JP2003524257A - Apparatus, method and computer program product for determining function coefficients - Google Patents

Abstract

SUMMARY The present invention provides an apparatus and method for providing coefficients of a function representing a signal, and a computer program product. The apparatus and method and the computer program product according to one embodiment of the invention take advantage of sample independence, giving a complete set of coefficients of the function as each sample is received, and using a rotating reference system. The updated coefficients are corrected for accuracy by applying a reference system). Thus, the apparatus and method and computer program product of the present invention can provide accurate coefficients with reduced latency. An apparatus, method, and computer program product according to another embodiment of the present invention use a learning model to derive a complete set of coefficients of a function as each sample is received. An apparatus and method and a computer program product according to another embodiment of the present invention use a learning model to determine an apparatus and method and a computer program product for generating coefficients of a function.

Description

Detailed Description of the Invention

[0001] This application is filed on Feb. 26, 2000, entitled "METHODS AND APPARATUS FOR PROCESSING AND ANALYZING INFORMATI.
ON) ”, US Provisional Patent Application No. S / N 60 / 185,346, 2000
"METHODS AND APPARATUS DERIVED FROM LEARNING MODE submitted on May 3, 2014
Claim priority based on "LS FOR PROCESSING AND ANALYZING INFORMATION". Further, in the present application, the contents of both of these patent applications are cited to form a part of the present specification.

[0002]

TECHNICAL FIELD OF THE INVENTION

The present invention relates generally to determining the coefficients of functions. In particular, the apparatus, method, and computer program product of the present invention determine, as each sample of an input signal is received, the coefficient of a function representing that input signal to provide a continuously updated coefficient. Regarding technology.

[0003]

[Prior art]

Signal processing is an important function of many electronic devices. Especially in many electronic devices,
Data is transmitted in the form of signals. In addition, some electronic devices analyze and monitor the operation of mechanical or chemical devices by observing the characteristics of signals such as vibration signals or other types of signals that are outputs from these devices. . With this in mind, methods have been developed to characterize the signal such that the information or data in the signal is available for data processing.

As an example, in many electronic devices, time domain signals are typically transformed into the frequency domain prior to signal processing. A common method for transforming a signal into the frequency domain is performed using a Fourier transform. The Fourier transform of the signal is based on the base frequency (base fre
quency) based on multiple samples of a time domain signal taken over a selected time period. The Fourier transform, based on these samples of the signal, provides a plurality of coefficients, each representing the amplitude of the frequency that is a multiple of the reference frequency. These coefficients of the Fourier transform, which represent the signal in the frequency domain, are then used by the electronic device in processing the signal.

Although the Fourier transform is some of the most widely used functions for processing signals, there are other functions currently in use or that will be used in the future, and their applicability. A better understanding of is recognized. These functions are
ssel function, Legende polynomials, Tschebysheff polynomials of the first and second kind, Jacoby polynomials, generalized Legendre polynomials, Hermite polynomials, and Bernoulli (Bernoul
li) contains polynomials, Euler polynomials, and various matrices used in quantum mechanics, linear analytic functions, wavelets and fractals, to name but a few.

Although the mentioned Fourier transforms and other functions are useful in characterizing the signals used in data processing, there are some deficiencies in their use. In particular, the application of these functions to signals generally requires a great deal of computing power. This is a disadvantage as it may be necessary to use a specialized processor to perform the data processing. Additionally, and more importantly, the time required to complete the number of calculations using these functions can cause unacceptable delays for many data processing applications. In fact, the goal of many data processing systems is the ability to process data signals in real time without delay.

For example, the Fourier series is defined as an infinite series of coefficients representing the signal. An infinite number of calculations would be required to transform the signal using the Fourier series. To remedy this problem, many conventional data processing systems are referred to as Discrete Fourier Transforms (DFT), as opposed to infinite Fourier series.
) Is used. DFT is a digital approximation of the Fourier series and is used to process digitized analog information. Importantly, the DFT replaces the infinite series of the Fourier series with a finite set of N evenly spaced samples taken over a finite period. Therefore, the DFT calculation provides as many coefficients as the received samples instead of the infinite number of samples required by the Fourier series. Therefore, using DFT provides the most satisfactory current means for processing the signal.

However, since it is important to reduce the time required to process a signal, methods have been developed to further reduce the number of calculations required to perform a DFT of the signal. In particular, the DFT means calculates each coefficient by similar processing. In the processing of the general coefficient, the normalized value of the independent variable x the angular rate sin (
Multiply each sample by sine or cos and add up over all samples. This procedure consists of N multiply sums for each of the N coefficients.
dd) Define steps. That is, this is equivalent to N ² product-sum calculations by DFT. The DFT of a signal requires a great deal of computational power, as many samples of the signal are generally needed to perform a good approximation of the signal.

One of the methods developed to reduce the number of calculations is the butterfly method.
od). This reduces the number of calculations from N ² to N × log (N). The butterfly method is based on the fact that many of the trigonometric values of the DFT are the same due to the periodicity of the function. Therefore, the butterfly method is
Reduce the matrix associated with to N / 2 two-point transforms (ie, the transform represents each coefficient a _n and b _n ). The butterfly method further reduces the extra trigonometric values of the DFT.

The butterfly method reduces the number of calculations on the more traditional DFT method, but it also adds complexity to the Fourier transform of the signal. In particular, the butterfly method uses a complex method for dealing with signal samples and matrices containing functions. This complexity requires the use of specialized processors and can increase the computational time of the Fourier transform. By its nature, the butterfly method is a batch processing method and does not begin determining coefficients until all samples have been received. As a result, this method causes a latency in the determination of the coefficients of the function, where the time between the arrival time of the last sample and the time when the coefficients are available is defined as the latency of the system.

Another approach to reduce the time required to process a signal is “Apparatus, Methods And Computer Program Products, submitted April 28, 2000.
For Determining The Coefficients Of A Function With Decreased Latency ''
No. 09 / 560,221 entitled "Computation of Discrete Fourier Transform" published internationally in November 2000.
It is described in CT patent application WO 00/67146. These are incorporated herein by reference. Both of these patent applications are invented and owned by Mr. Walter Pelton. He is also the co-inventor and assignee of the present application. Pelton's approach, which is fully described by these patent applications, reduces or eliminates the latency problem for processing coefficients by using an important property of functions such as DFT to reduce latency. . This property is independent of the sample. When a set of samples is transformed in the DFT process, each sample contributes to each coefficient based solely on the sine or cosine of the applied angle. In particular, each coefficient of the DFT is the sum of its application to the sine and cosine functions associated with each coefficient of each sample. Because each sample is related to each coefficient by addition, each sample is independent of the other samples and can be used to update the coefficients prior to receiving the other samples.

Using Pelton's approach, the complete set of coefficients can be derived for multiple samples. In particular, as each sample is received, the coefficient contribution for each sample is calculated. Also, the coefficient contributions are summed after they have been calculated. After adding the contribution of the last sample of multiple samples, the complete set of coefficients is available for all samples. The time needed to calculate the contribution of the last sample and add it is generally small. Therefore, the latency of the Pelton approach is characteristically low.

US Patent Application No. 09 / 560,221 and PCT Patent Application WO 00/6714
6 describes SAFT (Sliding Aperture Fourier Transform) along with apparatus and method and computer program product for performing such a transform. SAFT involves replacing the oldest coefficient contributions of previous samples with the coefficient contributions of the next received sample. Using this new sample, SAFT provides the next set of coefficients available for output. Thus, instead of producing a set of coefficients for each "batch" of samples, SAFT produces a set of coefficients when a new sample is received. An important feature of the SAFT operation is that SAFT uses the previously calculated coefficient contributions of the samples being received. SAFT provides a complete set of coefficients for a batch of samples by subtracting the coefficient contribution of the oldest sample when a new sample is received and adding the coefficient contribution of the new sample.

S described in Pelton approach and PCT publication WO 00/67146
Clearly, AFT can be used in many applications. Pelton approach and SAF
A few advantages with T are reduced with coefficient processing power of low or zero latency, so as to reduce power consumption for electronically processing more information of coefficients and samples of data. It is a simpler electronic device with hardware requirements and simpler programming requirements and implementations. However, there may be more desirable applications for the SAFT described in US patent application Ser. No. 09 / 560,221 and PCT Publication No. WO 00/67146 to provide coefficients with higher precision.

In particular, the SAFT described in these patent applications introduces an error in the calculated coefficient at the beginning of the process of subtracting the coefficient contribution of the oldest sample and adding the coefficient contribution of the new sample. Errors may occur because the continued processing of the coefficients causes a shift in the angle associated with each sample. For example, in the application of DFT, a particular angle is associated with the first sample of the set of N samples, and that angle is used in calculating the coefficient contribution of that first sample. Similarly, a "batch", such as a particular angle being associated with a second sample, etc.
The same for each of the N samples in SAFT, on the other hand, maintains a batch (a batch of samples) of one sample that is constantly changing. This means that if there are 8 samples (N = 8), the oldest sample, Sample 1, is removed and the next Sample 2 becomes the next Sample 1. This happens for each sample so that a new sample is sample 8. However, the coefficients updated during SAFT were derived from the calculation of coefficient contributions, where the sample is in line with the angle from the previous position. In other words, the updated coefficients include the error of calculating the coefficient contribution using the angles applied to the earlier samples.

In particular, the SAFT described in PCT Publication WO 00/67146 introduces an error into the calculated coefficient at the start of the process of subtracting the coefficient contribution of the oldest sample and adding the coefficient contribution of the new sample. An error occurs because the angle associated with each sample is offset by the continuous processing of the coefficients. For example, in a DFT application, a particular angle is associated with the first sample, and that angle is used in calculating the coefficient contribution for that first sample. Similarly, for each sample in the "batch", such that a particular angle is associated with the second sample. SAFT maintains a batch (a batch of samples) of samples in which one sample is constantly changing. This means that if there are 8 samples, the oldest sample, Sample 1, is removed and the next Sample 2 becomes the next Sample 1. This happens for each sample so that a new sample is sample 8. However, the coefficients updated during SAFT were derived from the calculation of coefficient contributions, where the samples were matched (or harmonized) with the angle from the previous position. In other words, the updated coefficients include the error of calculating the coefficient contribution using the angles applied to the earlier samples.

In the ideal SAFT process, a new sample has eight initial samples (N = 8).
), Sample 2 takes its place in the calculation for sample 1 and uses the corresponding angle for sample 1 in calculating the coefficient contributions. The same is true for each subsequent sample. However, this problem has been addressed by US Pat.
SAF described in No. 60,221 and PCT publication WO 00/67146
No special mention is made in the application of T. Instead, the SAFT described in these patent applications uses previously calculated coefficients to derive updated coefficients that include new samples. In other words, when a new sample is received after the initial N samples have been processed, the SAFT described in these patent applications is
Simply subtracts the contribution of the first sample N = 0 and adds the contribution of the new sample. The SAFT described in these two patent applications staggers the previously received samples 2-8 so that they are located in the calculation for their lower sample and corresponding to their lower sample position. It does not describe using angles to generate updated set coefficients. Instead, the contribution of the samples of the initial set, now the first sample of the new set, to the coefficients by the second sample is not at the angle of the first sample, but at the angle still associated with the second sample. Is based.

