hexagonally binary images sampled" by Peter 3. Burt in Computer Graphics and Imaqe Proce ssinq, 14, 271-280 (1980).

"Choice of features of local images through the Base Pyramid with applications to the Movement and Analysis of Textures" by Peter 3. Burt, in SPIE, Vol. 360, 114-124.

"Rapid filter transformers for image processing, by Peter Burt, Computer Graphics and Imaging Processing, 16, 20-51 (1981).

"Multiresolution Spline Line with Image Mosaic Applications" by Peter 3, Burt et al., In Image Processing Laboratory, Electrical, Computer, and Systems Engineering Department, Rensselaer Institute, June 1983.

- "The Pyramid as Structure of an Efficient Calculus", by Peter

3. Burt, Imprint Processing Laboratory, Electrical, Computer and Systems Engineering Department, Rensselaer Polytechnic Institute, 3, 1982.

The Burt Pyramid algorithm uses special sampling techniques to analyze the relatively high resolution within a hierarchy of N (where N is an integer) separate image components (in which each image component is a Laplacian image formed by different pitavas (which is formed by all spatial frequencies of the original image below the lowest octave of the Laplacian image component). The term "pyramid" is used here, due to the successive

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- reduction of the bandwidth of spatial and dense frequencies. _t of samples from each of the component-image hierarchies,

ranging from the highest image component to the lowest.

| x octave of image component.

ft

The first advantage of the Burt pyramid is that it allows the high resolution of the original image to be synthesized from the image components and the remaining image without the introduction of spurious spatial frequencies due to the introduction of errors in the calculated amplitudes of the lower frequencies of the Fourier analysis (aliasing). A second advantage of the Burt pyramid algorithm is that the spatial frequency bandwidth of an octave of each hierarchy of the image components corresponds to the properties of the human visual system, shown above. This makes it possible to selectively or subtly treat the spatial frequencies of each individual hierarchy of the image components in different and independent paths (ie, without the signal processing of any image component significantly affecting any other image component) for the purpose highlight or produce any other desired effect on the synthesized image derived from processed component images. An example of such an effect is the spline technique described in detail in the article "Multiresolution of Sample Lines with Applications to Image Mosaics", supra.

So far, Burt's pyramid algorithm has been used in non-real time through commonly used digital computers. The level of each pixel element of an original image is represented by a multi-bit number (eg 8 bits) stored in an individual address position of the computer memory. For example, an original bidj image.

g

relatively high resolution system consisting of 2 (512)

pixel samples in each of its dimensions requires a large memory of 2 (262 144) multibits numbers representing the levels of the respective pixel samples that form the original image.

The original image stored in memory can be processed by a digital computer according to the pyramid algorithm

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-6 from Burt. This processing involves the iterative execution of several steps, such as placing the pixel samples according to a preset internal weighting function, re

Sampling of samples, sample expansion by interpolation and subtraction of samples. The magnitude of the internal function (in one or

more dimensions) is relatively small (in terms of number of * pixels) compared to the size in each dimension of the total image. The sub-region or window of the image pixels (equal in size to the internal function and symmetrically disposed, in turn, around each image pixel) is multiplied by the internal weighting function and summed in a convolutional calculator.

The internal weighting function is chosen to operate as a low-pass filter of the multidimensional spatial frequencies of the image that has been treated. The nominal "cutoff" frequency (also known in the art of "corner" or "break" filters) of the filter, with low pass characteristics provided in each dimension by the internal function is chosen so as to be practically half the highest frequency of interest in this dimension of the signal being treated. However, the characteristic of these low-pass filters does not have a brick weakening for a given cut-off frequency, but may have a relatively gradual weakening, in which case the nominal cut-off frequency δ is defined as frequency for which a given actuation value (eg 5 db) takes place in this gradual weakening. Smoother weaker filters can be used because the Burt pyramid compensates for the introduction of spurious frequencies due to the aliasing errors caused by the gradual weakening characteristics of the low-pass filter.

The treated image is decimated by effective deletion in each of its successively considered dimensions, thereby reducing the number of pixels to half in each dimension of the treated image. Since an image is conventionally a two-dimensional image, a reduced image is formed by only a quarter of the number of pixels contained in the image before said reduction. The reduced number of pixel samples from this reduced image (which is called the Gaussian sample) is stored in

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memory.

_t Starting from the pixel samples of the original store image

The process is iteratively executed N times (in

3 that N is an integer) hence resulting (N + 1) images by opening the original high resolution image and a hierarchical pyramid of N additional reduced resolution Gaussian images in which the number of pixel samples (sample density ) in each dimension of each additional image is only half of pixel samples in each dimension of the immediately preceding image. If the original, high resolution stored image is designated Gg, the hierarchy of additional N stored images may be in particular from G1 to G3, the number of pixels being successively reduced in each of these N additional images stored in a separate memory No memories. Thus, counting with the original stored image, there is a total of N + l memories.

According to the non-real-time use of the Burt pyramid algorithm, the following computational procedure is to generate additional samples of interpolated value between each pair of stored G? Pixel samples in each dimension of these, thereby expanding means the reduced sample density of the stored image, restoring the sample density of the stored original Gg image. The digital value of each of the pixel samples of the expanded image G ^ is then subtracted from the stored digital value of the corresponding pixel sample of the original image Gg to obtain a differential image (known as Laplacia image). This Laplacian image (designated L _Q) and having the same sampling density than the original image GG is formed by spatial frequencies contained in the original image within the octave fg / 2 to FG more often a small component of error compensation for the lower frequencies which correspond to the loss of information caused by the reduction stage employed to obtain a reduced density sample of the image G1 and the introduction of interpolated value samples appearing in the expansion of the sample density replacing its value in the original image Gg. This Laplacian image Gg then replaces the original Gg image in storage, in the first of N + l memories

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-8th pyramid.

Similarly, by repeating this process, a

rarity formed by Nl additional Laplacian images from L to

It is obtained in turn and recorded in the corresponding memories

* the respective Nl additional ones, in which the Gaussian images

of Gj. up to G ^ are stored (thereby replacing the Gaussian images in G)

(which has the reduced native density of samples) is not replaced in its corresponding memory by the Laplacian image, but majr has stored in its memory a Gaussian remnant formed by the lower spatial frequencies (i.e., those below the eighth L ^) contained in original image.

The algorithm of the Burt pyramid allows the original image to be restored, without errors, by a computational treatment involving successive steps of expanding the remaining image Gy to the sampling density of the image L ^ __ ^ and then adding it to its image Laplaciana to get the total image.

This sum image is expanded in a similar way and added to the Laplacian image until the original high resolution image is synthesized by the sum of all Laplacian images plus the remaining image. In addition, following the analysis of one or more original images in N-Laplacian images, the Gaussian remnant can be introduced, and any special image processing or step changes can be made before synthesizing a complete high-resolution image from them.

The non-real time implementation of the Burt pyramid algorithm by computer processing is effective in processing the still image information. In this case the analysis of a stream of successively occurring images which can change continuously over time (eg, successive video images of a video picture) is not applicable. The real-time implementation of the Burt pyramid algorithm, as done by the present invention, is necessary for the analysis of these images which occur successively with variations in time.

More specifically, this invention is directed to a signal processing apparatus employing an architecture

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9 for pipeline analysis to analyze in a deferred time a frequency spectrum of an information component of a given time signal in which the most relevant frequency in this frequency spectrum is not greater than f _Q . Further, this information component of the given time signal corresponds to an information having a given number of dimensions. The apparatus is formed by a set of N translation means (translators) arranged in numerical order (where N is an integer multiple). Each of the translators includes a first and a second input terminals and a first and a second output terminals. The first input terminal of the translator of the set is connected so as to receive the given input time signal. The first terminal of each of the translators, from the second to the N-order, of this set is connected to the first output terminal of the immediately preceding translator of this set, so that each of the translators, from the second to N, to the sign of these to the immediately following translator of the set. The second input terminal of each of the translators is connected so as to receive the sampling signal from a periodic generator, clock. With this array, each translator of the set derives, at its first and second terminals, signals with a cadence equal to the sampling frequency of the clock applied to them.

In addition, each translator in the set has a transfer function between its first input terminal and its first output terminal for the signal information component applied to its first input terminal. The low-pass transfer function of each translator of the set has a nominal cut-off frequency which is a direct function of the clock sampling frequency applied to the second translator input of the set. On the other hand, the clock which is applied to the second input terminal of the first translator of the set has a sampling frequency which: a) is twice the frequency fg, b) provides to said information component a frequency cut-off function for said low-pass transfer function of the first translator of said set, which is less than fg. Further, the clock applied to the second

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The input terminal of each of the translators of the second to the degree N has a sampling frequency which: a) is less than the clock frequency applied to the second input terminal of the immediately preceding translator of the set, b) is at less than twice the maximum frequency of the information component applied to its first input terminal, and c) provides a nominal cut-off frequency which is lower than that of the immediately preceding tracer.

The signal derived from the second output terminal of each of the translators of the set corresponds to the difference between the information component applied to the first input terminal thereof and a direct function of the information component derived from the first output terminal of that.

Although not limited thereto, the information component of the given time signal processed by the signal processing apparatus of the present invention may, for example, correspond to the two-dimensional spatial frequency components of each of the successive images of a television picture that has been scanned in series in each of its dimensions.

In general, this invention is useful for analyzing the frequency spectrum of a signal derived from a spatial or non-spatial frequency source having one or more dimensions, without regard to the particular nature of the source. Thus, for example, the present invention is useful in the analysis of one, two, three or more dimensional complex signals from audio sources, radar sources, seismograph sources, automaton sources, etc., in addition to the sources of two-dimensional visual imaging, such as television images. In addition, this invention is also directed to equipment for treating signals using the pumping circuit architecture which respond to a set of analyzed signals for delayed real-time synthesizing such as in a complex signal.

Fig. 1 is a block functional diagram showing the present invention in a generally generic configuration;

Fig. Shows a digital configuration of a first

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-11species of any of the signal transducers shown in Figure 1;

Fig. Lb shows a digital configuration of a second es. of any of the signal transducers shown in Fig.

Fig. 1c shows an alternative digital configuration of the end of the set of translated signal translators of any first or second species of Fig. 1; Fig.

Fig. 2 shows an illustrative example of the internal weighting function that can be used in the construction of this invention;

Fig. 3 is a block diagram of a one-dimensional spectrum analyzer system, spectrum altering circuitry and signal synthesizer configuring aspects of the invention and including a label identifying certain blocks;

Fig. 4 is a block diagram of one of the analysis stages used in the iterative calculations of the preferred analysis process of Fig. 3, the analysis of which configures an aspect of the invention;

Fig. 5 is a block diagram of a modification which may be made in successive pairs of Fig. 4 of the analysis stages, in another embodiment of the invention;

Fig. 6 is a block diagram of one of the synthesis stages used in the iterative process of signal synthesis of Fig.

3 from the spectral components?

FIGS. 7, 8, 9 and 10 are block diagrams of the representative circuitry of the spectrum change of Fig. 3 for use with the invention;

Fig. 11 shows, in block diagram, modifications to the system of Fig. 3 used when it is advisable to align samples of the spectrum at the time for processing, according to one of the preceding claims. of the invention?

Fig. 12 is a block diagram of a two-dimensional space frequency spectrum analyzer using the pumping architecture to perform the real-time delayed spectral analysis; and

Fig. 13 is a block diagram of the signal synthesizing apparatus, which describes the sample field analyzed by Fig. 12, spectrum analyzer from its output spectrum. Fig.