From the above description, there is a need for the computing power of SAFT to perform coefficient processing quickly and with high accuracy. In addition, there is a general need for improved methods, apparatus, and computer program products for processing function coefficients with greater speed and efficiency.

Objects and Summary of the Invention As described below, the apparatus and method and computer program product of the present invention overcome many of the deficiencies in processing signals using functions such as Fourier transforms. To do. In particular, the present invention provides an apparatus and method and computer program product for determining coefficients of a function that represents an input signal with reduced latency and / or improved accuracy. Moreover, the present invention is an apparatus for determining the sliding aperture coefficients of a function, such as SAFT, which represents the input signal so that the coefficients are available accurately and quickly. And a method and a computer program product. Further, the present invention provides an apparatus and method and computer program product for deriving an apparatus and method and computer program product for determining coefficients of a function representing an input signal with reduced latency and / or improved accuracy. I will provide a.

The present invention ensures that, as each sample is received, a complete set of improved exact coefficients of the function representing the signal is available with low latency. An apparatus and method for deriving a providing apparatus and method and a computer program product and a computer program product are provided. In particular, the apparatus and method and computer program product of the present invention take advantage of sample independence, use previously derived coefficients, and update at least one coefficient as each sample is received. . The updated coefficients are corrected to account for the change in angle associated with each sample to reduce latency and provide accurate coefficients. The present invention also provides apparatus and methods and computer program products for generating the coefficients of a function that represents a signal. The present invention also provides an apparatus and method for providing a coefficient of a function representing a signal and a computer program product for generating a computer program product.

The apparatus in one embodiment of the present invention receives each sample one by one, and when each sample is received, the coefficient of the function is calculated based on each sample without waiting for the reception of the next sample. It includes a coefficient generator for updating. Therefore, the complete set of accurate updated coefficients is available as each sample is received.

An apparatus and method and a computer program product according to another embodiment of the invention, when a sample is received, first store each sample of those samples,
Generate a first set of coefficients when the last sample of the plurality of samples is received. Further, when a new sample of the input signal is received after a predetermined plurality of samples have already been received, the apparatus and method of the present invention and the computer program product apply a mathematical function associated with the coefficient to the sample. And generate a new sample-based term for each coefficient. To replace the new sample with the first sample of the plurality of samples, the generated term of the new sample is subtracted from the term associated with the first sample of the predetermined plurality of samples previously stored in the memory device. Be done. After this subtraction, the coefficient is updated with the difference between the new sample-based term and the first sample-based term of the predetermined plurality of samples. The accuracy of the coefficients is then improved by adjusting the phase angle to correspond to the correct number of samples.

An apparatus and method and a computer program product according to yet another embodiment of the present invention provide a term based on an oldest sample of a given plurality of samples to replace a new sample with an oldest sample of the plurality of samples. From each coefficient,
Add a new sample-based term to each coefficient. The accuracy of the coefficients is then improved by correcting the coefficients to account for the change in angle associated with the samples so that the phase angle corresponds to the correct number of samples. Phase angle correction is achieved by applying a rotating reference (coordinate) system to match the sample, phase angle and coefficient contributions correctly.

Additional aspects of the invention include Fourier transforms, Laplace transforms, polynomial formulas,
A method and apparatus that can replace the standard method of electronic calculation of mathematical information such as calculation with series formulas. In one embodiment of the present invention, a learning model (le
methods and apparatus for performing calculations such as Fourier transforms, Laplace transforms, polynomial formulas, series formulas, etc. using algorithms and circuits derived from arning models). Examples of suitable learning models include neural network-based learning models, fuzzy logic network-based learning models, genetic algorithm-based learning models, and learning models based on combinations of different types of learning models.

Another aspect of the invention includes a method for generating coefficients of functions such as Fourier transforms, Laplace transforms, polynomial formulas and series formulas, and methods for generating alternative designs of apparatus. . A method for generating an alternative design includes using a learning model to derive at least one component of an information processor. Examples of components of the information processor include algorithms, circuits, and electronics involved in the calculation.

[0026]

DETAILED DESCRIPTION OF THE INVENTION

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings. However, the invention may be embodied in many different forms and should not be limited to the embodiments described herein. These embodiments described below are provided for the purpose of clearly showing the technical scope of the present invention to those skilled in the art so that the disclosure will be thorough and complete. The same reference numerals are given to the same elements throughout.

As already mentioned, data processing systems have been developed for determining the coefficients of the function representing the signal. However, many of these systems are complex and do not compute the coefficients until all samples of the signal have been received, so these systems cannot analyze the signal immediately. Moreover, although improved systems have been developed that provide coefficients on a sample-by-sample basis, the accuracy of the coefficients may prove to be insufficient for certain specialized applications.

The present invention therefore provides an apparatus, method and computer capable of providing the exact coefficients of the complete set of functions that represent the signal when each sample is received such that the coefficients are available with low latency. Providing program products. In particular, the apparatus, method and computer program product of the present invention take advantage of sample independence and update at least one coefficient as each sample is received using previously derived coefficients. The updated coefficients are corrected to account for the angle change associated with each sample to reduce latency and provide accurate coefficients. The present invention also provides apparatus and methods and computer program products for generating the coefficients of a function that represents a signal. The present invention also provides an apparatus and method for providing a coefficient of a function representing a signal and a computer program product for generating a computer program product.

For purposes of explanation, various apparatus and methods and computer program products of the present invention are described below along with features of the Fourier series. However, the apparatus and method and computer program product of the present invention can be used with many different types of functions. For example, the apparatus, method, and computer program product may include Bessel functions, Legende polynomials, Tschebysheff polynomials of the first and second kind, Jacoby polynomials, and general Generalized Legendre polynomials, Hermite polynomials, Bernoulli polynomials, Euler polynomials, and various matrices and linear analysis functions used in quantum mechanics and functions such as wavelets and fractals can do. This list is by no means exhaustive and is only given as an example. This approach can be applied to any function that can be expressed as a series of values. The utility of applying these functions and other functions not listed is quite general. The method can provide a means for developing an apparatus and method for parallel computing and a computer program product and removing redundancy in a mechanical way.

An important concept of the present invention is the independence of the samples used to determine the coefficients of the function. This concept is based on US patent application Ser. No. 09 / 560,221 and P.
It is described in detail in CT publication WO 00/67146. Hereinafter, it will be briefly described. Sample independence can be explained in the context of the Fourier transform. The Fourier transform is based on the orthogonality principle. The Fourier transform is applied in the DFT, which provides a means for independently evaluating the amplitude of each frequency component of the signal as a whole. The frequencies used in the calculations are consecutive integer multiples of the reference frequency. The reference frequency is the time period required to take a set of samples. The sample of the signal is multiplied by each element belonging to the set of orthogonal functions,
Summed over one or more cycles of the reference frequency. The resulting coefficient is
Each is the real or imaginary part of the amplitude of one test frequency. Importantly, the calculation of the coefficients is independent of the calculation of the other coefficients. N converted by DFT
In the set of samples, each sample contributes to each coefficient of a function that is based on either the angle applied and the sine or cosine of the normalization constant.

According to one embodiment of the invention, the apparatus and method of the invention and the computer program product provide a new set of N Fourier coefficients based on the current set of samples to a new sample. Update to the next set of N coefficients based on the contribution and removal of the contribution of the oldest sample. Each set of coefficients is corrected to correspond to the classical Fourier transform of the N samples contained in each set. The new set of samples differs from the oldest set by adding a new sample, subtracting the oldest sample, and correcting the coefficients to account for the change in angle associated with the sample. Updates can be performed in the signal update procedure for each coefficient.

Correcting the coefficients for N samples is basically equivalent to changing the reference system for the samples. This is equivalent to rotating the reference system to match the proper angle to the proper sample. Conceptually, rotating referencing (rotating refer
ence system) redefines the position of the first sample. The position of the first sample must be redefined, since the oldest sample, the oldest first sample, is removed and a new sample is added to complete a new set of N samples. I won't. As a result of the rotating frame of reference, sample 1 is associated with the angle of sample 1 and sample 2 is associated with the angle of sample 2. The same applies to each of the other samples. Correcting the coefficient involves correcting the contribution to the coefficient of each sample so that the contribution includes the correct angle for each sample.

Referring to FIG. 1, there is shown a graphical representation of a rotating frame of reference for a set of samples represented by S and a set of coefficients represented by C. The coefficients are for a set of 8 samples and in this example it is assumed that all coefficients were set to zero at time zero. FIG. 1 shows the transformation of 8 samples when the coefficient corresponds to the reference frequency. The samples are evenly spaced in time. The magnitude of the coefficient is the distance from the origin, and the angle is the usual X-axis 2a.
Is the angle from. If the angle advances by one rotation (2 ^* π), there are N sample times (8 sample times in FIG. 1). Therefore, each sample time represents a rotation angle of (2 ^* π) / N (π / 4, that is, 45 degrees in FIG. 1) with respect to the reference frequency. When proceeding from the reference frequency to the N / 2 (n = 1, 2, ..., N / 2) frequency, the incremental rotation of the nth frequency is n times the rotation increment of the reference frequency, that is, (2 ^* n ^* π) / N.

The representation shown in FIG. 1 is intended to replace the conventional graph obtained by plotting the sample along the X-axis. This is usually shown as plotting each sample value as a value on the y-axis for one period and is commonly referred to as a waveform. Vectors in FIG. 1 represent contributions from each sample. The magnitude of the vector is given by the sample value. The direction of the vector is given by the index times the angular increment between samples. In this case, the increment is 45 degrees at the reference frequency (ie 360 degrees / 8 samples).

The rotational reference system shown in FIG. 1 can also be described using suitable mathematical formulae. In the following discussion, C and S are vectors (vectors are in bold). The coefficient and the sample are related by the following (Equation 3).

[Equation 3]

US Patent Application No. 09 / 560,221 and PCT Publication WO 00/6714
6 and the coefficients of the DFT function (ie, A0, A
l, A2 ,. ． ． And BO, B1, B2 ,. ． ． ) Is defined by the sum of the application of each sample to the sine or cosine function associated with each coefficient. In vector terms, A is the projection of the sample vector on the X-axis 2a and B is the projection on the y-axis 2b. These values are calculated by multiplying the values of the cosine and sine functions of the applied angle (a multiple of 45 degrees). The numerical index is the sample number. The k index K = 1 ... N / 2 represents the coefficient number corresponding to the increasing spectral frequency. (Equation 4) to (Equation 7) are written for N = 8, and therefore K = 1 ... 4. For k = 0,

[Equation 4]

[Equation 5] For k = 1,

[Equation 6] For any k,

[Equation 7] This gives the classical FFT coefficients for the first N samples (8 samples when N = 8).

Next, a SAFT (Sliding Aperture Fourier Transform) was developed to update to a new Fourier transform based on each new sample. When the 8th sample arrived, the coefficients were calculated based on the vector of the latest 8 samples, samples 1 to 8 respectively. When the ninth sample arrives, the coefficients are calculated based on the vector of the most recent eight samples, samples 2 through 9, respectively. The ninth sample has an associated vector pointing 45 degrees from the x-axis 2a, which is in the same direction as the first sample (oldest), and by convention S9 = S1 '.
Updating the new coefficient based on the new sample set involves adding S1 ′ and subtracting S1. The updated coefficient C ′ is represented by (Equation 8).

[Equation 8] The tenth sample has the associated vector oriented at the same angle as the second sample, and is therefore labeled S2 '. The coefficient updated after the arrival of S2 ′ is C ″ given by (Equation 9).

[Equation 9] The update calculation is also applied to the coefficients A1 and B1. (Equation 10) A sample calculation of A and B.

[Equation 10]

However, although the above calculation is sufficient and correct for C, the calculation of A and B, which are projections to the reference system, requires adjustment of the rotation of the reference system. Without it, those values given by (Equation 10) are inexact and different from the classical Fourier coefficients. Generally speaking, the coefficient is an appropriate trigonometric function of 45 degrees (for A, the cosine function cos, B
The first sample of the set weighted by the sine function sin) with respect to
It is defined using a second sample weighted by a trigonometric function of (2 ^* 45) degrees, and so on. However, the first sample of the new set (Samples 2 to 9) was the second sample of the initial set (1 to 8), and the calculation uses (2 ^* 45) trigonometric functions for weighting. Error has been introduced into the updated coefficient.

Embodiments of the present invention correct for errors in updated coefficients. The correct coefficient is obtained by providing a rotating frame of reference. This is shown graphically in FIG. 1A. FIG. 1A shows a rotated frame of reference represented by an x-axis 3a labeled X45 and a corresponding y-axis 3b. Based on the rotated reference frame, sample 2
With a contribution of 45 degrees. The x-axis 3a is a new axis whose projection is calculated. In fact, every time the oldest sample is replaced by a new sample, the frame of reference rotates. FIG. 1B is the sample size.

FIG. 1C shows the necessary coefficient modifications related to the rotation of the reference frame. In FIG. 1C, S
Represents the phase of the vector C (angle between the vector C and the X axis of the reference system). When the system rotates 45 degrees counterclockwise, the new phase becomes (s-45). Therefore, the following (Equation 11) is applied.

[Equation 11] For example, the values of A and B calculated by (Equation 10) are converted into A ′ and B ′, and a classical Fourier coefficient, that is, an accurate coefficient is obtained. Using the trigonometric identity of the difference between the two angles and substituting A and B for their equivalents, we get the following general formula (Equation 12) that represents the exact determination of A and B:

[Equation 12] If, for example, the polar form of the Fourier coefficient is sought, rather than the vector form described by (Equation 8) and (Equation 9) or the form shown by (Equation 10) and (Equation 12) The value of the coefficient C (the size of the vector) is given by the following equation.

[Equation 13] This leads to the general formula (Equation 14) for calculating the value of the coefficient C.

[Equation 14] Where i is the current coefficient number and p _i-1 is the phase between the previous coefficient C _i-1 and the current / most recent sample Si.

Squared Fourier coefficients may be preferred in certain applications. In other applications, it is possible to directly correct the coefficient value using (Equation 15).

[Equation 15]

[0042]   The general case equation for the phase of the coefficients is given in (Equation 16).

[Equation 16] Here, i = sample number, j = coefficient number, N = sample number, and π is a mathematical constant (
~ 3.14 radians).

It should be appreciated that the method of using a rotating frame of reference to generate accurate coefficients applies to other functions as well as Fourier transform calculations. The equations and relationships required to carry out the correction, ie the correction of the phase angle, depend on the function used. Techniques such as mathematical analysis can be useful in deriving correcting equations and relationships for other functions, as will be appreciated by those skilled in the art.

Those skilled in the art will also appreciate that the apparatus and method and computer program product of the present invention are not limited to any particular method for deriving the coefficient contribution of a sample. Basically any known or any new method for deriving coefficient contributions can be used in the embodiments of the present invention.

FIG. 2 shows a block diagram of the operations performed to determine the coefficients of a function that represents an input signal in one embodiment of the present invention. In a preferred embodiment, the operation is machine executable, such as an operation that can occur on a computer or other type of electronic device. After starting, there is the step of obtaining the complete set of coefficients (step 100). In practicing the embodiments of the present invention, any coefficient of the initial set can be generated by any suitable method.

The initial set coefficients may be real set coefficients corresponding to a set of real samples generated by standard methods for obtaining coefficients. If the coefficients are Fourier transform coefficients, they may be, for example, a fast Fourier transform or a method such as the Pelton approach described in US patent application Ser. No. 09 / 560,221 and PCT publication WO 00/67146 or a Fourier transform. Obtained by solving the DFT using any of the methods to derive the coefficients. Alternatively, the initial set of coefficients may be the "dummy" set of coefficients. Zero padding (the method o
It is appropriate to use the coefficients of the initial set derived using f padding with zeros). Basically, there is great flexibility in choosing the coefficients of the initial set. The initial set of coefficients can be stored in a memory, such as a computer readable memory.

The next step involves receiving a new sample, such as a sample of the signal to be represented by the coefficient (step 110). This new sample is used to calculate the coefficient contribution of the new sample (step 120). The coefficient contribution is calculated according to a mathematical formula representing the function from which the coefficient is derived. The Fourier transform coefficient contribution is calculated using the sample, the appropriate trigonometric function, the sample number, and the coefficient number.

The operation also includes obtaining the coefficient contribution of the oldest sample in the set of samples (step 130). The coefficient contribution of the oldest sample can be obtained using various techniques. For example, the coefficient contribution of the oldest sample can be pre-stored in accessible memory. Instead, the oldest sample is pre-stored in accessible memory and its coefficient contribution can be calculated using the oldest sample.

The coefficient contribution may be updated using the coefficient contribution of the oldest sample and the coefficient contribution of the new sample (step 140). The updated coefficient is obtained by subtracting the coefficient contribution of the oldest sample and adding the coefficient contribution of the new sample. If the generated coefficients are for Fourier transform coefficients, the updated coefficients obtained in this step are SAFT (Sliding Aperture F
equal to the coefficient provided by ourier Transform). In particular, the coefficients are inexact and do not equal the classical Fourier transform coefficients. To obtain the correct coefficients, the method and apparatus and computer program product according to embodiments of the present invention corrects the updated coefficients to provide coefficients that more accurately represent the signal (step 150).
The method and apparatus of the present invention and the computer program product incorporate a correct reference system for the set of samples containing the new sample such that the angle used in deriving the coefficient contribution is the correct angle for each sample. . Regarding the Fourier transform coefficient,
The correct coefficient corresponds to the classical Fourier transform coefficient.

As already mentioned, the rotating frame of reference gives the correct angle for each sample. A rotating frame of reference can be incorporated into an embodiment of the present invention to generate Fourier coefficients using (Equation 12) in the apparatus and method of the present invention and the computer program product. Applying a rotating frame of reference to another type of function may require a mathematical formula that is specifically applicable to that particular function. Optionally, the mathematical formula can be derived analytically. Alternatively, a learning model can be used to derive the mathematical formula.

After generating the correct coefficient, there may be an optional operating step that outputs that coefficient (step 160). At this step, the coefficients for the set of samples including the new sample can be used for display, analysis and further signal processing.

Another optional step after generating the coefficients is to replace the coefficients of the set of samples containing the new sample with the coefficients of the previous set (step 170).
). If the operation should continue, the operation returns to the step of receiving a new sample (return to step 110).

As already pointed out, the apparatus, method and computer program product of the present invention have the flexibility of using a wide variety of techniques to generate the initial set of coefficients. Similarly, the apparatus and method and computer program product of the present invention provide the flexibility to use a wide variety of techniques to generate the coefficient contributions of a sample. For example, in the Fourier transform, a fast Fourier transform can be used to provide the coefficients. Instead, US Patent No. 09 / 560,221 and PC
The Pelton approach can be used to provide the coefficients as described in T. Publication WO 00/67146. Similarly, coefficient updates can also be obtained using the technique of Pelton et al.

FIGS. 3 and 4 show examples of configurations of Pelton approaches suitable for determining coefficient contributions and / or coefficients used in the methods and apparatus of the present invention and computer program products. These figures are similar to those described in U.S. Patent No. 09 / 560,221 and PCT Publication WO 00/67146. Referring first to FIG. 3, there is shown one arrangement for determining the coefficients of the initial set of functions representing the input signal based on the sample of the input signal. The apparatus of this embodiment of the invention includes a coefficient generator 10. The coefficient generator includes a receiver 12 for receiving samples of the input signal. The coefficient generator includes a first gate 14 in digital communication with the receiver and a second gate 16 in digital communication with the first gate. It will be appreciated that digital communication is a connection means by which information can be transferred digitally. Various techniques can be used to implement digital communication. One example of digital communication is to use electrical signals, such as electrical signals for telecommunications. Another example of digital communication is the use of optical signals, such as optical signals for optical communication.

FIG. 4 shows the operation of the coefficient generator. In this figure, the coefficient generator is
Generate coefficients based on 8 samples. For each sample, the receiver receives a sample of the signal and inputs it to the first gate 14 (step 20).
0). For each coefficient, the second gate receives two values, one for the coefficient number 18 and the other for the sample number 20. Based on the coefficient number and the sample number, the second gate produces an orthogonal function portion of the signal (step 210).

For the zeroth coefficient A0, the sample value is added to the coefficient. For the first sample and coefficient A11, the orthogonal function is

[Equation 17] Becomes Here, C _n = coefficient number, S _n = sample number, N = sample number. The second gate receives the coefficient number 18 and the sample number 20 to calculate the first coefficient and the term for the first sample. Based on this, for the first sample Sn and the first coefficient Cn, the second gate is cos (2π · 1 · 1/8)
Alternatively, cos (2π / 8) is generated and this value is output to the first gate (step 210).

The first gate then receives the value from the second gate and the sample value from the receiver. Based on these values, the first gate produces a term that represents the sample's contribution to the coefficient (ie, S1cos (2π / 8)) (step 220). This term is then added to the coefficient A1 (ie, A1 + A11) (step 230).
). This is repeated for each coefficient (step 240 and step 250).

The above discussion describes how each coefficient is updated once for each sample. Furthermore, it should be understood that the coefficient generator can update all coefficients simultaneously in each sample. For example, the coefficient generator may include all the plurality of first and second gates coupled to the receiver. In this embodiment, the samples are fed to each set of gates at the same time, each set of gates simultaneously producing for each coefficient a term representing the sample's contribution to each coefficient, and each coefficient being updated simultaneously. In particular, the coefficient generator is generally implemented to update all coefficients at the same time. Further, in some cases, the coefficient generator is configured to receive inputs from several channels and generate a set of coefficients for each channel. However, in the exemplary embodiment described herein, the coefficient generator has been described as sequentially updating each coefficient in only one channel for purposes of clarity of explanation.