Referring to Fig. 1, each set of N sampled translators arranged in order 100-1 to 100-N, inclusive (where N is an integer) has two input terminals and two output terminals. A given time signal Gg defining the information is applied to the input of the first of two input terminals of the first translator 100-1 of the array. The time signal Gq may be a continuous analog signal (such as an audio signal or a video signal) or, alternatively, signal G _Q may be a sampled analog signal. In addition, in the latter case, each sampling level can be directly represented by a level of amplitude or can be represented indirectly by a digital number (ie, by passing each amplitude level sample by an analog-to-digital converter, which is not indicated in Fig. 1, prior to the application of the time signal Gg to the first input terminal of the translator 100-1), the frequency spectrum of Gg includes a range extending between zero (i.e. DC) and the frequency fg (i.e., a range which includes all frequencies of interest corresponding to the information having a given number of dimensions). More specifically, Gg may be a pre-filtered signal not containing frequencies greater than fg. In this case the clock frequency 2 fg of the translator 100-1 satisfies the Niquist criterion for all frequency components of fg. However, in the alternative, Gg may contain some frequency components higher than fg, which are of no interest. In the latter case, the Niquist criterion is not satisfied where some errors occur in the calculated amplitude of the lower frequencies (aliasing). From a practical point of view, although undesirable, these errors (provided they are not very large) can often be tolerated.

In Fig. 1 the first input terminal of each of the translators 100-2 ... 100-N of the set is connected to the first of two output terminals of the immediately preceding translator of the set. Specifically, the first output terminal of the tract 710

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is connected to the first input terminal of the translator 100-2? The first output terminal of the translator 100-2 is connected to the first input terminal of the translator 100-3, not indicated? ... and the first output terminal of the translator 100- (N1) also not indicated, is connected to the first input terminal of the 100-N translator. Thus, the signal processing equipment indicated in Fig. 1 utilizes the pipeline recorder architecture in linking each of the translators of the set to one another.

A separate sampling frequency clock is applied to the second terminal of the two input terminals of each translator of the set, 100-1 ... 100-N. More specifically, translator 100-1 has a sampling frequency clock CL ^ applied to the second input of that? the translator 100-2 has a sampling frequency clock CL ^ connected to the second input terminal ,,, and the translator 100-N has a sampling frequency clock CL ^ applied to the second input terminal. The relative values of the clocks CL4 ... CL4 are conditioned relative to each other in the manner indicated in Fig. 1. The meaning

this conditioning is discussed later.

On the other hand, in Fig. 1 the translator 100-1 delivers a second output signal Î ±, θ at its second output terminal. In the same way, the other translators 100-2 ... 100-N of the set of rivas second output signals L ₂ ... in the respective output terminals.

Each of the translators, individually, 100-1 ... 100-N of the set, without looking at its particular internal structure, can be seen as a black box that has a low-pass transfer function between its first erection terminal and its first output terminal for the frequency spectrum of the input signal information component applied to its first input terminal. This low-pass transfer function of each of the translators, individually, 100-1, 100-2, ..., 100-N, of the set has a weakening for a nominal cut-off frequency that is directly proportional to the sampling frequency of the clock applied to its second ter62 710

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mine entrance. As indicated above, in the case of the Burt pyramid, the weakening can be gradual, preferably a brick weakening / all.

More specifically, the translator 100-1 has an input signal Gg, shown above, applied to its first input terminal. The highest frequency of interest in the frequency spectrum of Gg is not greater than fg. Also, the sampling frequency clock CL ^, applied to the second input terminal of the translator 100-1 is equal to 2f _Q (i.e., has a frequency satisfying the Niquist criterion for all frequencies having an interest within the spectrum of Gg frequencies). Under these conditions the low-pass transfer function between the first input terminal and the first output terminal of the trunker 100-1 is such that only those frequencies within the frequency spectrum of Gg that are not higher than f ( is less than fg) pass to the first output terminal of the translator 100-1. In this way, a signal G1 is obtained at the first output terminal of the 1CQ-1 treadmill having a frequency spectrum (defined by the characteristics of the low pass transfer function) which is formed first by the lower portion. xa of the Gg frequency spectrum. This G2 signal is then applied as an input signal to the first input terminal of the translator 100-2.

As shown in Fig. 1, the sampling frequency clock CL ₂ (applied to the second input terminal of the translator 100-2) has a frequency lower than 2fg (the clock sampling frequency CL2) but is at least equal to 2f (twice the maximum frequency f in the frequency spectrum of Gj). Therefore, the sampling frequency of the clock CL ^ is still high enough to satisfy the Niquist criterion for the frequency spectrum of G ^ applied to the first input terminal of the translator 1C0-2, although it is not high enough to satisfy the Niquist criterion for the highest possible frequency of interest fg in the frequency spectrum of Gg applied to the first input terminal of the immediately preceding translator 100-1. This type of relationship (in which

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The clock sampling frequency applied to the second input terminal of the translator of the set becomes lower than the ordered position of the translator in the set becomes higher). It is a general mode. More specifically, the clock applied to the second input terminal of each of the translators 100-2 ... 100-N of the array has a sampling frequency which: a) is smaller than that of the clock applied to the second input terminal of immediately preceding translator in the set, b) is at least equal to twice the maximum frequency of the signal information component applied to its first input terminal and, c) reduces the nominal cut-off frequency of its transfer function to a which is less than that of its immediately preceding trader of the set. Thus, the maximum frequency f of the G ₂ signal appearing at the second output terminal of the translator 100-2 is less than f ... and finally the maximum frequency f in the frequency spectrum of the signal G (which appears on the first output terminal of the translator 100-fl) is lower than the frequency f _N of the frequency spectrum of the signal G ^^ (which appears on the first output terminal of the translator - not shown - of the set which immediately precedes the translator 100-N and which is applied to the first input terminal of the translator 100-N).

Again, by viewing each translator in isolation, 100-1, ,,, 100-N as a black box, each of the respective output signals L _Q ... L _w , taken respectively at the second terminal of each isolated translator 100 -1 ..., 100-N, of the set corresponds to the difference between the signal information component apli. to the first input terminal of the translator and a function di. straight from the signal information component derived at the first terminal, from the derived signal at the first output terminal of that translator. Thus, as is indicated in Fig. 1, Lg is equal to (or at least corresponds to) the difference Gg-g (G1) in which g1 G2 is either G1 itself or a direct G1 function. So it similarity is equal to (or corresponding to at least) -g ^ L (L _2); ...

Equal to (or at least corresponds to) -g ^ L ^ (L _w)

The processing equipment described in Fig.

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-16lisa □ original signal Gg for several parallel outputs formed by the Laplacian outputs Lg, ... (respectively obtained at the second output terminal of each of the respective pumping values of the translators 100-1 ... 100- N of the set) plus a Gaussian output G ^ (obtained at the first output terminal of the final translator 100-N of the set).

Generally, the only limitations on the relative values of the sampling frequency f respeotivas _Q ... Q i _{the Eu}

indicated in Fig. 1. However, it is advantageous to specify values of the sampling frequencies applied to the second input terminal of each of the respective translators 100-1 ... 100-N, such that the respective CL- (Or may be an integer power of 1/2 corresponding to the number of dimensions of the signal forming component to be analyzed) . This results in the analyzed output of the frequency spectrum of the original signal Gg which is divided into parallel bands of frequencies of the Laplacian composites of signals Lg ... L ^^, which (regardless of any sampling errors due to loss of signal information caused by the reduction of sample density or due to the addition of spurious frequency components) each has a hi. is bandwidth for each dimension of the information component and includes only those frequencies present in the frequency spectrum of the original signal Gg falling within that particular octave. Those frequencies of that original Gg signal falling below the lowest component of the Laplacian ^L N-1 signal ^{are of} P ° ^{is included in the} remaining Gaussian signal G2 of the analyzed output.

In general, N 'is an integer multiple having any given value of two or more. However, there are types of information in which a relatively small value of N may be sufficient to examine all frequencies of the original signal Gg with a sufficiently high resolution. With an example, in the case of visual images, it is often found that a value of seven for N is sufficient, so that in this case the frequencies in each dimension of the remaining signal G ^ is less than

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that 1/128 (l / 2) of the highest frequency f _Q of the frequency spectrum Gg of the original signal.

Referring to Fig. 1a, there is a general form, the digital configuration of a first kind of translator of the respective

sampled signal 100-1 ... 100-N of the pipeline circuitry shown in Fig. 1. In Fig. 1a, the first configuration species of any of the isolated translators 100-1 ... 100 (Nl ) of the set is denoted by lQOa-K and the first set-up species of one translator of the immediately following set is designated 100a- (K1).

The translator 1OOa-K is formed by a convolutional filter di. (where m is an integer multiple of 3 or more, preferably odd) a reducer 104, an expander 106, an n-shaped interpolation digital filter, 108 (wherein n is a multiple of 3 or more - preferably odd) a delay 109 and a subtractor 110. The sample rate clock CL ^

(i.e., the clock shown in Fig. 1 which is applied to the second input terminal of each translator of the translator assembly 100a-K) is applied as an input control to each of the elements 102, 104, 106, 108, 109 and 110.

The G 2 signal connected to the first input terminal of the translator 1Q0a-K is applied as an input to the convolution filter 102 and, after the delay 109, as input to the subtractor 110. The sampling densities shown in Fig. 1a are densities of samples per size of the information signal. Specifically, the G2 signal has a sample density in each dimension of the information signal which is delineated in the time domain by the clocking sample rate of the CL1 clock of the 100A-K translator. Thus, each and every sample comprising G ^ will be operated by the filter 102, the end of the convolution filter 102

is to reduce the maximum frequency of the output signal in relation to the maximum frequency of its input signal (as has been said

back in connection with Fig. 1). However, as indicated in FIG. 1a, the density of samples at the exit of the filter 102 still maintains the CL ^ sampling rate.

This outlet of the filter 102 is applied to the inlet of the gear unit

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Of the density (decimator) 104. The reducer 104 lets

their output is only certain (not all) of the successive samples in each dimension applied to their entry by the filter 102. Thus the density of samples in each dimension at the outlet of the reducer 104 is reduced, relative to the density of samples in that dimension are at the input of the reductant 104. More specifically, as shown in FIG. 1a, the density of samples CL4 ₊ in each dimeton is at the output of the reductant 104, such that in the time domain it can be delineated for cadence reduced value defined by the reduced sampling frequency clock CI_K _{+ 1} applied to the second input terminal of the immediately following translator 100a (K + 1). Then the reduced sample of the density samples in each dime is from the signal G2 at the output of the reducer 104, as delineated in the time domain, occurs in phase with the occurrence of the clock frequency CL ^ ₊ ^ applied to the second input terminal of the immediately following translator, 100a- (K + 1). In FIG. 1a, the output signal G ^ of the reducer 104 (which covers the signal from the first output terminal of the translator 100A-K) is applied to the first input stage of the immediately following translator 100a- (K + 1). Thus the isochron relationship between the master's sampling density after G1 at the first input terminal and the master's frequency, reduced clock time CL2 ₊ at the second input terminal of the translator 100a- (K + 1 ) is identical to the isochronous ratio between the highest sampling density of G1 samples at the first input terminal and the highest sampling frequency of the CL4 clock at the second input terminal of the QQa-K translator (described above).

Although not limited thereto, a preferred embodiment of the reductant 104 is one which, in each dimension of signal information, is effective in reducing the density of samples at their inlet to a density of half. In this case the reducer 104 is effective in letting in each dimension all other samples at its inlet for its output. Thus, for a signal information of one dimension, the density of samples CL4 _{+ 4} is (ΐ / 2), ie half the density of samples CLp2. For a two-dimensional signal information, the denser

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The sample size of the CL ₂₊ samples in each of the two dimensions is half, providing a sample density of (1/2) or a quarter.

Although the baseband frequency spectrum of G2 is the same at the input to the reducer 104 and the output of the reducer 104, the reduced density signal at the output of the reductor 104 results in the loss of a certain value of phase information which is present in the highest sample density signal G ^ applied to the input of the reducer 104.

When applied to the first input terminal of the immediately following translator, the output of the reducer 104 is also applied to the input of the expander 106. The expander 106 is used to insert,

as an additional sample, a null (digital number representing a level zero) in each sample position of the clock CL ^ in which an output sample of the reducer 104 is absent. Thus, the sample density at the outlet of the expander 106 is restored to the sample density value at the inlet of the reducer 104. In the preferred case where the sample density in each dimension is halved, the expander 106 inserts into each dimension between each pair of adjacent samples in that dimension at the outlet of the reducer 104.