The coefficient generators and operations shown in FIGS. 3 and 4 are used in embodiments of the invention to generate the initial set of coefficients and / or to generate the coefficient contributions. It is suitable for

FIG. 3 is a block diagram of multipliers, adders, dividers,
FIG. 7 is a diagram for explaining a mechanism for determining a coefficient and a coefficient contribution based on the use of a gate, such as another gate function. FIG. 5 shows US patent application Ser. No. 09 / 560,2.
21 and PCT Publication WO 00/67146, but is a diagram for explaining a mechanism for determining coefficients and coefficient contributions using at least one memory device. It may be advantageous to use a memory device as opposed to a gate, as many of the values that have to be calculated to determine the coefficient may be pre-stored in the memory device. Therefore, this can save time in determining the coefficients.

[0061]   Referring to FIG. 5, the coefficient generator in this embodiment is a signal sampler.
A receiver 12 for receiving the signal. The coefficient generator is in digital communication with the receiver.
And a second memory device 22 for digitally communicating with the first memory device 22.
Including a moly device. Optionally, the second memory device provides for each sample and coefficient
Contains an array of cells where each cell contains a precalculated value that represents the orthogonal function part of the signal
. For example, the second memory device may have cos (2πC) for the first sample and coefficient. _n S_n/ N) or the cell for the orthogonal function part of the signal equal to cos (2π / 8)
including. In this configuration, the first memory device may be a multiplier.

To describe the operation with reference to FIGS. 4 and 5, for each sample, the receiver receives a sample of the signal and outputs the sample to the first memory device 22 (
Step 200). For each coefficient, the second memory device has a token representing the address of the cell containing the orthogonal function part of the signal for that sample and coefficient.
) To receive. This token is provided by inputs 18 and 20. Here, one part of the token is the coefficient number Cn, and the other part is the sample number Sn. Based on this token, the second memory device reads the value associated with the coefficient and the sample and outputs the value to the first memory device (step 210).
. The first memory device then receives the value from the second memory device and the value of the sample from the receiver. On the basis of these values, the first memory device causes the term representing the contribution of that sample to the coefficient (for the first sample and the coefficient S ₁ cos (
2π / 8)) is generated (step 220). This term is then added to the coefficient (ie A1 + A1 ₁ ) (step 230). This is repeated for each coefficient (steps 240 and 250).

In some embodiments of the invention, the sample received from the receiver is one of many finite values. The orthogonal function part for each sample and coefficient is already known (ie (2πC _n S _n / N)), and each sample value and sample can be just one of a finite number of values. The values representing the number and the coefficient number can be calculated in advance and stored in advance. Thus, when a sample is received, the term representing the contribution of that sample to each coefficient may be determined by examining the value in the memory device based on the value of that sample, the sample number, and the coefficient number. it can.

Taking this into account, according to a further embodiment, the first memory device is
A memory device including an array of cells. Each cell of the first memory device contains a pre-calculated value representing a respective sample value, sample number and coefficient number. For each coefficient and sample, the memory device includes a group of cells in which each cell therein has an orthogonal function associated with the coefficient and sample times the possible value of that sample. For example, for the first sample and the coefficient, there is a group of cells having a value of S ₁ cos (2π / 8). Here, each cell represents a value for a different possible value of Si. Further, the second memory device has an array of cells in which each cell has a token that represents an orthogonal function part for each sample and coefficient.

In operation with reference to FIG. 4, for each sample, the receiver receives a sample of the signal and outputs the sample to the first memory device 22 (step 2).
00). For each coefficient, the second memory device receives from inputs 18 and 20 a value representing the address of the cell containing the token representing the orthogonal function part of the signal for that sample and coefficient. The second memory device reads the token associated with the coefficient and the sample and outputs the token to the first memory device (step 210). The first memory device then retrieves the token from the second memory device,
The value of that sample is received from the receiver. Based on the values of the token and the sample, the first memory device looks up the cells corresponding to these values in the array and finds the term representing the contribution of that sample to the coefficient (ie, the first sample and For the coefficient, S ₁ cos (2π / 8)) is output (step 220). This term is then added to the coefficient (ie A1 + A1 ₁ ) (step 230). This is repeated for each coefficient (steps 240 and 250).

Again, the device of this configuration operates in a parallel configuration to update each coefficient simultaneously by providing a plurality of first and second memory devices for each coefficient all connected to the receiver. It must be understood that you can. In this embodiment, each of the first and second memory devices receives the samples at the same time, and each set of the first memory device receives the samples.
And the second memory device is appropriately addressed to address the values for the different coefficients. In this way, the contribution of the sample to each coefficient is determined simultaneously in parallel.

Referring to FIG. 5, in another arrangement for providing an initial set of coefficients and / or for providing coefficient contributions, a coefficient generator is in digital communication with a second memory device. A counter 26 for The counter can be incremented by a clock, not shown, which allows the calculations to be performed in a timed manner. The counter may include two outputs 18 and 20 representing a coefficient number and a sample number for addressing the second memory device. During operation, for each sample, the sample number remains constant, while the counter increments the coefficient number during each cycle or cycles of the clock. From this the second memory device is then addressed to determine the contribution of the sample to each coefficient. After all the coefficients have been calculated for that sample, the counter sample number is incremented and the coefficient number is reset so that the next sample is now evaluated for each coefficient.

As described in detail, in order to reduce the calculation time, according to one embodiment of the present invention, a memory device for storing a pre-calculated value and a token for addressing the memory device. Is used. An important concern in many electronic designs is the desire to minimize the number of components needed to drive a circuit and the need to use off-the-shelf components wherever possible. With this in mind, there is a need for a way to evaluate design needs and determine a design solution that minimizes component count and allows the use of standard components.

As noted above, US patent application Ser. No. 09 / 560,221 and PCT Publication WO 00
/ 67146, the number of values that must be stored in order to calculate the coefficients of the function is to remove the extra value and store only the magnitude of that value,
It is reduced when the value is zero or by using token bits to indicate the sign of the value. Thus, FIG. 6 is a diagram for explaining the updating of each coefficient for each received sample, showing a coefficient generator with additional gates to reduce the amount of values that must be stored. Further, FIG. 6 shows a first memory device having a minimum number of stored values, a second memory device with a token containing a bit to indicate a sign or zero, and a signed input value. input value) and to provide a structure for determining the coefficient contribution and / or the coefficient of the function.

The coefficient generator 10 of FIG. 6 includes first and second memory devices 22 and 24. Both memory devices include cell arrays for storing values. The second memory device contains tokens representing coefficient numbers and sample numbers, and the first memory device contains all possible unique values of the samples combined with the orthogonal function part for each sample and coefficient. Although any system or device can be used to address the second memory device, a counter 26 for addressing the second memory device is shown in this embodiment.

The coefficient generator of this embodiment further includes an adder 44 in digital communication with the output of the first memory device. A crossbar or selector 46 and a third memory device 48 are connected to the adder 44. The coefficient generator includes a null or pull-down device 50 in digital communication with the crossbar and a NAND gate 5 connected to the output of the counter.
2 and an AND gate 54 are also included.

Further, the coefficient generator of this embodiment includes a first AND gate 28 and a second AN.
It also includes a D gate 30 and an XOR gate 32. At the output of the second AND gate 30, an adder 36, which is typically introduced to sample the twos complement of the signal.
Are connected. The XOR gate 32 is in digital communication with the output of the second memory device and the gate combination 40. The coefficient generator of this embodiment also includes a null or pull-down device 34 in digital communication with the output of the first memory device.

This coefficient generator is a code converter in digital communication with the receiver 12 for converting the input signal into a 12-bit value consisting of 11 bits representing its value and 1 bit representing its sign, if necessary. (Code converter) 38 is also included. The coefficient generator of this embodiment also uses a 6-bit token stored in the second memory device to address the value stored in the first memory device. If the sign bit of the token indicates a negative value, this token works in conjunction with the second AND gate 30 and the adder 36 to take the negative output of the first memory device. Further, if the token indicates that the value should be zero, the null or pull-down device 34 and the zero bit of the token act to null the output of the first memory device.

Still further, the coefficient generator includes a first latch 60 for latching the input signal and a second latch 62 for latching out the output coefficient value. The coefficient generator has an input 44 for using the coefficient generator to determine the coefficient of the inverse function of the signal.
And a gate combination 40 is also included. In addition, the coefficient generator includes a reset device 64 for resetting the memory and outputs 56 and 58 for outputting the coefficient number and the channel number.

The operation of this embodiment will be described with reference to FIG. 7. Similar to the previous embodiment, for each sample, the receiver receives a sample of the signal and stores that sample in the first memory device. 22 (step 300). For each coefficient, inputs 18 and 20 representing the sample number and coefficient number are provided to the second memory device (step 3
10) Based on their inputs, the second memory device outputs tokens (step 320). Based on the token and the sample, the first memory device generates a term representing the contribution of the sample to the coefficient (step 330).

If the sign of the signal is negative or the sign bit of the token is aggregated, the second AND gate outputs a carry bit to the adder 36. The adder makes the output of the first memory device negative (steps 340 and 350). Similarly, if either the signal or the token indicates a zero value, the zero value is the first AND
It is output by the gate 28. The zero value is output to the first memory device, disabling the first memory device. Due to the disabling of the first memory device, the null or pull-down device 34 outputs a zero value representing the value of the coefficient (steps 360 and 370). In the zero case, the sign is ignored. Then, the coefficient term is output.

Then that term is added by adder 4 which also receives the previous values of the coefficients from the third memory device 48.
4 is provided. The third memory device is also connected to the second memory device. The token from the second memory device addresses the coefficients stored in the third memory device,
This coefficient is now output to the adder to add to the term. The term is added to the existing coefficient by the adder (step 380). All samples have been received,
This continues until the sample-based coefficients are calculated to provide the first set of sample-based coefficients.

The apparatus and methods and computer program products described in the various embodiments above process multiple samples and generate function coefficients based on the samples.
In some embodiments of the invention, after multiple samples are received, the apparatus and method of the invention and the computer program product output the generated coefficients and reset the coefficients to sample the signal again. To do. However, in some implementations it may be advantageous to generate and output a complete set of coefficients as each new sample is received and processed. This is SAFT (Sliding Aperture Fou
rier Transform) is called.

In this embodiment, the apparatus and method and computer program product of the present invention do not reset each coefficient to zero after the final sample of the plurality of samples has been received and the coefficient has been output. Instead, the apparatus and method and computer program product of the present invention replaces the first sample of the previous plurality of samples with the next received sample. Using this new sample, the apparatus and method of the present invention and the computer program product output the next set of coefficients. Thus, instead of producing a set of coefficients for each "batch" of samples, the apparatus and method of the present invention and the computer program product produce a set of coefficients each time a new sample is received. And thereby provide a new set of coefficients each time a new sample is received.