When the expander 106 increases the sample density of its output relative to its input, there is no change in the information of the output signal G ^ from its output relative to its input. However, the introduction of nulls has the effect of summing up images or repeats of the signal information G2 of the baseband appearing as the sideband of the harmonic frequency spectrum CL.

The G2 signal at the output of the expander 106 then passes through the interpolation filter 108. The interpolation filter 108 is a low pass filter which passes the G2 signal of the baseband but suppresses the sideband of the frequency spectrum CL harmonics. Accordingly, the filter 108 is effective in replacing each zero value zero sample with samples having an integer value, each of which has a value defined by the respective values of reference samples-information surrounding it.

The effect of these interpolated value samples is to define

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resolution of the information reference samples. Thus, the high frequency components of the signal G ,, at the output of the expander 106 which are above the base band are virtually removed by the interpolation of the filter 108.

However, the interpolation filter 108 does not and can not add any information to the signal at the output thereof which is not already present in the reduced sample density of the signal at the output of the reducer 104. In other words, the expander 106 serves to expand the sample density reduced in each dimension of the G2 signal by resetting the sample density in each dimension of the G1 signal at the output of the convolution filter 102. The subtractor 110 serves to subtract the G2 signal which appears at the output of the filter of interpolation 108 of the signal G2 connected to the first input terminal of the CC0a-K translator and applied to the input of the convective filter 102 and through the delay 109 to the subtractor 110. The delay 109 provides a delay equal to the general delay introduced by the convolutional filter 102, reducer 104, expander 106 and interpolation filter 108. Thus, as both signals applied to the inputs of the subtractor 110 have, in each dimension thereof, the same density d and CLA samples and undergo equal delays, the subtractor 110 subtracts the value represented by the digital number of each sample of the input signal G2 from the level represented by the digital number of the sample corresponding to the input of G2. subtractor 110 is the Laplacian signal L ^. obtained at the second output terminal of the translator 10K-K.

Each and all translators 100-1 ... 100-N may have the translator configuration 100a-1 of Fig. 1a. In this case the remaining signal G _fJ of the analyzed output obtained at the first output terminal of the last translator 100-N of the set will have a sampling density in each dimension of that which is smaller (preferably half) of the density of samples in each signal dimension Gpj-i applied to the first input of that. However, by definition, there is no translator to follow the 100-N translator so it is not essential for most applications (one exception is the application to compressed data transmission) that the signal density of the remaining signal G ^ be smaller than

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The signal density of the signal G2 applied to the first input terminal of the 10C-N translator. Therefore, in this case, unlike what is used throughout the translator structure 100A-K, the final translator 100-N of the set may alternatively be formed by the structure configured in the manner indicated in Fig. 1c (although each and every one of translators 10D-1 ... 100- (N1) of the first-set set is further configured by the translator type 100a-1. In FIG. 1a, the output signal of the convolution filter 102 (having the same sample density in each dimension of that as the signal G 2 applied to the input of the convolution filter 102) does not pass through the reducer, but goes directly with the remaining G ^ output signal of the last 100th-N translator of the first species set. Since, in this case, there is no reduction, there is no need for expansion and interpolation. Thus, the G2 signal at the output of the convolutional filter 102 is applied directly, as the G1 input to the subtractor 110. In other words, the configuration of the translator 100a-N in Fig. 1c is different from that of the lODa-K translator of Fig. Fig. 1a, in the absence of the reducer 104, of the expander 106, of the interpolation filter 108. In this case the line 109 provides only a delay equal to that introduced by the convolution filter 102,

The first species, shown in Fig. 1a (or alternatively in Fig. 1a and 1c), provides a real-time implementation of the Surt pyramid algorithm. Of course, in its most usual form, each of the Laplacian components of the analyzed output obtained by the Burt pyramid algorithm has an octave in the band gap in each dimension of that. This more practical form of the Burt pyramid algorithm is achieved in the real-time implementation of FIG. 1a by making the sampling frequency of the clock in each dimension with half the value of the clock sampling frequency CL1 in that dimension.

Reference is now made to another type of hierarchical pyramid, which is an alternative to the Burt pyramid. The FSD pyramid does not have certain advantageous qualities of the Burt pyramid, but the FSD has some advantageous properties that the Burt pyramid does not have. property

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of the Burt pyramid (not existing in the FSD pyramid) is the inherent compensation of the Burt pyramid in the synthesis of the original signal reconstructed for spurious frequencies, which are present in each of the respective Laplacian and remaining components of the analyzed output. On the other hand, in some applications the FSD pyramid requires less hard work and is therefore less expensive to construct than the Burt pyramid.

The signal processing equipment of this invention in preaching the pipeline architecture is also useful for obtaining a real-time implementation of the FSD pyramid. The FSD pyramid comprises a second kind of structural configuration of the respective set of translators 100a ... 100-N which are indicated in Fig. 1, using translators or floors, such as 100b-K shown in Fig. 1b (instead of floors described above 100a-K which are used in the Burt pyramid).

The translators 110-bK of Fig. 1b show a digital configuration of the aforesaid second species, in which each single translator 100-1, ..., 100 (N1) of the set indicated in Fig. 1 uses the translators, such as 10B-K and 100b- (K + 1) indicated in Fig. 1b. In addition, the translator 100b- (K + 1) in Fig. 1b represents that translator 100-1 ... 100-N of the set which is immediately following the translator lOOb-K,

As indicated in Fig. 1b, the IQOb-K translator is formed only by a convolutional digital filter, with m outlets, a reducer 104, a delay 109 and a subtractor 110. The structural configuration of a second species translator 10Qb- Fig. 1b is similar to the structural configuration of the first species translator 100a-K (Fig. 1a) with the addition that the signal (which has a sample density CL4) is applied

as an input to the filter 102 and through the delay 109 as an input to the subtractor 110, and that the output signal 0 ^ (also having a sample density CL ^) passed through the reducer 104 so as to reduce in each of the sample densities of the G2 signal to G4 ₊ before applying the reduced signal density of the G4 signal to the immediately following translator input terminal 100b- (K + 1).

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The second type of translator 10Q-K differs from the first-rate translator 1OOa-K by a direct application to the G 1 input of the subtractor 110 of the density of samples C ^ (in each dimension) of the signal G ^ which is applied to the output of filter 102 at the input of the reductant 104. More specifically, it differs from the first-order 1000a-K translator employing the sampling density

(in each dimension) of the signal G2 at the output of the reducer 104. Thus, the first species needs an expander 106 and an interpolation filter 108 to restore the G2 signal to its sampling density (in each dimension) before to be applied to the G 1 input of the subtractor 110. Because the G 1 input to the subtractor 110 of the second 100b-K translator species is not obtained from a reduced sample source, there is no need for the expander 106 and interpolation filter 108 in the lOOb-K translator configuration. Thus, in Fig. 1b, the delay 109 establishes a delay equal only to that which is introduced by the convolution filter 102. In addition, the output of the subtra

tor 110 is formed by only those components of relatively high frequencies of the signal frequency spectrum G 1 - ₁ that are not also present in the G 2 signal at the output of the convolution filter 102.

According to the second species, the final translator 100-N of the set may also have the structural configuration of the translator lOOb-K or, alternatively, may have the structural configuration of Fig. Lc.

The respective configurations of the first and second species indicated in Figs. la and lb are digital settings. In these digital configurations an analog-to-digital converter is used to convert the analog signal into digital signal samples, the level of each sample being usually represented by a multi-bit binary number. However, it is not essential that both the first and the second species of the present invention be configured in digital form. Sampled signal translators employing charge-coupled-dies (CGDs) are well known in the art. For example, CCD cross filters such as

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9

such as window filters, can be constructed as convolutional filters and as interpolation filters. The signals (CCD) are formed by discrete sample series. However, each sample has an analog amplitude level. In this way, this invention can be executed both in digital form and in analogical form.

The filtering characteristics of a filter with sockets depend on various factors such as the number of sockets, the delay time between sockets and the specified levels of magnitude and the polarity of the respective weighting factors individually associated with each socket. For purposes of explanation, the convolutional filter 102 is supposed to be a five-dimensional filter. 2 represents an example of the levels of magnitude specified for the weighting factors having all the same polarity (positive in Fig. 2) which are respectively associated with the five individual shots. It also repre- sents the effective delay time between each pair of adjacent sockets. More specifically, as indicated in Fig. 2, the actual delay time between each pair of adjacent sockets is 1 / CL2, the sampling period defined by the sampling frequency clock CL4 individually applied to the convolutional filter 102 of each of translators 100-1 ... 10Q-N of first or second species (shown in Figs 1a, 1b and 1c). Thus the absolute value of the latency time CL ^ of the convolutional filter 102 of each translator 100-2 ... 100-N is greater than that of the immediately preceding translator of the set.

In Fig. 2, the weighting factors associated with the five sockets all have positive polarities and have amplitude levels which are symmetrically distributed relative to the third socket. More specifically, in the illustrated example indicated in Fig. 2, the weighting factors associated with the third socket has the specified value of six, the weighting factors associated respectively with each of the second and fourth sockets, which has the same value as four, and the weighting factors associated with each of the first and fifth sockets have the same value specific, even lower and equal to one hundred. THE

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(And hence the shape of the filter characteristics in the frequency domain) of the convolution filter 102 of each translator 100-1 ... 100-N of the set. Specifically, because all 200: (1) samples have the same polarity (positive

in Fig. 2) J (2) are symmetrically arranged around a central (third) sample; and (3) the level of the sample becomes smaller as it moves away from the central sample, the convolution filter has a low pass filter characteristic on each of the respective translators 100-1 to 100-N. Although in Fig. 2 they have the same (positive) polarity this is not essential to a low pass filter. Some of the weighting factors may have opposite polarity (negative) signs as long as the algebraic sum of the weighting factors is different from zero. The waveform of the internal function (such as the envelope 202 of Fig. 2, for example) may be identical for all the convolutional filters 102 of the respective translators of the array, so that the relative low-pass frequency characteristics of the filter characteristics in the frequency domain) are the same for all filters 102 (although this is not essential). However, the absolute value of the nominal low-pass cutoff frequency of the filter, for each individual translator, has a time-lag which depends on the sampling frequency period 1 / CL ^ for that filter. At an appropriate choice, the levels of the weighting factors 200 (which is not required to have the particular values 1, 4 and 6 indicated in Fig, 2) a nominal low-pass cutoff frequency for the signal G ^ to the output of the convolution filter 102 (having in each dimension a sampling density CLp) which is practically half of the maximum frequency (or, in the case of Gg, the highest frequency of interest fg) of the input signal to the 1C2 convective filter. In this case, the reducer 104

reduces in each dimension the density of the one-dimensional sample of the G2 to CL2 / 2 signal by taking any other sample in this dimer. However, the signal G2 (which is defined by the sample envelope 202) remains essentially the same at the input and output of the reducer 104 (although there are some loss of information

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Phase due to the lower sample density at the output of the reducer 104).

Certain preferred embodiments of the real-time use of the Burt pyramid, which form the first species (shown in Fig. 1a) of Fig. 1, will now be described.

Reference is made to Fig. 3 which shows the block scheme of a spectrum analyzer, spectrum alteration circuitry and operation as a signal synthesizer operating on an electrical signal representing one-dimensional information (such as any type of signal varying nc time, for example).