The present invention provides several apparatus and methods and computer program products for generating a set of coefficients each time a new sample is received. In each of these embodiments, the apparatus and method of the present invention and the computer program product replace the first sample contribution of the previous plurality of samples with the received next sample contribution and output new coefficients. To do. For example, the apparatus and method and computer program product of the present invention may store each sample first when they are received, and when the last sample of the plurality of samples is received, the first set of samples may be stored. Generate the coefficients. Further, when a new sample of the input signal is received (after a predetermined plurality of samples have already been received), the apparatus and method of the present invention and the computer program product provide a new mathematical function associated with the coefficient. Applied to various samples,
Generate a new sample-based term for each coefficient. To replace the new sample with the first sample of the plurality of samples, the generated term of the new sample is associated with the first sample of the predetermined plurality of samples previously stored in the memory device. It is deducted from the term. After this subtraction, the coefficients are updated with the difference between the new sample and the first sample-based term of the predetermined plurality of samples.

In another embodiment of the invention, the apparatus and method of the present invention and the computer program product replace the new sample with a first sample of a plurality of samples, and The one sample-based term is subtracted from each coefficient and a new sample-term based term is added to each coefficient. Thus, according to one embodiment, the terms of the new sample and the oldest sample are subtracted from each other and the residue is added to the coefficients. On the other hand, according to another embodiment, the term associated with the oldest sample is subtracted from each coefficient and the term associated with the new sample is added to the coefficient. In this second embodiment, which is shown in FIG. 6, it generally has a smaller computational drift.

In this embodiment, the coefficient generator of FIG. 6 includes a fourth memory device 66 in digital communication with the third memory device 48 for storing the term associated with each sample of the plurality of samples. . The coefficient generator digitally communicates to the third and fourth memory devices for subtracting the term associated with the first sample of the previous plurality of terms from the term associated with the newly received sample. Is further included. The fourth memory device is also connected to the second memory device.

According to this embodiment of the invention, when a new sample is received after the initial coefficient is determined from the samples of the first set, the coefficient is updated with the information from the new sample. Also, the contribution of the oldest sample is subtracted to give SAFT. In particular, referring to FIGS. 6 and 7, the token from the second memory device was stored in the fourth memory device representing the term associated with the first sample of the plurality of samples (ie, the oldest sample). Address the term. This term is adder 68
, Where the term is subtracted from the updated coefficients (step 390).
). The term associated with the new sample is stored in the fourth memory device (step 40).
0), the updated coefficient is stored in the third memory device (step 410) and is also output (step 420). Until all coefficients are updated with that sample,
The above steps are repeated (steps 430 and 440).

The apparatus and method of the present invention and the computer program product can be used in parallel for a series of channels. The present invention produces, for each channel, the coefficients of a function that represents the signal on the channel. As detailed above, the present invention determines the coefficients of a function that represents a signal by combining each sample as it is received with the mathematical functions and coefficients associated with that sample. Further, as detailed above, different combinations of samples and coefficients can be pre-computed and stored in an addressable memory device, or can be computed by a gating function with reference to the value associated with the token. Generally, the tokens that address the cells of the memory device are derived from the state information obtained from a counter that indicates the coefficient and the sample. In normal operation, tokens and memory devices are used to determine the coefficients of the function that represents the signal, but these tokens and memory devices are used repeatedly by adding bits to the counter at the appropriate locations. As a result, multiple channels can be served. According to this configuration, the additional coefficient memory cell holds the additional coefficient, and the channel number is output to the user for convenience. It is still possible to utilize the electrical signal to determine the forward coefficient or the inverse of the input.

Furthermore, in normal operation, the token and memory device are used to determine the coefficients of the function representing the signal, but these token and memory device add a bit to the counter at the appropriate location. It can also be used repeatedly, so that it can serve multiple channels. According to this configuration, the additional coefficient memory cell holds the additional coefficient, and the channel number is output to the user for convenience. So that successive samples are treated as different channels,
It is possible to create an interleaved transform.
The interleaved transform can be sent to a second similar process to produce a two-dimensional transform, for example.

According to one embodiment of the present invention, the device shown in FIG. 6 has an additional electronic component (FIG. 6) for converting the coefficients into the correct reference frame, in particular for rotating the reference frame. 6 (not shown in FIG. 6) to correct the updated coefficients. Additional electronic components may include components that use gates, such as multipliers, adders and other gated functions.
Alternatively, the apparatus according to the embodiment of the invention shown in FIG. 6 may use memory and a stored function to provide a rotating frame of reference. For Fourier transform calculations, an additional component or memory derives the corrected coefficients according to equations such as (Equation 12) and (Equation 15).

As already mentioned, the coefficient generator of FIG. 6 continuously updates the coefficients as new samples are received by subtracting the effect of the oldest sample and adding the effect of the new sample. Realize a SAFT configuration that enables As explained above, this can generally be done in two ways. First, the effect of the oldest sample can be recalculated and subtracted from the coefficient, to which the new effect of the new sample can be added. Similarly, the effect of the oldest sample is calculated,
It can be subtracted from the effect of the new sample and the residue then added to the coefficient. These methods implement SAFT techniques that allow the coefficients to be continuously updated as each new sample is received, but these methods simply replace the oldest sample with a new sample. , Which does not pose the problem in the first sample of the new set (in the situation of N = 8) starting at 2 * 45 degrees as opposed to 45 degrees.

In view of this, according to one embodiment, the invention provides a coefficient generator that corrects the coefficients by rotating the reference frame of the samples and thereby giving the classical DFT. In particular, the fourth memory device 66 and the adder 50 of the embodiment shown in FIG. 6 simply subtract the effect of the oldest sample and add the effect of the newest sample. However, embodiments of the invention rotate the reference frame to further correct the coefficients so that when the oldest sample is subtracted and the newest sample added, the sample has the correct angular value for the calculation ( compensate). In particular, FIG. 8 shows a block diagram of the architecture of an apparatus according to an embodiment of the invention for correcting Fourier transform coefficients using a rotating frame of reference. The apparatus shown in FIG. 8 is suitable for use in the coefficient generating apparatus as shown in FIG. In particular, FIG.
Shows the additional logic needed to add coefficient correction to the coefficients generated by the apparatus shown in FIG. Importantly, the apparatus of FIG. 8 performs the calculation of (Equation 12) to correct the coefficient for differences in the angular rotation of the sample.

In particular, the device of this embodiment includes a fifth memory device 70 for connecting to the output of coefficient number 72 and the output of phase code 74 of latch 62. The memory device includes an array containing precomputed values for the sine and cosine contributions associated with each coefficient number and sample number. For example, if the coefficient generator uses eight samples to determine eight coefficients, the fifth array of memory devices may store the coefficient numbers and samples of the sine and cosine parts of the correction equation (14), respectively. Would include all calculated values for the combination of.

The device of the present invention comprises a fifth memory device and a coefficient output 8 of the latch 62 shown in FIG.
It further includes two multipliers 76 and 78 connected to both 0 and. The first multiplier 76 multiplies the cosine portion of (Equation 12) by the coefficient output value of the latch 62, and the second multiplier 78 multiplies the sine portion of (Equation 12) by the coefficient output value of the latch 62. Multiplier 7
Connected to 6 and 78 is an adder 82 having an output 84 with corrected coefficients.

The operation of the apparatus for correcting the Fourier transform coefficient using the rotation reference system will be described with reference to FIG. In particular, as shown in FIG. 6, the coefficient generator first generates a set of coefficients based on the first set of samples (step 500). After this first set of samples has been received, the coefficients have been calculated, and the next sample has been received, the coefficient generator's fourth memory unit 66 and adder 68 subtract the contribution of the oldest sample, Add the contribution of the newest sample (step 510). As already mentioned, the fourth memory device 66 and the adder 68 do not correct the angular rotation of the samples due to dropping the oldest sample and adding the newest sample. From this point of view, the apparatus shown in FIG. 8 of the present invention realizes this correction.

In particular, the coefficient generator latch 62 to the fifth memory device 70 receive a coefficient number 72 and a phase code 74, respectively, which represent the coefficient number and the sample number (
Step 520). Based on these values, the fifth memory device reads the cosine and sine parts of (Equation 12) associated with the coefficient number and the sample number from the array of stored values and multiplies these values by the multiplier 76. And 78 (step 530). In particular, if the coefficient number is 7 and the sample is 5, the fifth memory device provides the cosine and sine parts of (Equation 12) corresponding to these values. The multipliers respectively receive the cosine and sine values from the fifth memory device, and they also receive the coefficient value 80 from the latch 62. This coefficient value is
Memory unit 66 and adder 68 previously corrected by subtracting the contribution of the oldest sample and adding the newest sample. Using these values, the multiplier calculates the value of the correction equation (Equation 12), and the adder 82 adds the values from that multiplier to obtain the corrected Fourier transform coefficients using the rotating frame of reference. give(
Step 540).

An additional aspect of the invention is sample independence. In particular, since each sample affects each of the other coefficients, the coefficient of interest can be selected for updating, but the other coefficient is not selected. Another aspect allows the user to track one coefficient without having to calculate all other coefficients.

As mentioned previously, there is a need for methods and apparatus that allow for faster generation of coefficients and / or require simpler hardware configurations. further,
It was previously mentioned that embodiments of the present invention may use various techniques for generating coefficients in SAFT applications. Improved coefficient generation techniques and hardware provide updated coefficients, which can further improve the utility of SAFT to provide updated corrected coefficients.

In response to that need, another embodiment of the invention relates to automatically determining the model for generating the coefficients of the function representing the signal. In these embodiments, learning techniques are used to determine the model. In general, transforms such as Fourier transforms are mappings between variables. The main definition of mapping is usually analytical.
Several models of calculations for mapping can be determined. Some models are more effective than others, depending on what computational technique is employed.

The definition of the Fourier transform relates variables in the time domain to variables in the frequency domain. D
In the case of FT, the mapping is between temporally consecutive samples and the coefficient at a particular frequency. The coefficients can change for every sample to characterize the set of samples, including the most recent sample. The calculation method for calculating the coefficient involves mapping between some parameter with sufficient information and the value of the coefficient. In particular, the computational model can be a mapping between an input consisting of the last set of coefficients plus the last sample and a new set of coefficients. In fact, there can be several such models.

One embodiment of the present invention includes a method for automatically determining a model when trained from input and output data that describes the mapping between samples and Fourier coefficients. The techniques described are general and can be applied to the learning model for either mapping. As a specific case, most of the examples presented here will relate to learning computational models for the mapping between the last set of coefficients plus the most recent sample and the new set of coefficients. Unlike standard techniques, embodiments of the present invention apply these approaches to polynomial and series formulas as well as functions such as Fourier and Laplace transforms. In general, embodiments of the invention implement computationally simpler, faster, or more parallel hardware. In some embodiments of the invention, US patent application Ser. No. 09 / 560,221 and PCT Publication WO 00/6714.
SIFT (Sample Integrated Fourier Transform) and SA described in No. 6
It may include, but is not limited to, techniques such as the FT method.

The solution model can be exact or approximate. Each method presented here is used to create a solution to the described set of mapping functions. Although the models are each based on different disciplines and require different methodologies, they employ error estimation and judgment to select errors that are small enough to meet the required parameters. Is similar. The embodiments provided are not exhaustive and are only intended to show, by way of example, members of a family of applied approaches. It will be clear to a person skilled in the art that alternative embodiments of the invention can be derived by the decision making to choose some similar valuation methods and revert to the same function in a slightly different way.

A variety of learning modeling approximation modeling techniques are suitable. Examples of two types of modeling techniques are discussed. The first technique is a universal functimeter, here exemplified by neural networks and fuzzy logic.
including using specialized structures as onal approximators). The second technique works well for any structure and provides a general approximation (model identification) scheme where the elements of the model are synthesized by a search technique, here exemplified by a genetic algorithm. Including using.

An example of a basic block of a specialized structure is the neuron of a neural proxy meter and the fuzzy rules of a fuzzy system proxy meter. The properties of the universal functional approximation have been officially demonstrated for both types of aproximators. Fuzzy logic processors are known in the art and are commercially available. Fuzzy logic processors are available, for example, in the form of computer-executable code that can be run on a computer or electronic device. Similarly, neural network processors are commercially available. Neural networks can be implemented as software in the form of computer executable code. Further, there are commercially available neural network chips that can be used as neural network processors.

One embodiment of the present invention includes a neural network chip that is trained with a given sample and a given coefficient to map the coefficient to an input sample. In a further embodiment, the neural network chip is connected to a receiver for receiving the samples. The samples are sent to the neural network chip so that the neural network chip can generate coefficients or coefficient updates based on the samples. In another embodiment of the present invention,
It includes a fuzzy logic processor chip that is trained with a given sample and a given coefficient to map the coefficient to an input sample. In a further embodiment, the fuzzy logic processor chip is connected with a receiver for receiving the samples. The samples are sent to the fuzzy logic processor chip so that the fuzzy logic processor chip can generate coefficients or coefficient updates based on the samples.

In the case of general approximation schemes, the basic building blocks can be almost any kind. If used to find an electronic circuit solution, the basic blocks are, for example, logic gates such as adders and multipliers or higher level digital building blocks, transistors, available amplifiers,
It can be an R, L, C component. In this case, a special case, eg N
There is no proof of universal approximation other than the implementation of some logical function, such as using only AND gates. The area of a general proxy meter whose basic building blocks are electronic components and whose model identification is based on an evolutionary algorithm or a genetic algorithm is also called EHW (Evolvable Hardware).

A feature of embodiments of the present invention is that the approximation can accommodate any degree of accuracy. In other words, the degree of accuracy is a controllable parameter. This is advantageous because a high degree of accuracy may be desired for some applications, while lower accuracy is allowed for other applications.

An important step in using the learning model involves generating data for learning and training. The model identification of the proxy meter mentioned above is
Usually a training / learning / search proced
ure). In this case, the set of I / O pairs obtained from the modeled system is used for training. In the case of determining the coefficients of the Fourier series, the training pairs consist of pairs of vectors, eg samples and coefficients. For the SAFT problem, the pair can be sample and coefficient update. Choosing the right training set has a great impact on the feasibility of modeling. The following example uses 8 samples coded on 5 bits.

For example, “At each new sampling time, the value of the sample together with the coefficient of the current set (input + current state) determines the coefficient of the new set. Coefficient (t + 1) = function (sample (T + 1), coefficient (t)) ”, the model determined by the mapping expressed in terms. First, a random vector that is an input sample in the time domain is generated.
The magnitude of the vector can be model dependent. Usually, each sample index (in
It should be understood that there is a training pair corresponding to dex). This training pair can be thought of as an expression connecting the inputs and outputs. The number of equations that may be needed depends on many factors. For example, the number of expressions may depend on how many variables are in the model. If a linear model is possible, a linear transformation will be calculated and a number of equations equal to the number of unknowns will give the exact solution. A small number of formulas (ie training pairs) are insufficient for generalization. In general, if the data is stochastic, more equations are needed.

The next step is to generate the Fourier coefficients for each group of samples by any convenient method (discussing a set of 8 samples, one group is sample number 1-8,2- 9 and 3-10). Examples of convenient methods for Fourier coefficients include FFT, butterfly method and SIFT (US patent application Ser. No. 09/5).
60,221 and PCT publication WO 00/67146). This means that for each sample index, there is a set of coefficients that characterize the samples in the window ending with this index sample. The coefficient of this set is the desired target output for training. In another implementation, the problem can be decomposed into a model that computes only one coefficient. In this case, the vector of values of that coefficient is the target.

In this example, the input for training is a combinatorial set consisting of a set of coefficients corresponding to the last sample and the samples in the previous window (ie up to the sample before the exponential sample). In particular, for a window of 8 samples, the input / output training pair is the pair corresponding to each index. The input consists of one value for the sample at (t + 1) and eight values for the coefficient at time t, and the output consists of one or more coefficients at time t + 1.

Table 1 shows the code for generating data for the learning model and the training model.

[Table 1]

One embodiment of the present invention includes neural modeling. Neural modeling uses neurons as the main building blocks. A neuron is a computational block that maps a set of inputs to an output. The mapping is usually a generally non-linear function with the total contribution of all inputs integrated. Each contribution is multiplied by a weight factor.

Neurons are interconnected in a topology such that the output of some neurons provides the input for other neurons. They can be organized into groups called layers and interconnects restricted to middle layer networking.
For example, all neurons in layer 1 have their outputs routed to all neurons in layer 2. Each link between neurons has an associated weight, and it is common for neurons to have an associated bias term. Learning a neural model typically involves determining the topology of the interconnections, the weight values, and the bias values. The topology of the interconnect is usually imposed by the trainer.

Next, FIG. 10 shows an embodiment of the present invention. FIG. 10 shows a model of a neural network that maps the last set of coefficients and the most recent sample to the next set of coefficients. The definition for omission is LS (Latest Sample) = last sample,
CCi (Current Value of Coefficient i) = current value of coefficient i (i = 1: 8),
NCi (New Value of Coefficient i) = new value of coefficient i. As an example of training a neural network to learn the mapping between pairs, an input is set that contains one value for the sample at time t + 1 and eight values for the coefficients at time t. The output contains 8 new coefficients at time t + 1. To modify the weights to minimize the difference between the output given by the neural model and the target output, a simple gradient descent routine (simple
gradient descent routine) is appropriate. An example of a suitable measure of this difference is a measure such as mean square error. An example of MatLab code for this problem is shown below.

[Table 2]

In a few iterations, a neural model can be found using this code. This special problem can actually be solved in one layer as follows.

[Table 3]

As a special case, the mapping can be a linear transformation. In this case, the set of mathematical expressions is A * X = B. A is an input value, X is a transformation matrix, and B is an output set. 9
In the special case of interest for 9 training pairs, 9 equations with 9 unknowns, A is 9x9, X is 9x8, and B is 9x8. The first index is 9
For individual training pairs. The solution can be found by X = A * B. Table 2 shows an example of the MatLab code in this case and the results.

[Table 4]

[Table 4 (continued)]

Another embodiment of the invention involves fuzzy logic modeling. Fuzzy models are characterized by a set of rules that map inputs to outputs. In the following description, the examples relate directly to Fourier mapping for 8 samples,
The input contains one value for the sample at (t + 1) and eight values for the coefficient at (t), and the output contains (one or more) coefficients at time (t + 1). The following notation simplifies the description. LS-Last sample, CCi-Current value of coefficient i (Current V
alue for Coefficient i) (i = 1: 8), NCi-new value of coefficient i (New Va
lue for Coefficient I), NB-Negative Big, NM-Negative Medium, NS
-Negative Small, ZR-About Zero, PS-Positive Small, PM-Positive
Medium, PB-Positive Big.

For an embodiment of the invention, possible fuzzy models for the first coefficient NCI are:

[Table 5] In general, the number of rules depends on the problem and the degree of approximation desired. The meaning of the language set NS-PB associated with the fuzzy set defined on the standardized area [-1,1] can be shown in FIG.

The main variables of the fuzzy model are the rule set and the fuzzy set. Other variables are inferential types, interpretation of fuzzy connectives in rules (ie & as logical
AND can be interpreted by MIN, Product, or more general as parametric t-norm, and OR can be used by modeling such as MAX, Probabilistic sum, and parametric s-norm).

Here, for example, basically all parameters are fixed exception rules and membership functions / fuzzy sets. These variables will be modified by a learning mechanism to minimize the distance between the model and the target output. Examples of suitable learning mechanisms are gradient-based mechanisms and genetic algorithms.

Training (model identification) may include various instructions. For example, sample LS
= 0.8 evaluates to 0.8NS and 0.2NM and is thus input into the rule evaluation. Extra rules can be added. That is, some terms in the rule may be omitted. Finally, after training or tuning,
A membership function as shown in Figure 12 will appear.

In general, evolutionary algorithms perform multiple iterations that perform a mechanism to select the best-fitting solution of a set of candidate solutions and then interbreed the best-fitting solution to generate new candidates. , Generate and test, simultaneous search algorithm. In particular, in an embodiment of the invention, the sought-after candidate solution is a Fourier mapping calculation solution. The solution can be an algorithm such as a set of instructions in a given machine-enabled language. Instead, this solution can be analytic in the sense of a set of possible operator-based expressions. As another option, the solution can be electronic in the sense of a circuit based on a collection of basic components such as gates, transistors and resistors. If the desired solution is electronic, the candidate solution is represented in the form of a hardware description language, such as VHDL, Verilog, or SPICE net-lists, with many components in a fixed arrangement. . Typically,
Candidate solutions differ in at least one of the number of components, component type, and component placement.

The technique of applying evolutionary algorithms to search for possible computer room is called genetic programming (GP) and has the goal of reaching a series of instructions that produce the desired result. Program G
P-based search, from high-level powerful language with high expressive power to machine language,
It can be in any language. High level language solutions may need to be compiled or assembled into the CPU's machine language for execution. However, searching for programs is an option. Another option involves directly searching for program implementations in hardware such as circuit solutions.

Modern hardware devices are flexible enough to allow architectural reconfiguration and programming. And FPGA (Field Programmab
le Gate Array) A program that describes a function can be developed as a high-level instruction and converted into a configuration command. Alternatively, the search can be at the configuration command level. This has the potential to force the device into many temporary configurations. Another option is to separate the search for information processing algorithms from the search for the corresponding hardware implementation after the algorithm solution has been determined. As another option, it is possible to perform a unique search for a hardware solution that solves the problem. The isolated alternative has a smaller arranged search space, but
To have a stronger expression, if that expression is not suitable for the problem and an integrated search is preferred, the same would work rather badly.

The idea behind the synthesis or design of evolutionary circuits employs a genetic search or optimization algorithm that works in the space of all possible circuits to achieve the desired functional response. response) to determine the solution circuit. Genetic search is strongly associated with the coded representation of circuits. Each circuit is associated with the genetic code or chromosome. The simplest representation of a chromosome is a binary string, a sequence of 0s and 1s that encodes a circuit. Assembly is the search for solutions in the chromosomal space that correspond to circuits with the desired functional response.