Fig. 3 shows the original electrical signal to be analyzed spectrally, when O is applied in analog form to an analog-to-digital converter (ADC) 305 for scanning. Res. ADC digital post 305 is called Gg. The higher frequency response of Gg, a high-pass spectrum Lg, is selected on a zero-order analysis stage, 310, to release G2, which is a low pass filtered Gg response. The higher-frequency portion of G ₁ , a band-pass spectrum is ex. from the first-order analysis stage 315 to release G? / low pass filtered response to G?. At the higher frequency portion, a bandpass spectrum below the band pass spectrum is extracted in a second order analysis step 320 to release G4, the low pass filtered response of G2. The higher G portion of frequencies in a band pass spectrum below the band pass spectra and is extracted from a third order analysis stage to release G4, a low pass filtered response of G2. The portion G ^ higher frequencies, a spectrum bandpass spectrum is extracted below a floor of the fourth order analysis p_a 330 Ra release G _5, in response filtered low-pass G ^. The higher frequency portion of G2, band pass spectrum below the other band pass spectra is extracted from the fifth order analysis stage 335 to release G4, the remaining G4 low pass filtered response. The answer G ^ is, with effect. to, a six-pass low-pass filtered Gg signal.

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Analysis stages 510, 315, 320, 325, 330 and 335 include low pass filtering stages 311, 316, 321, 326, 331, 336, respectively, with successively narrower pass bands. The low pass responses of these filters 311, 316, 321, 326, 331, 336 are sufficiently narrower than their input signals so that they can be re-recorded with a second rate before proceeding to the next analysis stage . Sample reduction is done by selection on a regular basis in the reduction circuits 312, 317, 322, 327, 332, 337 followed by the filters 311, 316, 321, 326, 331 and 336 respectively. In the octave spectrum analysis, which is used, alternating samples are eliminated by the reduction process (decimation).

The higher frequency portions of the input signal applied to each analysis stage are separated by withdrawing the low frequency portions of its input signal. The lower frequency portion of the input signal has the problem of being undesirable because in a matrix of samples has a lower resolution than the input signal and are undesirable because they delay in relation to the input signal. The first of these problems is solved in the expansion circuits 313, 318, 323, 328, 333 and 338 by introducing nulls at points where sampling in the array of response samples from the pas, sa-low filter is then eliminated by filtration the spurious harmonic spectra concomitantly introduced. The second problem is solved by delaying the input signals of the analysis stages prior to subtraction of the expanded low pass filter responses provided by the circuits 313, 318, 323, 328, 333, 338.

Delay and subtraction processes are performed in the circuits 314, 319, 324, 329, 334 and 339 respectively in the analysis stages 310, 315, 320, 325, 330 and 335. (In certain cases, as will be described, advantageously dividing elements between the initial low-pass filter and the delay and subtraction circuits of each analysis stage).

The spectral analysis described hereinabove is, by nature,

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pipeline and is progressively larger in the time away from the samples samples L ^ samples, samples and samples L ₅ with respect to samples L _Q. The term "time skew" as used herein refers to the differential time delay of predetermined known values occurring between the samples of the corresponding informational related information signals such as between the samples of the analyzed output signals, Lq, L ^, L _2, L ^ L ^, and Lg spectrum analyzer shown in Fig. 3. the signal from the synthesis methods of the spectra, to be described requires removal times opposing the respective sets samples. This can be established by delay lines 340, 341, 342, 343 and 344 (typically formed by offset registers or other memory satisfying the equivalent function - for example, read-after-register ( read-then-u / rite)) to Lq, L ^, L _2, L ^, U ^, samples respectively before their change in circuits 345, 346, 347, 348 and 349, as shown in Fig. 3. Alternatively, the spectra and the sample of the altered spectrum may subsequently be changed, or the delay may be apportioned before and after the change, in several ways - for example to allow for spectrum changes to be made in parallel time. to conceive that different delays within the changeover circuits 345, 346, 347, 348 and 349 may be used as portions of the overall set of different delay requirements in some circumstances.

The spectra L1 and are changed in the switching circuits 350 and 351. In some applications of signal processing some switching circuits are not required and will be replaced by the respective direct links. The rapidly described spectral analysis procedures can be extended, using an additional analysis steps, or truncated by the use of a few analytical steps. The low pass spectrum remains, at the end of the spectral analysis it will not be in such cases G ,.

O

In signal synthesis, by recombination of the possibly altered spectrum analysis components, the reduction of the matrix

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from the analysis stage to the analysis stage should not be done since the spectrum samples can be summed using the adders 353, 355, 357, 359, 361, 363. That is, in addition to the correction of the time lag in the delay circuits 340-344. The reduction is replaced using the expansion circuits 352, 354, 356, 358, 360 and 362 which are essentially like the expansion circuits 338, 333, 328, 318 and 313 respectively. In fact, by multiplexing, an isolated circuit can perform a dual function. The remaining low pass spectrum, Gp, is shifted forward in time relative to the adjacent bandpass spectrum, Lq so that its expansion aligns its samples in time with those L (j-1) ' ^L & i7 ^ 6 & 9 ^u changed (new Gg ') and ex

in the expansion circuit 352, then summed in the adder 353, to an altered L q (Fig. ₅ in Fig. 3) resulting in a new Gg '. The output of the adder 353 is expanded in the expander circuit 354 and summed in the add-on circuit when delayed and changed

to synthesize new G ^ '. The output of the adder 355 is expanded in the expander circuit 354 and summed in the adder 357 to the delayed and altered to synthesize new G ^'. The output of the adder 357 is expanded in the circuit 358 and summed in the adder 359 to the delayed and modified L ₂ to synthesize new G ₂ '. & adder output 359

is expanded in the expander 360 and summed in the adder 361 in the delayed and altered L ₂ to synthesize new G ^ '. Finally, the output of the adder 361 is expanded in the circuit 362 and summed in the adder 363 to synthesize new Gg '. The new Gg ', G'', G * _2, G'',G'',G'',Gg' are shown in Fig. 3 in the signal synthesis circuit. New Gg can be converted into analog form by means of a digital-to-analog converter (not indicated) if desired.

The expansion circuits 352, 354, 356, 358, 360 and 362 are. tab-up rejection band at each step of the synthesis process. When the bandwidth of the spectra is not wider than one octave, this establishes the suppression of any harmonics generated by the alteration circuits 345-351 which instead force the synthesis of odd signals which introduce spurious frequencies.

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Fig. 4 shows more explicitly the construction of a spectrum analyzer for a one-dimensional information such as 510, 515, 520, 525, 550 or 555 used for octave spectrum analysis. The step is of the order K of the spectrum analysis step, where t is equal to zero or a positive integer. In the case of the spectrum analysis stage is of zero order, the frequency clock for the floor will have a cadence R for sampling the original input signal, Gg, the spectrum of which

is to be analyzed. In case K is a positive integer to K

clock frequency is reduced to 2.

The input signal, G ^, for the spectrum analysis stage, Fig. 4, is applied as input to the first offset register 470 with M stages and will operate at the clock frequency R / 2. The (N + 1) samples with progressively higher delays supplied by the shift register 470 are erected and output from each of their output functions as a delay line with multiple outlets of a low pass delayed line filter. The samples are weighted and summed in the circuit 471 to provide samples of the response of a pas filter. sa-low linear phase, 6m all-stage analysis,

except for the initial one, in which the K stages exceed zero, the clock rate reduced by half (compared to the clock rate of the previous stage) used in the first des register. and the sum of the weighting and summing circuit 471, reduces relative to G2. The response Gq2 is applied to an input of the multiplex 472 which provides an alternating selection between its input signal G2, and a null entry, to

zk

that is done with the R / 2 cadence, to generate a signal

(K + 1)

The G signal,

has a frequency band spectrum

(K + 1)

(K + 1)

double sideband, suppressed carrier, with the amplitude of peak of Note, in passing that the subsequent floor

can use the timed value instead of as input. The signal is applied as an input signal to another shift register 475 having several outlets (which may be the same as or different from M)

of a two fold basis, mixed with a harmonic spectrum

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and connected to the R / ^f 2 cadence \ The (M + l) samples provided by shift re gistador 473 whose input signals and output of each of the levels are provided to another circuit to circuit 471. Circuit 474 0

harmonic and provides

in an array of samples with as many samples as G ^.

weighting and the like sum 474 suppresses the spectrum of the former an expanded version of G / ,,. \

In an adder circuit 475, this expanded version of G "is subtracted from G ^, after G ^ has been delayed in the shift register 470 and in the delay circuit 476, the delay of Gp cycles, in the shift register 470 compensates for delaying I / 2 cycles of the central sample weighting circuit and adds 471 corresponding to G 'sample to the floor of Fig spectral analysis. 4, and similar delay M / 2 cycles between ^EAA ^ ^{ost :} central ^ca for eir

and the sum of the weighting and summation functions 474. The delay circuit 476

introduces a delay to compensate for delays in performing the addition in the weighting and summing circuits 471 and 474 and the offset 476 can simply be established by an extension of the shift register 470 by the required number of additional fields. The output signal, L ^, of the adder circuit 4 5 5 is one of the components of spectrum analysis, its lower frequency limit established by the low pass filtering done on the spectrum analysis stage K shown in Fig. and has its highest frequency established by the low-pass filtering of the analysis stage of the preceding spectrum.

Fig. 5 shows a means for reducing the number of stages of displacement registers used in a spectrum analyzer constructed in accordance with the invention. Samples for set 'that are to be weighted and summed to perform low-pass filtering associated with the interpolation is obtained from the delay line structure with sockets used to support low-pass filtering ^ G ^ _{+ 1} in successive spectrum analysis stages, preferably the use of shift registers 473.

Fig. 5 shows, by way of example, how this is done

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between the zero-order analysis floor used to generate Lg and the succeeding analysis stages · Elements 570-0, 571-0, 575-0 and 576-0 are those zero-order elements of the spectrum analysis floor that correspond to elements 470, 471, 475 and 476 of the K spectrum spectrum analyzer of Fig. 4. The first order analysis elements 570-1 and 571-1 are analogous to elements 570-0 and 571- 0 of the zero-order spectrum analysis stage except that to work at a half-rate · The four samples drawn from the input and the first three outputs of the shift register 570-1 are provided in parallel with the clock rate of R / 2 ·

They are interspersed with nulls and the results are seriously weighted in two steps by the seven ABCDCBA filters to generate the pair of successive samples that must be replaced at the retarded Gg R rate in the subtractor 575-0.

The first sample of each pair of successive samples to be subtracted from the delayed Gg is obtained by multiplying the input of the shift register 570-1 to its first three outputs by weighting the filters A, C, C and A in the weighting circuits 580 , 581, 582 and 583 then summing the weighted samples in the sum circuit 587. The interleaved nulls will fall at the points to be weighted by B, D, B for this positioning of G4 vis-a-vis with the weighting standard of filter. The last master of each pair of the successive samples to be substituted for the delayed Gg is obtained by multiplying the input of the data recorder. 570-1 and its first two inputs by the weight of the filters B, D and B weighting circuits 584, 585 and 586 then summing the weighted samples in the adder circuit 588. The nulls will drop at the points to be weighted A, C , W,

A for this positioning of G, vis-a-vis with the weighting factor of the filters. The multiplax 589 will operate 1 clock rate R alternately selected from the samples outputted from the summing circuits 587 s 588 to provide the flow of samples to be subtracted from the delayed Gg in the subtractor 575-0.

Fig. 6 shows in more detail a floor of Fig. 3 of the signal synthesizer. The G1 (or delayed or altered) samples are interspersed with nulls in a multiplier 692 and signal

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The expanded array 6 is applied to the input of the tester 693 having M (or other multiple number) floors and is operated at the rate of the expanded samples. The double-cadmulated G 2 '(or G) spectrum, devoid of harmonic structure, is then supplied from the weighting circuit and sum 694 to an adder 695 to be combined with the time-delayed altered to align with the filtered filtered Gjc * (° ^u G β) being added samples. The multiplex 692, the offset radiator 693, and the weighting and summing circuit 694 may be multiplexed to serve as elements 472, 473 and 474 in the spectrum analysis process.