A genetic search is a “generate
It follows the "generate and test" strategy. The corresponding circuit is then evaluated, the best candidate is selected and reproduced for the next generation. This process continues until the performance goal is reached. In ancillary evolution, the search for electronic circuitry is performed by software with the intention that the final solution will be downloaded or become a hardware blueprint. The candidate solution is evaluated as a software model of hardware such as VHDL, Verilog, or Spice netlist. Evaluation is usually performed using a simulator. In the essential evolution, the candidate solution is in the form of a programmable device or architectural physical hardware configuration and is evaluated in hardware in a loop usage test or evaluation device.

The main steps of evolutionary synthesis are shown in FIG. First, a population of chromosomes is randomly generated. Chromosome is a control bit string (control bit-string) downloaded to a circuit model or programmable hardware.
strings)). The circuit response is compared to the target response specification and the individuals are ranked based on how close they are.

Separate model identification for each individual coefficient of the Fourier transform
When discussing identification or circuit synthesis, the candidate circuits take the input values determined by the previous coefficient and the latest sample, and their goal is the new coefficient.

In preparation for a new iteration loop, a new population of individuals is generated from the pool of optimal individuals in the previous generation. It follows generally random selection of individuals from a pool of optimal individuals, random exchange of parts of chromosomes (crossover operations), and random flipping of chromosome bits (mutation operations). This process is repeated over several generations, resulting in ever better individuals. Randomness helps avoid being caught in local optima. Monotonic convergence can be compelled by the optimal transition of the optimal individual from the previous generation to the next generation. Evolutionary and genetic searches are considered optimal choices for very large and fairly unknown search spaces. The search process is usually stopped after many generations or when the target response is approached to a sufficient degree. One or more solutions can be found in the last generation of individuals.

For illustration, we will discuss the search for an electronic solution consisting of CMOS transistors only. The underlying architecture can be based on the arrangement of transistors interconnected by switches as shown in FIG. The transistor arrangement of Figure 14 can be extended by adding layers to the extra layer to the right between V + and V-, forming a "sea of transistors".

FIG. 14 shows a fragment of “Sea of Transistors” that can be a skeleton of a transistor model. As an example, consider the input training set and the nine input signals corresponding to the outputs. The inputs are connected using programmable switches to different points in the architecture such as the gates N5 and N6 of the transistors. Similarly,
The output is connected by switches to intermediate probing points.

Each switch interconnects transistor terminals, interconnects inputs to transistor terminals, interconnects transistor terminals to outputs (eg, one output since the model is independently determined by each coefficient), eg, closed. And 2 corresponding to 0 and 1 like open
Have two states. In this way, this transistor model is topologically equivalent and is specified by a sequence of 0's and 1's which are the chromosomes that describe the candidate model.

One embodiment of the present invention includes the following steps for one sample and eight coefficients. A population of chromosomes, for example 100 chromosomes, is generated. A corresponding Spice netlist is generated, which replaces 0s and 1s with the voltages that determine the opening and closing of the transistors. Each input is connected to a signal source such as a voltage source. The signal source has a signal pattern that is determined by the time variation of the input training set for multiple samples. The first input signal corresponds to the sample. The next eight inputs correspond to the eight coefficients respectively. The circuit provides a particular response on the output side. The circuit response is compared to the target response. The target response may include parameters such as coefficient values.

Multiple circuits are tested. Each circuit gets a fitness value depending on how close the output of the circuit is to the target. As an example, the proper value can be a measure of how small the sum of squared errors at multiple points is. The optimal circuit is selected for inclusion in the mating and subsequent generations. Preferably, the final solution is a circuit with a minimum distance between the target and the output.
In addition, for any combination of inputs (eg, last sample and Fourier coefficient), the final solution preferably provides a target output within a given tolerance.

One embodiment of the present invention is an apparatus that includes a computer-readable medium having computer-executable steps for calculating and processing DFT coefficients. Here the computer-executable steps are derived using a learning model.

[0133] In another embodiment, an apparatus is an application specific integrated circuit (code) having executable steps for calculating and processing DFT coefficients.
n-specific integrated circuit). Here the computer-executable steps are derived using a learning model.

The apparatus in another embodiment includes an integrated circuit, such as an application specific integrated circuit, for deriving the coefficients of the function. Integrated circuit designs are created using learning models.

Another embodiment of the present invention includes a method and apparatus for performing DFT, inverse DFT, etc. calculations to process information. The method and apparatus includes an algorithm or circuit or algorithm and circuit derived from a learning model.

In addition to providing an apparatus and method, the present invention also provides a computer program product for determining a coefficient of a function representing an input signal based on a predetermined plurality of samples of the input signal. The computer program product comprises a computer readable storage medium having computer readable program code means embodied therein. The computer readable storage medium can replace the coefficient generator and perform the functions of the coefficient generator and coefficient contribution generator by software. Further, the computer-readable storage medium controls the coefficient generator by providing addresses for determining the coefficients and coefficient contributions.

Computer-readable program code means
ram code means) includes first computer instruction means for receiving each sample one at a time. Further, computer readable program code means are provided to reduce the latency required for the coefficient contributions to materialize that the correct angle is used for the appropriate sample and thereby determine the exact coefficient of the function. And including second computer instruction means for updating the coefficient of the function based on each sample without waiting for the reception of the next sample when the sample is received and correcting the updated coefficient. According to a further embodiment, each coefficient consists of at least one term based at least in part on the combination of sample and mathematical function. In this embodiment, the computer readable program code means includes a third computer instruction for determining each term of each coefficient by combining each sample upon receipt of the sample and a mathematical function associated with the coefficient. Means are further included.

1 to 14 and Tables 1 and 2 are charts showing graphs, block diagrams, learning models, flowcharts and control flows of the method, system and program product according to the present invention. It will be appreciated that each block or step of the block diagram, flowchart, control flow diagram, and combinations of blocks in the block diagram, flowchart, control flow diagram block may be implemented by computer program instructions. The computer program instructions can be loaded into a computer or programmable device to create a machine, the instructions executed on the computer or other programmable device being a block diagram,
Generate means for implementing the functions specified in the flowchart, control flow block, or control flow step. These computer program instructions can be stored in a computer readable memory that can be directed to cause a computer or other programmable device to function in a particular manner, and the instructions stored in the computer readable memory are , A block diagram, a flowchart, a control flow block, or an article of manufacture containing instruction means for implementing the functions specified in the control flow steps. The computer program instructions may be loaded into a computer or programmable device such that a series of operational steps may be performed on the computer or other programmable device to create a computer-implemented process, on the computer or other programmable device. The instructions executed in provide the steps for implementing the functions specified in the block diagram, flowchart, control flow block, or control flow step.

Accordingly, a block or step in a block diagram, flowchart, or control flow diagram may be a combination of means for performing a particular function, a combination of steps for performing a particular function, and a particular function. And program instruction means for supporting. Each block or step in a block diagram, flowchart, or control flow chart, and combination of blocks or steps in a block diagram, flowchart, or control flow chart, is a function or step of special purpose hardware and computer instructions. , Or a special purpose hardware-based computer system that performs the combination.

Many modifications and other embodiments of this invention will occur to those skilled in the art who have the benefit of the teachings related to this invention and presented in the above description and the accompanying drawings.
Therefore, it is to be understood that this invention is not limited to the particular embodiments disclosed, modifications and other embodiments are intended to be within the scope of the following claims. Although specific terms have been employed herein, they have been used in a generic and descriptive sense only and not for purposes of limitation.

[Brief description of drawings]

FIG. 1A shows a graphical representation of a rotating frame of reference for determining the exact coefficient of a function representing an input signal based on the sample of the input signal, in one embodiment of the invention, for each sample received. FIG. 6 is a schematic diagram showing that a set of accurate coefficients is output for. B is a schematic diagram showing a graphical representation of the sample size shown in A. C is a schematic diagram showing a graphical representation of the necessary coefficient modification related to the rotation of the reference frame in one embodiment of the present invention.

FIG. 2 is a block diagram of the operations performed, in one embodiment of the invention, to determine the exact coefficients of a function representing an input signal based on the samples of the input signal, for each received sample. , A set of accurate coefficients is output.

FIG. 3 is a block diagram of an apparatus for determining a coefficient of a function representing an input signal based on a sample of the input signal using a gating device, in an embodiment of the invention.

FIG. 4 is a block diagram of operations performed to determine coefficients of a function representing an input signal based on a sample of the input signal in one embodiment of the invention.

FIG. 5 is a block diagram of an apparatus for determining a coefficient of a function representing an input signal based on a sample of the input signal using at least one memory device, in an embodiment of the invention.

FIG. 6 is an apparatus for determining a coefficient of a function representing an input signal based on a plurality of samples of the input signal using a memory device and a gate, in one embodiment of the invention, FIG. 6 is a block diagram of an apparatus in which a set of coefficients is output for each sample.

FIG. 7 is implemented in one embodiment of the invention to determine a coefficient of a function representing an input signal based on a plurality of samples of the input signal using a memory device and a gate,
6 is a flowchart of the operation for outputting a set of coefficients for each received sample.

FIG. 8 is a block diagram of an apparatus for applying a rotation reference in performing coefficient correction for use with the apparatus shown in FIG. 6, in an embodiment of the invention.

9 is a block diagram of operations performed to apply a rotation criterion in performing coefficient correction for use with the apparatus shown in FIG. 6, in an embodiment of the invention.

FIG. 10 illustrates a model of a neural network that maps the last set of coefficients and the most recent sample to the next set of coefficients in one embodiment of the invention.

FIG. 11 is a schematic diagram showing possible fuzzy logic membership functions at the beginning of training in one embodiment of the present invention.

FIG. 12 is a schematic diagram graphically showing possible fuzzy logic membership functions at the end of training in an embodiment of the invention.

FIG. 13 is an operational block diagram showing operational steps used to perform evolutionary integration of electronic hardware.

FIG. 14 is a schematic diagram showing a fragment of a “sea of transistors” that may be the skeleton of a transistor model for genetic programming in one embodiment of the invention.