At this point the low pass filtering characteristics to be used in the step-by-step filtering step of the spectrum analysis procedure and in the steps of expanding the spectrum analysis and synthesis processes will be considered. The low-PAAT filter is linear phase, so that the type of filter weights 6 symmetrical with respect to a central sample. The sum of the weights of the filter is equal to the unit so as to suppress as much as possible the low frequencies in the high-pass spectrum in the spectrum Lg and in the band pass spectra L ^, L ^, L ^, ... If the analysis of spectrum to be done in octaves, with reduction made for two in subband recoding removed by low pass filtering on each stage of spectrum analysis, it is intended to remove frequencies lower than two-thirds of the center frequency of the spectrum during filtering low pass The filter response response step (called a brick uall) introduces a sharp drop in the filtered signals, increasing the dynamic range of both functions G ^ + jj extracted from the spectrum analysis stage, and generated by the subtraction of expanded and of G2. This is an example of the "Gibbs Phenomenon", which can be tempered by the use of a less abrupt cut of the Fourier series. There are several cut-off windows giving a low Gibbs filter response; for example those attributed to Bartlett, Hanning, Hamming, Blackman and Kaiser. Reference is made, for example, to section 5.5 of the book "Digital Signal Processing" by A. U. Oppenheim and RW Schafar, published by Prantice-Hali Inc.

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(i.e.

· ^/ Βτ

-Englawood Cliffs No. 3 "in 1975, whose section is entitled" Construction of FIR Filters Using Windows "and appears on pages 239-251.

In the pticatica the number of samples in the low-pass filtering are usually few. In a filter using an odd number of samples the filter response will be formed by a direct component and a series of cos harmonics, and in a filter using a pair of samples the filter response will be formed by a direct component and a series of harmonics of the breast. The desired response is approximated from that obtained in a computer to perform a process and error selection of the coefficients of determination.

It is possible to create spectra of equal quality (θ) with different band widths of the octaves, according to the invention, although making an approximation that restricts their complete use. The cut-off of the low-pass filter responses to select all third harmonics and filtering frequencies below half the center frequency of the band-pass spectrum to obtain the low-pass response produces a set of successively narrower band pass spectra in width bandwidth, for example one-third instead of one-half

The sample changing circuits 345-351 of Fig. 3 may take a variety of forms and certain of them may be replaced by direct bonds. To eliminate low level background noise in the various spectra, for example, each switching circuit 345-351 may include a base line clip-on connector 700 of Fig. 7. Such a connector 700 may be either single or with cut of the least significant bits of the signal.

Fig. 8 shows a circuit that can be used for each of the switching circuits 345-351 to establish a spectrum-scanning circuit. The rotary switch 897 is wired to give a binary code for each of di. axle displacements. This code is provided through a single memory circuit (latch) 898 to a two-quadrant multiplier to multiply samples from the input spectrum to generate samples of an output spectrum for

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be synthesized to generate Εθ '. The simple memory (latch)

898 maintains the input code for multiplier q 889 while rotary switch 897 is being changed. Each of the octave spectra to be subdivided can be arranged using digital filters employing the same sampling rate as used for produce the octave spectrum or a half sample rate, and then individually adjust the hooks of the spectral subdivisions. The subdivision of the octaves to twelve provides individual pitch and half tone adjustments of the encoded musical signals, for example.

The change circuits can be ROM-type (read-only-msmories) for storing non-linear transfer functions. For example, a ROM 990 storing a log response for the input signal in Fig. 9 may be used in each of the sample altering circuits 345-351 of a transmitting device and a ROM 1091 storing an exponential response to the input signal in Fig.

10 may be used in each of the sample changing circuits of a receiving device to pre-emphasize the signal prior to transmission and de-emphasize upon reception. Other emphatic or non-sympathizing complementary characteristics may alternatively be stored in the ROM changer circuits of the transmitter and receiver of the signal-to-spectrum analyzers.

Fig. 11 shows the modification of the signal synthesis and spectrum analysis system in Fig. 3 in which delays between the analysis and the synthesis are partitioned to provide spectral samples without time-out for processing. Such alignment is desirable, for example, in a spectrum analysis compression system used to separate signals within the spectra prior to compression, so that the compressed spectra can be filtered to suppress distortions generated during rapid compression or decompression of the signal. The amplitude of the original signal supplied to the analog-to-digital converter (ADC) 305 Fig. 3 may be detected to deliver in the -1130 circuits the DC compression control signal

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which is supplied to each of the compressors 1110, 1111, 1112,

1113, 1114, 1115, 1116 to establish a rapid attack, and a slow descent in compression of the signals they compress. The compressors 1111-1116 may essentially be formed by digital multipliers with two quadrants, with the control signal CC produced from of a digital analogue converter in cascade after the conventional analog circuits for the detection of the signal to be compressed and to produce in response to this detection an analog signal of control of compression

The compressors 1110, 1111, 1112, 1113, 1114, 1115 and 1116 work on the Lg, L ^, L ^, L ^, θ

have been differentially delayed using the delay circuits 1100, 1101, 1102, 1103, 1104 and 1106 to time align their respective samples. The delaying circuits 1120, 1121, 1122, 1123, 1124 and 1125 are then spaced apart from the compressed signals Lg ', L', 'β

For the process of signal synthesis using the elements 352-363 of Fig. 3.

The delays in the delay circuits 1106 and 1125 are essentially M / 2 clock cycles R / 2 ^, where K is either five or 16M clock cycles of the base clock R, whose delay takes part in the assembly of samples for the weighting circuit and the sum 474 óltimo floor of spectrum analysis 335. This delay 16M cycles will increase the time delay to accommodate the amount of time in the expansion circuits 338 and 352 and a P delay ^ara accommodate the sum of times in the delay and subtraction circuits 334 and in the adder 353. The entire addition process will be assumed to be carried out at the rate of the clock R and and are expressed as numbers of these clock cycles.

The delay in the delay circuit 1104 will be greater than 1M + D 2 + D? cycles of the clock rate, R, by the time difference it takes to produce from G ^ and the time it takes to produce from G ^

Taking produce from 6 L ^ M cycles of R / 2 ⁵ the clock rate to twice the sampling for weighting

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-37β sum, or 32M cycles of the basic cadence, plus 2D for two sets of sample sum plus for the subtraction of the mixtures. The time it takes to produce from G4 is M / 2 cycles of R / Of the clock rate to take samples for weighting the sum, or 8M cycles of the basic cadence plus D2 for the sum of the samples plus for the subtraction of the samples. This takes 24M + D cycles of the clock basic cadence of an extra delay to align samples in time with samples. In this way the delay circuit 104 will have an overall delay of 4QM + 2D + D2 cycles of the base cadence R. Calculations similarly determine the base cadence cycles R by which the backsamples are to be delayed in the delay circuits 103, 102, 101 and 100 are delayed by 52M + 3D2 + 582 + 4D2 + + + D2 and (62 1/2) M + 6D4 4-D2, respectively.

The delay required for the delay circuit 1124 is in excess of that provided by the delay circuit 1125, or the time taken for expansion in the circuit 354, D2 associated with the addition at the adder 55. The first delay was M / 2 cycles of R / 2% of the clock rate taken to collect samples for weighting and summation, 8M cycles of cadmium R, plus associated with the sum in weighting process s sum. The total delay in the delay circuit 1124, 1122, 1121 and 1120, in terms of cycles of the basic cadence R, are: 28M + 3D ₂ + 3D ₂ , 30M + 4D ₁ + 4D ₂ , 31M + 5D ₁ + 5D ₂ β (31 1/2) M + 6D ₁ + 6D ₂ respectively.

Similar calculations may be used to determine the delays in the delay circuits 340-344 of Fig. 3 admitting change patterns 345-351 all having equal delays. Delay circuits 340, 341, 342, 343, 344 and 345 have respective delays in cycles of basic cadence R 77M + 12 0 ^ 702 '76M + 10D ₁ + 6D ₂ 72M + 8D _jl + 5D ₂ 64M + 6D ₁ + 4D ₂ and 48M + 4D ₁ + 3D ₂ .

The digital filtering used in the spectrum analyzer is a hierarchical filtering class of general interest in this low passband or filtering passband which extends over many, many samples are made with relatively low

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number of samples that are weighted and summed at any time

Although the present invention is applicable for use in the spectrum of a signal representing unidimensional information, the Burt pyramid was designed to primarily analyze the spatial frequencies of bidimensional image information. The present invention enables real-time spectral analysis of spatial frequencies of image information change, as occurs in successive video images of a television viewer

As known in the television technique, successive video images (in the American format NTCS) appear successively with a cadence of images of 30 images per second. Each image is formed by a track of 525 interspersed horizontal scan lines. Successive horizoji scan lines numbered with odd numbers of an image are transmitted sequentially during a first field period. Scan lines of an even numbered image are transmitted sequentially during a second field period following the first field period. This is followed by the first field period of the next image. The duration of each field period δ l / 60 of the second. However, storage must be provided for at least the number of pixels at a field time that is capable of defining the full spatial frequency spectrum of the deferred real-time image.

The technique, known as progressive scanning, is known in the art of television to derive from an NTSC television signal, successive complete images of 525 lines with a cadence of 60 frames per second. This technique involves delaying each of the successive NTSC fields for a field period of 1/60 of the second. Accordingly, successive scanning lines of an odd field that occur currently are interspersed with the successive scan lines of an immediatly preceding field for which it has been delayed from a field period to provide a complete pixel image image during that occurrence of the odd image of each successive image.

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. In a like manner the successive scanning lines of a currently occurring field are interleaved with the scanning lines occurring successively in an immediately preceding odd field which has been changed by field period to give a full pixel image during that even period of current field of each of the successive images

The progressive scan technique described above is particularly used to obtain high resolution imaging in what is known as high definition television (HDTV) which is now being known in the television arts. The present invention is also used in HDTV to provide visuals. enhancement of improved images.

Fig. 12 shows a spectrum analyzer embodying the principles of the present invention for operating signals representing two-dimensional information, such as spatial frequency image information contained in progressively and successively scanned television video images. Alternatively, however, such two-dimensional information may be obtained from a non-interleaved television camera or from a television camera with interleaved lines followed by an appropriate buffer.

The monochromatic processing of the luminance signals will be described in Fig. 12, for the sake of simplicity of description, but the tactics to be described may be applied indivi- dually to the primary colors of color television signals or to signals appearing therefrom. algebraic registration. An original video signal is provided in a trace-scan format to an analog-to-digital 1205 converter for sampling if it is not sampled, for resampling if already sampled, and for final scanning. The digitized video samples, as signal, are called Gg and contain the full spectrum of two-dimensional spatial frequencies of the original signal and the harmonic spectra of that attributable to the sampling processes. These aspects of harmonics are symmetrical with respect to their respective sampling rate and

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-Your harmonics. These harmonic spectra will be treated specifically in the following description. The main fact of its existence is verified because the harmonic spectra must be considered in the design of the two-dimensional Low-Frequency Spatial-Frequency filters used in the spectrum analyzer of Fig. 12. This is due to the fact that these harmonic spectra give increase at the lower frequencies of the Fourier series during the spectral analysis and during the synthesis of the signal from that spectral analysis.