─────────────────────────────────────────────────── ─── Continued front page    (81) Designated countries EP (AT, BE, CH, CY, DE, DK, ES, FI, FR, GB, GR, IE, I T, LU, MC, NL, PT, SE, TR), OA (BF , BJ, CF, CG, CI, CM, GA, GN, GW, ML, MR, NE, SN, TD, TG), AP (GH, G M, KE, LS, MW, MZ, SD, SL, SZ, TZ , UG, ZW), EA (AM, AZ, BY, KG, KZ, MD, RU, TJ, TM), AE, AG, AL, AM, AT, AU, AZ, BA, BB, BG, BR, BY, B Z, CA, CH, CN, CR, CU, CZ, DE, DK , DM, DZ, EE, ES, FI, GB, GD, GE, GH, GM, HR, HU, ID, IL, IN, IS, J P, KE, KG, KP, KR, KZ, LC, LK, LR , LS, LT, LU, LV, MA, MD, MG, MK, MN, MW, MX, MZ, NO, NZ, PL, PT, R O, RU, SD, SE, SG, SI, SK, SL, TJ , TM, TR, TT, TZ, UA, UG, US, UZ, VN, YU, ZA, ZW F term (reference) 5B056 BB12 BB42

Claims (37)

[Claims] 1. An apparatus for determining a coefficient of a function representing an input signal based on a predetermined plurality of consecutive samples, the apparatus comprising: a coefficient generator that updates at least one of the coefficients upon receipt of each sample. An apparatus, wherein the coefficient generator is for correcting the coefficients such that the coefficients represent a correct sample sequence. 2. Each of the coefficients comprises at least one term that is based at least in part on a combination of a sample and a mathematical function, the coefficient generator receiving each sample as each sample is received. Determining a respective term for each coefficient by combining the mathematical function associated with the coefficient with this sample, and the coefficient generator determines, for each coefficient, its respective term as the previous term for that coefficient. The apparatus of claim 1, wherein the coefficient is updated by adding to the value. 3. The coefficient generator updates each of the coefficients with each of the plurality of samples as each sample is received, and each coefficient is updated with a last sample of the plurality of samples. 3. The apparatus of claim 2, wherein each coefficient is then corrected such that the contribution of that coefficient is based on the appropriate angle of each sample and the coefficient generator outputs the coefficient. 4. The coefficient generator simultaneously updates each of the coefficients when each of the samples is received based on each of the plurality of samples, and when the coefficients are updated and corrected, the coefficient The apparatus of claim 2, wherein a generator outputs the coefficients. 5. The coefficient generator of claim 2, further comprising a memory device, the coefficient generator further storing each sample in the memory device when the sample is received. apparatus. 6. The coefficient generator outputs the coefficient after the coefficient generator receives and processes the predetermined plurality of samples, and the coefficient generator outputs the coefficient of the input signal after the predetermined plurality of samples have already been received. When a new sample is received, the coefficient generator subtracts the first sample-based term of the predetermined plurality of samples previously stored in the memory device from the new sample-based term and the coefficient 6. The apparatus of claim 5, wherein the generator updates the coefficient with the difference of those terms based on the new sample and the first sample of the predetermined plurality of samples. 7. The coefficient generator outputs the coefficients after the coefficient generator receives and processes the predetermined plurality of samples, and outputs the coefficient of the input signal after the predetermined plurality of samples have already been received. When a new sample is received, the coefficient generator subtracts a term based on the first sample of the predetermined plurality of samples previously stored in the memory device from each of the coefficients, the coefficient generator The apparatus of claim 5, wherein a new sample-based term is added to each said coefficient. 8. The mathematical function of the input signal is the previous value of the Fourier transform coefficient, and the output is C _{i the} new coefficient, C _{i-1 the} previous coefficient, and S _{i the} new coefficient. As a sample, The apparatus according to claim 2, which is a new coefficient according to the equation given by 9. There is at least one preselected coefficient of interest,
The coefficient generator receives each of the samples one by one, updates the preselected coefficient of the function based on the sample as each sample is received, and replaces the preselected coefficient with the others. The apparatus according to claim 2, which is configured so that it can be evaluated independently of the coefficient of. 10. The apparatus of claim 9, wherein the coefficient generator outputs the preselected coefficient when the coefficient updates. 11. The function of the input signal is a Fourier transform, the mathematical function associated with each coefficient and signal is a trigonometric function, and the coefficient generator updates the coefficient based on a rotational reference system. , The correct coefficient is A′i and B′i are correct updated coefficients, and Ai ^* and Bi ^* are updated coefficients. The apparatus of claim 2, associated with the updated coefficients according to an equation given by. 12. A method for continuously determining the coefficients of a function representing an input signal based on a predetermined plurality of samples of the input signal, the method comprising: A) a complete set of coefficients for a sample of a set. C), B) receiving a new sample, C) calculating the coefficient contribution of the new sample, D) acquiring the coefficient contribution of the oldest sample, E) the The sum of the contribution of the oldest sample and the contribution of the new sample gives C
And F) calculating a corrected coefficient from the updated coefficient by replacing the angle in the trigonometric function with the angle corresponding to the appropriate sample number, and G) said Repeating steps B to G. 13. The method of claim 12, further comprising storing each of the samples when received at a memory device. 14. The calculating step corrects the coefficient and outputs the coefficient after the receiving step receives the predetermined new sample and the updating step updates the predetermined new sample. 14. The method of claim 13, wherein 15. The method of claim 12, wherein the function of the input signal is a Fourier transform and the mathematical function associated with each coefficient and signal is a trigonometric function. 16. The method of claim 12, further comprising outputting a preselected coefficient when the coefficient is updated. 17. An apparatus for determining coefficients of a function of an input signal based on a given sample of the input signal, each coefficient being at least partly in combination with the sample and a mathematical function. A first memory device for storing a value representing the mathematical function associated with the sample and each coefficient, the first memory device being in digital communication with the memory device, For each coefficient, receiving a sample of the input signal, accessing the memory device, and multiplying the sample by the value representing the mathematical function associated with the sample and the coefficient to define a term. And a coefficient generator that updates the coefficient by adding the term to the previous value of the coefficient and then corrects the coefficient. 18. A computer program product for determining a coefficient of a function representing an input signal based on a plurality of samples of the input signal, the computer readable program code means embodied therein. A computer readable storage medium, the computer readable program code means including first computer command means for receiving samples of the signal; and updating and correcting at least one of the coefficients. Means for updating at least one of said coefficients upon receipt of each sample and for compensating said coefficients such that said coefficients represent the correct sequence of samples. A computer program product comprising. 19. The second computer instruction means receives each of the samples one by one, and when the samples are received, the second computer instruction means does not wait for the reception of the next sample. 20. The computer program product of claim 18, wherein reduces the latency required to determine the exact coefficient of the function by updating the coefficient of the function based on each sample. 20. Each coefficient comprises at least one term based at least in part on a combination of a sample and a mathematical function, the computer readable program code means receiving each sample upon receipt of the sample. And third mathematical command means for determining a respective term for each coefficient in combination with the mathematical function associated with the coefficient, the second computer command means comprising: 20. The computer program product of claim 19, wherein the coefficient is updated by adding the respective term of the coefficient to a previous value of the coefficient. 21. Each sample only contributes one term of each coefficient, said second computer instruction means updating, upon reception, each of said coefficients on the basis of each sample, after which said sample 21. The computer program product of claim 20, which does not need to be stored. 22. As each sample is received, the second computer instruction means updates each of the coefficients with each of the plurality of samples, updating each coefficient with the next sample, and The computer program product of claim 20, wherein the second computer instruction means outputs the coefficient. 23. The computer program of claim 20, wherein the computer readable code means further comprises fourth computer instruction means for storing each of the samples in a memory device upon receipt of the samples. Product. 24. The second computer command means after the first computer command means receives the predetermined plurality of samples and the second computer command means processes the predetermined plurality of samples. Upon outputting the coefficients and receiving a new sample of the input signal after the predetermined plurality of samples have already been received, the computer readable code means is based on a first sample of the predetermined plurality of samples. Further comprising fifth computer instruction means for subtracting from the new sample-based term, the second computer instruction means:
24. The computer program product of claim 23, wherein the coefficient is updated by a difference in terms based on the new sample and a first sample of the predetermined plurality of samples. 25. An apparatus for determining coefficients of a function representing an input signal based on samples of the input signal, the apparatus including a coefficient generator providing the coefficient after each sample, the coefficient generation A receiver for receiving new samples; a learning model processor trained with the predetermined coefficients and the predetermined samples to map new coefficients to the new samples; A device connected to the learning model processor and capable of providing the new model to the learning model processor. 26. The apparatus of claim 25, wherein the learning model processor comprises a neural network processor. 27. The apparatus according to claim 25, wherein the learning model processor includes at least one of a neural network type integrated circuit chip and a fuzzy logic processor chip. 28. The apparatus of claim 25, wherein the learning model processor comprises a fuzzy logic processor. 29. A computer program product for determining a coefficient of a function representing an input signal based on a sample of the input signal, the method including a coefficient generator providing the coefficient after each sample, The coefficient generator is a computer program product that includes executable learning model code that is trained with predetermined coefficients and predetermined samples to map the new coefficients to new samples. 30. The computer program product of claim 29, wherein the learning model code comprises neural network code. 31. The computer program product of claim 29, wherein the learning model code comprises fuzzy logic code. 32. A method for determining a coefficient of a function representing an input signal based on a sample of the input signal, wherein a complete set of coefficients is generated for each sample, the predetermined set of samples and the predetermined set of samples. Providing a set of coefficients, training a learning model using the predetermined set of samples and the predetermined set of coefficients to map the coefficients to samples, and Different samples, and enabling the learning model to derive the coefficients for the new samples. 33. The method of claim 32, wherein the coefficients include Fourier transform coefficients. 34. A method of designing a system including at least one of hardware and software for determining a coefficient of a function representing an input signal based on a sample of the input signal, the method comprising: Providing a sample and a predetermined set of coefficients, generating a training set having the predetermined set of samples as an input and the predetermined set of coefficients as an output, the input and the output A) between: a) generating a population of chromosomes encoding the mapping; b) generating candidate mapping solutions in at least one form of hardware description and software description; c. ) Associating the chromosomes with the components of the description; d) the candidate input being a candidate A step of evaluating the goodness of the result when given to the ping solution, and e) selecting an optimal chromosome and combining the optimal chromosomes to obtain a new chromosome for testing as a new candidate solution. And f) using a genetic algorithm to determine by: f) repeating said steps a) to f) until a solution mapping with a low error below an imposed requirement is found. . 35. A method of determining new values of a subset of Fourier coefficients from previous values of a subset of Fourier coefficients and values of a subset of recently received samples, the method comprising: providing a learning model processor. Training the learning model processor with an input of a predetermined subset of Fourier coefficients and an output of the next subset of Fourier coefficients, the learning model being a subset of the Fourier coefficients. A method capable of generating a subset of Fourier coefficients that are mapped to the inputs of the set. 36. A computer implemented method for designing an apparatus for deriving a coefficient of a function representing an input signal based on a sample of the input signal, comprising: a) selecting a generation of randomly selected chromosomes. Generating an input value determined by b) matching each chromosome to a circuit model, c) a predetermined sample, and at least one of a predetermined set of coefficients and a predetermined set of coefficient updates, Assigning to each circuit, d) providing a target response specification, e) deriving a circuit model response and comparing the model response with the target response specification, and f) the circuit response being Ranking each circuit model according to how close it is to the target response, and g) the circuit model with the highest ranking in the previous generation. , A step of generating a new population of circuit models, h) randomly swapping parts of chromosomes and randomly flipping the bits of chromosomes, and i) several generations to achieve a better circuit model. Repeating the process over, j) after reaching a predetermined number of generations and / or when the proximity between the circuit model response and the target response is sufficiently close, A step of terminating. 37. The coefficient is a coefficient for Fourier series.
The method according to 6.