On the zero-order spectral analysis floor, 1210 □ high-pass spectrum Lg or separate from Gg. The high-pass operation is essentially performed by filtering G _Q , delaying Cg in its timing at the output of the ACD converter 1205 to the same degree as the lower frequency portions of Cg. so delayed by the low pass filter response, and subtraction of the low pass filter response from the delayed 0θ. Assuming that the spectral analysis will be processed by octaves, the cutoff frequency at the two two-dimensional low-pass spatial frequencies of the filter 1211 is chosen to be the highest frequency of the next octave bandwidth of the passband spectrum a be analyzed - that is, four-thirds of its central frequency. In the splitter 1212, lines are routed to alternating columns of samples to sample the filtered Gg signal with R / 2 cadence spatial frequency, whose sample cadence signal is reduced as the low-pass output of stage 1210 for the next spectral analysis. The Gg signal, low pass filtered with reduced sample rate, is then subjected to interpolation following the methods established by RW Scbafer and LR Rabiner in his paper published in PROCEEDIBGS 0F IEEE, Vol. 61, n. 6, June 1973, and entitled "Processing of Approximate Digital Signals for Interpolation", p. 692-702. In the expansion circuit 1213 the samples eliminated in the reducer 1212 are replaced with nulls to provide input signal to another two-dimensional low pass spatial frequency filter 1214. This filter can use the same weighting coefficients as the low pass filter but in any case it has practically the same cut-off frequency

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than the initial low pass filter The resulting signal has a sampling matrix coextensive with that of Gq when delayed in the delay circuit 1215 and is subtracted from the Gg set in the subtractor 1216 to deliver a high pass output response, Lq. Lq is not only the high-pass portion of Gq but also contains phase error correction terms for the lower frequencies as indicated above, to be used during the re-synthesis of the video signal from the spectral analysis, to compensate for the errors introduced by resampling Çq at the lowest sampling rate on the 1212 gear unit ·

This separation of the two-part signal from a low-pass, which is re-sampled with half the cadence, and another pass-through is repeated on each stage of spectrum analysis. • Each successive stage of spectrum analysis receives as its input signal the re-sampled low-pass output response of the preceding spectrum analysis stage with the sampling rate reduced to half in each successive stage of spectrum analysis relative to the cadence of the preceding spectrum analysis stage. The answer. the output pass-through of each spectrum analysis stage 1220, 1230, 1240, 1250, 1260 after the initial stage 1210 has a higher threshold imposed by the low pass response characteristic of the preceding stage so that these response responses output signals are effectively band-pass spectra of equals Q of descending spatial frequencies. Since the reduction of initial filter responses is low, on each floor, a factor of two and the cut-off frequency of the filters going down, on each floor, two-thirds of the central frequency of the analysis spectrum it generates, these are the factors that cause these spectra of equal Q to the descending octaves of two-dimensional special frequencies.

The low pass-down response of G ^ of the spectrum analysis stage 1210 applied from its reductant 1212 as input signal to the next spectrum analysis stage 1220. The spectral analysis stage 1220 has elements 1221, 1222, 1223, 1224 and 1226 analogous to elements 1211, 1212, 1213, 1214, 1215 and 1216 respectively of stage 1210 of the analysis of the

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^ qglgr

-40 spectro; the differences in operation lie in the fact that the operating frequencies on stage 1220 are half the value in both dimensions in relation to stage 1210. sa-bass 1221 and 1224 have weighting coefficients such as the low-pass filter 1211 s 1214, respectively; but halving the sampling rate on stage 1220 compared to that of stage 121Q cuts the cutoff frequencies of the filters by half

1221 and 1224 compared to the filters 1211 and 1214. The delay before subtraction in the delay circuit 1225 is twice as large as in the circuit 1215; said delays being similar to the 2: 1 lag ratio provided by the ratio 2: 1 of the respective clock rates in the delay circuit 1225 and in the delay circuit 1225, delay circuit 1215 · The high pass output response of the spectrum analysis stage 1220 is a band pass spectrum of spatial frequencies immediately below the spectrum Lg ·

The low, low pass G-response output of the spectrum analysis stage 1220 S is provided from its reductant

1222 as the input signal to the next spectrum analysis stage 1230. The L-band spectrum is one octave below L-

6 is the high pass output response of the spectrum analysis stage 1230 to its input signal G0 · 01230

spectrum analysis is formed by elements 1231, 1232, 1233, 1234, 1235 and 1236 corresponding respectively to elements 1221, 1222, 1223, 1224, 1225 and 1226 of spectrum analysis stage 122Q, except for the sampling rate that half·

The low, low G 2 output output response of the spectrum analysis stage 1230 is provided from its reductant 1232 as the input signal of the following stage of spectrum analysis 1240: the bandpass spectrum Lj a octave below L ^

The high-pass output response of the spectrum analysis stage 1240 for its input signal G 0, the spectrum analysis stage 1240 is formed by the elements 1241, 1242, 1243, 1244, 1245, 1245 and 1246 respectively. elements 1231,

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1232, 1233, 1234, 1235 and 1236 of the 1230 spectrum analysis stage, except at the sampling rate which is half

The reduced low pass-through response of G1 of the spectrum analysis stage 1240 is provided from its reductant 1242 as the input signal for the following step 1250 for analyzing the L1 spectrum. The L spectrum ^, one octave below L ^, 6

the high pass output response of the spectrum analysis stage 1250 to its input signal G2. 0 floor analysis

1250 is formed by elements 1251, 1252, 1253, 1254, 1255 and 1256 corresponding respectively to elements 1241, 1242, 1243, 1244, 1245 and 1246 of stage 1240, except at the sampling rate which is half.

The low-pass, low G 2 output response of the spectrum analyzer 1250 is provided from its reductant 1252 as the input signal to the following spectrum analysis step 1260. The L-band spectrum is one octave below the high-pass output response of the spectrum analysis stage 1260 for its G-Spectrum analysis input signal 1260 formed by elements 1261, 1262, 1263, 1264, 1265 and 1266 corresponding respectively to elements 1251, 1252, 1253, 1254, 1255 and 1256 of the spectral analysis stage 1250, except at the sampling rate which is one half.

The low-pass, reduced G &quot; output response provided by the final stage spectrum analyzer reducer, where Gp is the Gg value provided by the reductant 1262 of the spectrum analysis stage 1260, a low pass-through response of the spectrum . It serves as a basis for the synthesis of signals by the sum of the interpolated band pass spectral responses of the last stages of spectrum analysis and the most important high pass spectral response step of initial spectral analysis. ί.θ, L ^, I_ _2, Lj, and Lk are spaced in time, being provided with increasing delay values. The remaining low pass spectrum (here Gg) precedes in time the last passband spectrum L (here L ^) in time away from directly opposite

to.

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As will be described hereinafter the iterative methods of signal synthesis from the spectral components also require that the spectral components Î ± -θ, LÎ ±, LÎ ±, LÎ ±, and are at this time apart directly opposite each other · Before describing the treatment of spectral analysis and synthesis of signals from the spectral analyzes of the processed signals, a more detailed description of the structures of the analysis stages of the spectrum is given

The first consideration will be on the structures of the two-dimensional input low-pass filter

As known in the art of filter construction, the structures of a two-dimensional filter may be non-separable or alternatively of a separable nature. Separate filtration in the first and second dimensions may be accomplished by first filtering in a first direction using a first one-dimensional filter and then filtering in a second orthogonal direction relative to the first direction using a second-dimensional one-dimensional filter. Thus, since the respective low-pass filter characteristics of the two separate one-dimensional filters forming a separable two-dimensional filter are completely independent of each other, the internal function a and the structure of each of these low-pass filters may be similar to that described above in connection with Figs. 2a and 2b and Figs.

3-11. ·

In the case of television images, formed by a track of horizontal scan lines, the two orthogonal directions of a separable filter are preferably horizontal and vertical. If separable two-dimensional low pass filtering is employed in the implementation of this invention, there are certain advantages that are achieved in performing horizontal low pass filtering prior to vertical low pass filtering while there are other advantages in performing a vertical pass filtering bottom before horizontal low-pass filtering. For example, by performing horizontal filtration and reduction first, the number of pixel samples per horizontal scan line would be halved, which would have been treated by the vertical internal function

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-4-

during the vertical filtration following. However, by performing the vertical filtration first it becomes possible to use the same lagging structure as is necessary to obtain the relatively long delays required for vertical filtration and to obtain the respective compensation delays (1215, 1225, 1235, 1245, 1255 and 1265) to follow the respective Gg-G signals to the positive terminal of each of the respective subtractors 1216, 1226, 1236, 1246, 1256 and 1266 of the stages 1210, 1220, 1230, 1240 , 1250 and 1260 of the spectrum analyzer indicated in Fig. 12

The overall response of the filter formed by two-dimensional filters of spatial frequency may be square or rectangular in a cut parallel to the plane of the spatial frequencies. However, the non-separable filter filter response may present another type of section. Of particular interest are the circular and elliptical sections for the filtering of television signals as the filters having responses having the indicated sections can be used to reduce the excess of day-to-day resolution in television signals. Uniformity of image resolution in all directions is important, for example in television systems where the image is to be rotated between the camera and the display.

A filter weighting matrix having an aspect having a quadrangular symmetry and a linear phase response - particulary advantageous filter characteristics for use as 2-D low pass filters,

1211, 1221, 1231, 1241, 1251 and 1261 and 2-D low pass filters 1214, 1224, 1234, 1244, 1254 and 1264 of Fig.

ABC Β ADEFEDGH 3 HGDEFEDABG Β A

An internal function matrix having these kind of weighting features, in turn, functions in each of the successive image samples, wherein each pixel sample, when operated,

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-4-

corresponds in position to the weighting factor 0 located in the center of the matrix. In a low pass filter the weighting factor 3 has the relatively higher level of magnitude and each of the other weighting factors has a level of magnitude that becomes smaller and smaller as the weighting factor moves away from the central position A, of the corners, has the lowest level of magnitude.

In the case of a non-separable two-dimensional filter, the selected specific values of the levels A, B, C,

D, Ε, Γ, G, H and J are completely independent of each other. However, in the case of a two-dimensional separable filter, as the weighting factor level quantities result from the cross-product of the respective terms of the one-dimensional internal function weighting factors indicated in the horizontal to vertical lines, the respective values A, B, C , D E F G,

H and 3 are not completely independent.

Apparatus for synthesizing an electrical signal from components of the spectra which may have the general form indicated in Fig. 13 is of importance for the invention. The components of the spectrum G ^ *, ', L ^', L ^ ',, L ^, and Lg * are the answers

to the organs shown in Fig. 12 of the spectrum analyzer equipment. The components of the spectrum Lg, L2, L2, L2, L2, L3, L4 and L4 are provided progressively later in time by the spectrum analyzer of Fig. 12 and must be differentially delayed to give G8 ', L · ^, U ^ 'L ^' ^ 2 '* 1 ^{U' 0} ^ 0 * P ^ro 9 ^{3pessivaraente} later to the synthesizer of Fig signals · 13.

13 shows a signal synthesizer having a plurality of successive signal synthesis stages 1360, 1365,

1370, 1375, 1380, 1385. Each floor, through the use of in terpolation, expands the sample array of a spectral component to be coextensive with that spectral component which follows, higher in the spatial frequency and allows its addition spectral component. The expansion of the sample matrix is done by interleaving sampling points in the matrix with nulls and filtering the result in low pass to remove the harmonic structure. Low-pass filtering has

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Fig. 12 shows the same filter characteristic of low-pass filtering associated with the respective interpolation process in Fig.

The low-pass filtering associated with interpolation in the signal synthesizer suppresses the harmonics associated with the

or L 2, being altered by a non-linear process, which may arise in alteration circuits (such as those described above in connection with Fig. 5) which may be inserted between the spectrum analyzer of Fig. 12 and the Fig. 13 Such nonlinear features may increase imperfections in the synthesized composite image when the low-pass filtering does not occur with the filtering associated with the interpolation processes used in the signal synthesizer

In the Fig. 13 synthesizer, the Gg * samples are intercalated with nulls in the expansion circuit

1361 b pass through a 2-dimensional low-frequency filter 1362, similar to filter 1265 of Fig. 12 of the spectrum analyzer. The filter response samples

1362 are added to the L1 'samples at the adder 1363 to generate G2 similar to or identical with the hypothetical time delayed G2 replicate. Then, the G1' samples are null-interleaved in the expansion circuit 1366. This signal passes through the low-pass filter 1367, similar to the low-pass filter 1254 of Fig. 12 and summed to L1 in the adder 1368 to generate G2, similar or identical to the time delayed G2 replicate. The G1 'samples are interpolated with nulls in the expansion circuit 1371 and the low pass filter result in the filter 1372, similar to the filter 1244 of Fig. 12. The filter response 1372 is added to at the adder 1373 to generate G 2 ', similar or identical to the delayed G 1 replicate. The G 2 samples are interspersed with nulls in the expansion circuit 1376 and the low pass filter result in the filter 1377, similar to the filter 1234 of Fig. 12. The filter response 1377 is added to L1 in the adder 1378 to generate G2 * similar or identical to the delayed G1 replicate. The G1 samples have nulls inserted between them

in the expansion circuit 1381 and the result and low pass filtering in the filter 1382. The filter response 1382 is added with

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L 2 'in the adder 1383 to generate G 2', similar or identical to retardation. The G 2 samples are provided for integration into an expansion circuit 1386 β to a low pass filter 1387 similar to the filter 1214 of Fig 12. The filter response 1387 is added with Lq * on the adder 1388 to provide Gg 'the descriptive synthesized signal of the same image described by Gg, possibly with changes

Since the two-dimensional implementation of the present invention is especially advantageous for use in the processing of real-time spatial frequency imaging, it is to be understood that the two-dimensional information with which the present invention is related is not confined to the spatial frequency spectrum of two-dimensional images · For example one of two diodes may correspond to spatial frequency information and the other of two dimensions may correspond to time frequency information ·

Further, this invention is useful in analyzing the real-time frequency spectrum of the information defined by more than two dimensions. For example, in the case of three-dimensional information, all of the three dimensions may correspond to the usual or alternatively two of the dimensions may correspond with spatial information when the third dimension corresponds to temporal information. In this aspect of interest is the image processing apparatus responsive to the occurrence of motion in a visualized television image. In this case, the frequency spectrum zone spatial data of the displayed image corresponding to the stationary objects remains the same from image to image of the video information, while the area of the spatial frequency spectrum of the affixed image corresponding to the moving objects changes from image to image in the video information A spectrum analyzer incorporating the principles of p The present invention can be used in an image processing apparatus using 3-D low pass filter. Two of the three dimensions of these low-pass filters are spatial and correspond to the two spatial dimensions of the low-pass and 2-D filters incorporated into each floor of the bidirectional spectrum analyzer of Fig.

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These are the characteristics of the fine structure of the three-dimensional spectrum due to variations caused by moving objects in the values of magnitude levels of the corresponding pixels of the image viewed from image to image.

In the above description of the configurations of the present invention, it is assumed that the time signal Cg is a baseband signal having a frequency spectrum which defines information with one or more dimensions. As known such baseband information is often reported in the frequency-multiplexed format in which Baseband information 6 formed by the sidebands of a carrier frequency that has been modulated by a compo- nent of the baseband information. By employing suitable modulators and demodulators in the respective translators 100-1 ... 100-N of Fig. 1, Cg and / or any C ^ ... C ^ e or any of Lg a may be frequency-multiplexed signals.

The term "shift register" 6 is to be interpreted in the claims as including means for performing equivalent function - for example, a read-after-write (read-tben-write) memory

Claims (39)

A signal processing apparatus for analyzing the frequency spectrum of an information component (Cg) of a given time signal in (N + 1) separate frequency bands, wherein said component corresponds to information containing a given number of dimensions; wherein N is an integer and the highest frequency of interest in said fraction spectrum is not greater than the frequency fg; was that, in order to analyze said real-time delayed frequency spectrum, said equipment comprises: a pipeline circuit (Figs · 1, la, lb) formed by a set of N translators of sampled signals mounted by numerical order (100-1 ... 100-N); 62 710 RCA 79870/79581 Each of said translators (Fig. 1a) includes first and second input terminals and first and second output terminals; said first input terminal of the first translator of said set is connected so as to receive said time signal (G _q ); said first input terminal of each of said second to N translators of said set is connected to each of said first output terminal of the immediately preceding translator of said set to follow the signals (G, G ₂ ··· etc ·) of each of said translators for each of the immediately following of said translators of said set; and said second input terminal of each of said translators of said set is connected to receive a sampling frequency clock (CL ^, CL ₂ > ... etc.) in order to obtain in said first and at the output terminals of those translators the respective sampled signals at a rate equal to the sampling frequency of the generator applied thereto; and wherein: each of said translators of said set has, for said information component, a low-pass transfer function between its first input terminal and its first output terminal, said transfer function of said translators of said together with a nominal cut-off frequency that is directly proportional to the clock sampling frequency applied to the second input terminal of each of said translators of said set; the clock β applied to the second input terminal of said first translator of said set has a sampling frequency which: (a) twice fgj and (b) establishes for said information component 62 71Q RCA 79870/79581 A nominal cut-off frequency for said transfer function passes low of said first translator of said set, which is less than fg? the clock applied to the second terminal of each of said second N-translators of said set has a sampling frequency which: (a) is less than the clock frequency applied to the second input terminal of each of the immediately preceding translators of said set; (b) is at least equal to twice the maximum frequency of the signal information component applied to its first input terminal, and (c) provides a nominal cut-off frequency for its low-pass transfer function which is less than that of the immediately preceding translator of said set? and the information component of said signal derived from said second output terminal of each of said translators of said set corresponds to the difference between the signal information component applied to said first terminal of those and a separate function of the information component of the set signal obtained in the first terminal of the output of those? so that said separate frequency bands (N + 1) are formed by N signals respectively connected to said second output terminals of said N translators, together with the signal from the first terminal of the N-order translator output . The apparatus of Claim 1, wherein the clock applied to the second input terminal of each of said second and second translators of said set has a sampling frequency, relative to the clock frequency applied to the clock second input terminal of the immediately preceding tracer of said assembly, such that: each dimension of the signal information component applies 62 710 RCA 79870/79581 to its first terminal 6 sampled with half of the cadence to which is sampled the same size of the signal information component applied to the first terminal of said translator immediately preceding said set. The apparatus according to Claim 2, wherein the clock applied to the second input terminal of each of said second to N, translators of said set, has a sampling frequency, relative to the clock frequency applied to the second input terminal of the immediately preceding tracer of said assembly, such that: a rated cut-off frequency is established for its low-pass transfer function which for each dimension of the information component of said signal applied to its first terminal is practically equal to one-half of the nominal cut-off frequency provided for the corresponding size of that one with the information function for the transfer function passes underneath said immediately preceding translator of said set; the information component of said signal derived from the second output terminal of each of the translators of said set corresponds in each such dimension to an octave difference of the frequency of the spectrum of the information component for said given time signal with that dimension. An apparatus according to Claim 1, wherein said given time signal is an analog signal formed by an information component, corresponding to a one-dimensional information. The apparatus of Claim 1, wherein said time signal is formed by a video signal defining a two-dimensional image information. The apparatus of Claim 5, wherein said video signal corresponds to successive scans of television images. Equipment according to Claim 1, in which 62 710 RCA 7987Q / 79581 -53- each of said translators (ΐ00 ^ _ ^, 100 ^ _ ^ in Figures 1a and 1b) of said set are formed by: first means (102, 104) connected to the first and second input terminals and a first output terminal to provide said low-pass transfer function of said translators; the first means including a convo lution filter with m outlets (102) wherein m is an integer multiple to contain the signal information component applied to the first translator terminal with a predetermined integer (kernel) function for a a sampling frequency corresponding to that of the clock applied to the second input terminal of said translator, said predetermined internal function and said sampling frequency of the convolution filter respectively the nominal form and frequency of cut of the transfer function passing low of the translator in each dimension of said information component; and second means (109, 110) connected to said first means and to the terminals of the second input and the second output of said translators, to obtain said difference signal in the second output terminal of said translators; these second means include sample subtraction means (110) and third delay means (106, 108, 109 of Fig. 1a; Fig. 1b to 1c) for connecting said sample subtraction means through said said subtractive means being subtracted in time alignment to the sampling frequency of the samples involved in this translator, one of the respective levels of the samples occurring simultaneously in the samplings involved in each of the corresponding successively occurring levels of the component of signal information applied to the first steplet terminal of this translator before they are processed by said nuclear function of the translator convolutional filter, whereby the output of said subtractive means of samples includes each of the difference levels of successively occurring samples the sampling frequency 62 710 RCA 79870/79581 iB Of the samples involved in the translators, said difference in sample levels constituting the information component of the derived signal in the second output terminal of the translator The apparatus of Claim 7 wherein said predetermined nuclear function of at least one of said translators of said set defines a form of low-pass transfer function for said translational means having a weakening with respect to Crimp frequency (roll-off) that extends above said nominal cut-off frequency The apparatus of Claim 7, wherein the respective core functions of at least two of the translators' referrals of said set are substantially similar, relative to each other. Equipment according to Claim 7 in which: said information component comprises at least two dimensions, and the convolution filter of at least one of said translating means is a non-separable filter in at least said two dimensions. An apparatus according to Claim 7 wherein: said information component contains at least two dimensions> the convolution filter of at least one of said translators is a separable filter in said two dimensions. Equipment according to Claim 7 in which: said first means (102, 104) of at least one of said translators of said set of a given type being said first media formed by said convolution filter (102) and a density reducer (104) connected in series between the output of said convolution filter and the first output terminal of said translators of said set- Said convolution filter of said die type of 62 710 RCA 79870/79581 -55ΊΡΙΓΙ'ι'ι '^; first means produces at its output a sample density at each dimension of said information component which corresponds to the sampling frequency of the clock applied to the second input terminal of one of the translational means, and said density reducing means of said first type means of the first means passing in each of said dimensions of said information component only certain but not all of the samples involved appearing at the exit of the convolution filter of said data type first means for said output terminal of said translating means, whereby the density of the reduced samples of said amestra involved in each of said dimensions of said information component in said first output terminal of the translators is reduced relative to said particular sample density of the corresponding size of said information component to the output of the convolutional filter of the translators. The apparatus according to Claim 12, wherein said density reduction reducer of said first type of said first and second digester is selected from the group consisting of: the means for passing in each of said dimensions of said information component all of the other samples which are newly received at the output of the convolution filter of said first type of the first means for said first output terminal of the translators, whereby the density of reduced samples in each of said dimensions of said information component is reduced to one half of said particular sample density of the corresponding size of said information component. The apparatus according to Claim 12 wherein: within said at least one of said translators (206 _b _ _K, Fig. lb), said third means includes a quajç ments means, connected between the output of said filter convolutional and said subtractive means samples applied directly mind to said subtractive sample means (110) said information component involved from said convective filter. 62 710 RCA 79870/79581 The apparatus according to Claim 12, wherein: (106, 108, 109, Fig. 1) further comprises means (106, 108) connected between said density reducer and said sample subtraction means, to expand the density of reduced samples of said samples involved in each dimension of said information component at said first output terminal of those translators back to said spatial sample density of said samples involved in said dimension in said sample subtraction means, said rooms including a sample expander (106) for inserting additional samples correspondingly occurring in sequence to each sample involved in the output of said convolutive filter which lacks this reduced sample density, each of said additional samples inserted a zero value level and interpolation means (108) which are effective in replacing an interpolated value sample level to the zero value level of each of said additional samples. The apparatus of Claim 14 wherein: said density reducer of said first type of first means passes, in each of said dimensions of said information component, which other of the masters after appearing at the output of the convolution filter, of said first- to said first output terminal of each of the translators. said expander inserts an additional sample between the pair of successive samples involved in said reduced sample density in each dimension of said information component, and said interpolation means is comprised of an n-interpolated filter (where n is an integer) having a low-pass transfer function. Equipment according to Claim 14 or 15 on what: the signal information component in the first terminal 62 710 RCA 79870/79581 The input of said translators is applied to said sample subtraction means through said delay means, and said delay means of said translators inserts a time delay substantially equal to the total time of attraction inserted by the convolutional filter, said density reducer and said fourth means of those translators. 18 - Equipment according to claim 12 wherein each of said first through (Nl) of said set translators include first means of said given type (LQQ _{and "b} _ or 100 _K). The apparatus of Claim 18, wherein said N-order translators (Fig. 1c) of said assembly also include first means of said type data. The apparatus of Claim 18, wherein said N-translating means (Fig.1c) of said assembly includes first means of an alternate type, wherein the output of said convolution means is applied directly to said first terminal of said traditional means N. 21 - Claim gears 20, wherein the information signal component (L _n _ ^) in the first entry of said order translator means C of said set is applied to said subtracting means samples through said (109) by inserting said delay means of said N-degree translators of said assembly, a time delay substantially equal to that which is inserted by said convolution filter. 22 - Equipment (Fig. 1) to perform spectral analysis in real time, including: a cascade connection of sampling filters passes through. (102, 104 of Fig. 1a, 1b within 100-1, 100-2, ... etc.) operating at successively lower sampling rates (CL, CL, etc.), an input signal (Gg) for said cascade, which is the signal over which the analysis is to be performed 62 710 RCA 79870/79581 (G ^) of said cascade the remaining spectrum passes low; means (106, 108 of Fig. 1a) for interleaving samples in the reduced response (decimation) of each of the low pass sample filters (102, 104), with nulls and low pass filtering of the result in order to obtain the respective interpolation ; means (109) for delaying the input samples for each low pass filter of said cascade connection having a value equal to the sum of the filter lags and delay in low pass filtering of the null interleaved response; and means (11Q) for differentially combining the input delayed r samples for each low pass filter of said cascading with the result of the interpolation from its response, so as to obtain the respective input signal to said cascade connection 23 - Equipment (Fig. 1) performing real-time spectral analysis of an electrically sampled (G _q ) signal with a R-cadence, including: a plurality, number n, of analysis stages (100-1, 100-2 ... etc.) numbered consecutively from zero to nj each floor analysis (Fig. 4) provides a first output signal (G ( _«+] j) ⁰⁰¹ responding to lower frequency components of its input signal (L ,.) and a second separate output with a response ( L ^) for the higher frequency components of its input signal (G2); wherein said analysis stage with the number zero (lO-l) receives said elaptric signal for spectral analysis with its input signal and each of said other analysis stages receives as its input signal the first signal of analysis output from the analysis stage with the immediately lower numbering; said second output signals of all said stages β the first output signal of the n-axis analysis stage provide the results of the spectral analysis; and 62 710 _r CA 79870/79581 -59s of floors wherein each of said analysis pluralities (eg Fig. 4) includes respectively: a first m-shift offset register 470 being m an integer, having input signal (G ^) to said analysis stage applied at its input which is periodically examined (ciocked) with a clock rate equal to R / / 2 ^K , where K is the number of the analysis stage means (471) weighting the input signal (G2) of the analysis stage and wherein said input signal is delayed on each stage of said first displacement register by a set of coefficients and whose sum of the weighted signals, to generate a low pass and linear phase (G _{K + 1} ) filtered response to said analysis floor input signal, is said output signal from the first analysis floor. a multiplexer (472) operative to make the alternate selection between said output signal of the first analysis stage and a null value, with said rate of R / 2 an additional offset register (474) having the signal selected by said multiplexer, applied in its in and is periodically connected (ciocked) to said cadence. f [/ -i) of clock, equal to R / 2 ^V , means (474) weighting the selected signal from said analysis stage and said delayed signal on each stage of said additional m-storey register with said set of weighting coefficients and summing the weighted signals to obtain a first signal of output, re-sampled, for this analysis; and means (475) subtracting said first output signal, re-sampled, for this analysis stage, with the delayed input signal for this analysis stage, so as to produce the second output signal (L ^) for this floor analysis. An apparatus according to Claim 23, wherein m is the same for each analysis stage and wherein each stage of analysis 62 710 RCA 79870/79581 £ 0. zgar -60- '' "" χτ'πιιι ι analysis uses identical sets of values as weighting coefficients. 25. The apparatus of Claim 23 wherein said delayed input signal for each analysis stage is obtained from the first stage of its first m-stage shift register and is further delayed (by 476). Digital filter (Fig. 1) providing at least one output response and including: a plurality of delay lines with timed sockets (eg 470 of Fig. 4 in each of 100-1, 100-2, etc.) consecutively numbered in order and periodically connected (clocked) with successively higher cadences (R / 1, R / 2, etc.) as the numbering increases means for applying an input signal (Gg) to be filtered, at the input of the first of said delay lines (eg, 471 in every 100-1, 100-2, etc.) for weighting sample samples from each line of delay and combination of the weighted samples to obtain respective filter responses (G1, ee means for applying to respective filter responses obtained from the samples taken in each delay line except the one with the highest numbering at the input to the highest numbered delay line at least one part (G1) of the response of the respective filter obtained from the samples taken from the higher numbered delay line, being used in generating said overall response. A digital filter according to Claim 26 in which the samples weighted from the sockets of each delay line are combined so as to obtain the responses of the respective filters (G 1, G 2, G 2, etc.). which by nature are low pass. Digital filter according to Claim 27 which includes: 62 710 RCA 79870/79581 An additional clocked delay line (473) operating at the same rate as selected (470) of said plurality of delayed pickup lines; means (472) for selectively applying the output of the selected delay line and the nulls to the input of said additional delay line; means (474) for weighting samples from the take-off of said additional delay line and from combining samples, so as to obtain a low pass filter response; and means (475) for differentially matching the response of the low pass filter, thus obtained, to the output of the selected delay line from said plurality, to produce an output response (L ^) of said digital filter ' A digital filter (Fig. 5) according to Claim 27 wherein the weighted samples obtained from the selected sockets (570-1) of said plurality of delay line sockets (570-0, 570-1) having a higher number (1) higher by one unit than the ordinal number (θ) of the line of prior delay; (a) are weighted differently in each of the clock cycles of said forward delay line and (b) are combined in each of said clock cycles to obtain a low pass filter response; and wherein the low pass filter response thus obtained is combined differentially (at 575-0) with the output of said preceding delay line (575-0) to produce a salt response (Lq) of said digital filter. Digital filter according to Claim 26, including: an additional delay line with socket (473) operating at the same rate as selected (470) of said plurality of socket delay lines; means (472) for selectively applying the output of the selected delay line and the nodes & input of said additional delay line, means (474) for weighing the samples from the take RCA 79870/79581 of said additional delay line and to combine the samples so as to obtain a response; and means (475) for combining the response thus obtained with the delayed input (G2) to the prerecord delay line to produce an output response (L2) of said digital filter A digital filter according to Claim 31 wherein the delayed input to the preceding delay line is obtained by incorporating the delay (476) into one of its outlets. A digital filter according to claim 34 wherein the weighted samples of the outlets of one of the delay lines selected from said plurality of delayed pickup lines having a higher ordinal number by one unit than the preceding delay line , are weighted differently in alternating clock cycles of the preceding and combined delay line in each of the clock cycles, the result being combined with the delayed input to the preceding delay line, to produce a re- injured digital filter. The digital filter according to claim 33 wherein the delayed input to the preceding delay line 6 is obtained. delay in one of its outlets. (See Fig. 3) to synthesize an isolated time signal (Gq) from a set, sorted in numerical order, of the N separate time signals (Lq-GiI) where N is an integer in which : with the aim of synthesizing said time signal on a deferred real time basis: (1) said time signal is formed by a determined stream of information component samples which defines the frequency spectrum of the information having a given number of dimensions with a particular density of samples in each of said dimensions; 62 710 HCA 79870/79581 (2) the first (L _q ) of said sets of N separate signals arranged in numerical order, formed by a stream of samples of information components defining the highest position in the frequency spectrum of said information, with a density of samples which is substantially the same as said density of samples in each of said dimensions; (3) each of the ordered sets of N separate signals, from the second to (N1), (L2 ... L2), is formed by a stream of samples of information components defining an individual portion of the spectrum of frequencies of said information which in each dimension thereof is below the corresponding size in said spectrum of said portion defined by the previously prior signals of said set and is above the corresponding size in said spectrum of said portion of said next set of countries signs of said set! (4) corresponding to said stream of samples of information components each, up to (N1), (L2 ... L2) of said sorted sets of N separate signals, there is a sampling density for each one of the dimensions of the information, which is smaller than the sample density of the corresponding sample stream information dimension of the information component corresponding to its previous separated signal from said set; and (5) said sample streams of information components occurring with said time spacing between them; s said apparatus in Fig. 3 comprises: a group of sample combining means 363-353, each of which (e.g. 363, 362) is individually associated with a respective first (Lg, e.g.) of the injured first to to said (N1) (Lg-L2) of said set of separate signals, for combining the first (e.g. Lg) of said set of separate signals, which is associated 62 710 RCA 79870/79581 with those combining media, with the commative total (eg GJJ of all those separate signals (eg, L1, ..., g1) which follow this signal separated from a unit of said assembly; and wherein: each of said combination means (p 'ex' 362, 361) associated with the first (Lg) to said (N-2), (L ') of said set of separate signals includes an adder (e.g., 361) to follow the output of the adder (e.g., 361) of the combination media (eg, 361) associated with the separate signal (eg G2) immediately following its ordinally separated signal , as the second input, to its adder with the same sample density as that of its separate signal; said combining means (353, 352) associated with said (N1) separate signal (L1) of said set, includes an adder (353), said means (350) for applying said signal (N1) as a first input to its adder, and third means (352) for applying said separate N-order signal (G2) as a second input to its adder (353) with the same sample density as the separate command signal (N1); and said first means (340, 341, etc.), said second means (362, 360, etc.) and said third means of said (N1) means of combining said group respectively insert predetermined amounts of delay in following said time slots of the signals separated from said set, in such a way that: each of said respective (Nl) combining means, responsive to information samples of respective stream of samples of information components in the first input and at the second input of the adder, occurs practically in coincidence of time with each other; whereby said synthesized temporal signal is obtained at the output of the sum of said combining means associated with said first signal SBparted from said set. 36 - Equipment (Fig. 6) defined according to Revision 33 was that; seconds (e.g. 362 in Fig. 3) of the respective combination means individually associated with each of 62 710 RCA 79870/79581 Eur-lex.europa.eu eur-lex.europa.eu ✓ ^z _ W | (I.e., Nl), (eg, of said set of separate signals includes a sample expander (692, 693, 694) which responds to the lowest density of information compound samples (G1) in said output of the adder to insert additional samples into the next stream to increase the sample count at the second input of the adder (695) of said combination means to the signal density of the signal separate from the order (L ( _K jj) associated with said combination means, each of said additional samples having a zero value level and interpolating means (693, 692) which are effective in replacing sample values of values interpolated by the zero level valer of each of said samples additional · The apparatus (Fig. 6) defined according to Claim 36, wherein: said separate N-order signal (gH) of said set has a lower sampling density than that of the separate (N-1), (L ') signal of said set? and said third means (352) includes a sample expander to interpolation means (692, 693, 694) as those of said second means for transmitting said separated signal of the N order to the second input of the adder of said third means. The apparatus of Claim 37 wherein: said command signal N (G 1) of said set has substantially the same sampling density as said si. (N-1), (L, -) of said assembly; and said third means directly transmit said separate signal of the order N to the second input of the adder of said third means. The apparatus of Claim 36, wherein: said stream of information component samples corresponds to each of at least the second (L1) to (N1) (4) of the N separate signals of the ordered set in numerical order has a density of samples for each of its own 62 710 RCA 79870/79581 Information dimensions which is equal to one half of the sample density of the corresponding information stream dimension of the information component samples corresponding to its immediately preceding separated signal from said set; and in each of said combination means (Fig. 6); said expander (692) of said second means is in an additional sample between each pair of successive samples of said lower sample density, wherein each sample stream of the information component in said output of the adder is transmitted; β said expander means is formed by an interpolation filter (693) with n sockets wherein n is a given integer having a low-pass transfer function. Equipment according to Claim 35, was that: said third means and each of said respective second means of said group of N-1 combining means. sampled signals insert their own, time-lagged, time-delayed transmission of their stream of information component samples with a second input to their adder; and each of said first means of said group of Nl combining means of the sampled signals includes delay means (340, 341, etc.) which inserts a particular delay time value in the transmission of its separately ordered signals as the first input of the its adder which in both cases depends on (1) the respective spacing between its separate signals and each of those separate signals from said set following its separate signal and (2) the total time delay value inserted by said third means and all second means of those combination means associated with the separate signals of said set which follows the order of the separated signals said particular delay signal being such that corresponding the samples RCA 79870/79581 The respective information component streams at the first input and at the second input of their adder occur substantially in time coincidence with one another. Note the leading edge of the sheet 64 seconds *