JP2011228993A - Thinning-out filter and thinning-out program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a thinning-out filter and a thinning-out program that are applicable even when intervals of sampling are irregular.SOLUTION: A thinning-out filter 1 comprises: first counting means 10 of generating an index (k) for sequentially selecting a plurality of output sample points present nearby an output sample point P1 of interest; second counting means 20 of selecting two contiguous output sample points based upon the index (k), sequentially generating integer values in a section between the two selected output sample points as sample point positions (x), and normalizing the sample point positions (x) in a time direction to generate normalized coordinates (v); function value generating means 30 of substituting the normalized coordinates (v) in a fundamental function f(x) to generate function values f(v); section tap coefficient generating means 40 of multiplying the function values f(v) by the reciprocal number of the distance between the two output sample points to generate tap coefficients h(x) by sections; and tap coefficient generating means 50 of generating tap coefficients corresponding to input sample points based upon the sample point positions (x) and tap coefficients h(x).

Description

  The present invention relates to a thinning filter applied prior to signal sampling, and more particularly to a digital processing thinning filter and thinning program that can be applied even when sampling intervals are non-uniform.

  Conventionally, when an analog signal is sampled or an already sampled signal is further sampled (sub-sampled) at a coarser sampling interval, the spectrum of the input signal exceeding the Nyquist frequency is folded, resulting in aliasing distortion. In order to reduce this, a thinning filter (decimation filter) is applied before sampling.

  In order to completely suppress the aliasing distortion with respect to any signal input, the decimation filter needs to be a low-pass filter that cuts off a frequency exceeding 1/2 of the sampling frequency. On the other hand, in order to suppress the deterioration of the signal after sampling, it is desirable that the thinning filter has an amplitude gain of 1 and a phase that does not change for frequencies that are ½ or less of the sampling frequency. A thinning filter that ideally satisfies these conditions is called an ideal low-pass filter.

  Conventional decimation filters are configured with analog electronic circuits (for example, LC resonance circuits) to approximate ideal low-pass filters, digital circuits (digital filters) consisting of delay devices, multipliers, adders, etc. It is composed of a digital filter using a computer or ALU (Arithmetic Logic Unit). Particularly, a thinning filter having a tap coefficient obtained by cutting off an impulse response (sinc function) of an ideal low-pass filter with a finite length is often used for a thinning filter constituted by a digital filter.

  As a conventional decimation filter, for example, as disclosed in Patent Documents 1 to 4, a device devised with respect to the architecture of an arithmetic unit is known.

Japanese translation of PCT publication No. 7-500461 JP-A-6-244733 Japanese Patent Laid-Open No. 2-140009 JP 2001-77667 A

  Such a conventional decimation filter is premised on subsampling being performed at equal intervals. For this reason, if sub-sampling at unequal intervals is performed using a conventional thinning filter, high frequencies are lost more than necessary and degradation (blur) occurs at locations where the sampling interval is narrow, while the sampling interval is wide. In some places, aliasing distortion occurs, and the signal quality deteriorates. In addition, since blurring and folding appear locally, the homogeneity of the entire signal is impaired. Such deterioration in signal quality is recognized as nonuniformity in an image signal, for example, and is recognized as an intermittent or frequency-changing beat in an audio signal.

  Therefore, an object of the present invention is to provide a thinning filter and a thinning program that can be applied even when subsampling at unequal intervals is performed.

  The decimation filter according to claim 1, which has solved the above problem, is an output that is a list of predetermined output sample point positions indicating sample point positions used for sub-sampling input sample points that are sample points of an input signal. A tap coefficient for the input sample point is generated based on the sample point list and an attention index for identifying an output sample point of interest in the output sample point list, and includes a first counting unit, It comprises a counting means, a function value generating means, a segmented tap coefficient generating means, and a tap coefficient generating means.

According to such a configuration, the thinning filter generates a count value for sequentially selecting a plurality of output sample points existing near the output sample point of interest by the first counting unit.
The decimation filter selects two adjacent output sample points based on the count value generated by the first counting unit by the second counting unit, and classifies the selected two output sample points as a section. The integer values in the section are sequentially generated as sample point positions, and the sample point positions are normalized in the time direction to generate normalized coordinates.

  Further, the thinning filter generates a function value by substituting the normalized coordinates generated by the second coefficient unit into the impulse response waveform used for sub-sampling at equal intervals by the function value generating unit. Note that sub-sampling at equal intervals may be, for example, dividing a frame, which is a fixed section of an input signal, into a plurality of blocks and performing sub-sampling at the same sampling interval for each block.

  The decimation filter generates a tap coefficient for each section by multiplying the function value generated by the function value generation means according to the section by the reciprocal of the distance between the two output sample points by the section tap coefficient generation means. . In other words, the impulse response waveform used for equally spaced sub-sampling can be expanded and contracted for each segment corresponding to the interval between adjacent output sample points, so that even if the interval for each segment differs, An appropriate tap coefficient corresponding to the interval can be generated.

  Then, the thinning filter generates a tap coefficient list in which tap coefficients for each section are arranged and connected in accordance with a time series of sample point positions sequentially generated by the tap coefficient generation means. Thereby, subsampling can be performed by the subsampling device based on the tap coefficient list regardless of whether the sampling interval is equal or unequal.

  In addition, the thinning filter according to claim 2 divides between adjacent output sampling points as sampling point positions used for sub-sampling the input sampling points that are sampling points of the input signal, Scaling the impulse response waveform used for equally spaced subsampling according to the interval between the adjacent output sample points, and generating a tap coefficient corresponding to the scaled impulse response waveform for each section And a tap coefficient generating means for generating a tap coefficient for the input sample point by connecting the tap coefficients for each of the sections.

  According to such a configuration, the thinning filter divides the adjacent output sample points that are the sample point positions used for sub-sampling the input sample points that are the sample points of the input signal into segments, and is equally spaced for each segment. By scaling the impulse response waveform used for sub-sampling according to the interval between adjacent output sample points, the impulse response waveform can correspond to the interval between output sample points for each section.

  According to this, when sub-sampling is performed at equal intervals, it is possible to obtain the same operation as a decimation filter as in the conventional case. It can be carried out.

According to a third aspect of the present invention, in the thinning filter according to the first or second aspect, a sinc function or a sinc function having a limited domain is used as the impulse response waveform.
According to such a configuration, the thinning filter can suppress aliasing of frequency components exceeding the Nyquist frequency of the input signal when performing subsampling at equal intervals. Further, the thinning filter can suppress approximate aliasing when performing non-uniformly spaced subsampling.

The thinning filter according to claim 4 is the thinning filter according to claim 1 or 2, wherein the impulse response waveform is a product of two sinc functions or a product of two sinc functions with a limited domain. It is characterized by using.
According to such a configuration, the thinning filter can suppress aliasing of frequency components exceeding the Nyquist frequency of the input signal when performing subsampling at equal intervals. Further, the thinning filter can suppress approximate aliasing when performing non-uniformly spaced subsampling.

  The thinning-out program according to claim 5 is an output sample point that is a list of predetermined output sample point positions indicating sample point positions used for sub-sampling an input sample point that is a sample point of an input signal. In order to generate a tap coefficient for the input sample point based on the list and an attention index for identifying an output sample point of interest in the output sample point list, a computer is provided with a function value generation means, a first count Means, second counting means, section tap coefficient generation means, and tap coefficient generation means.

According to such a configuration, the thinning-out program generates a count value for sequentially selecting a plurality of output sample points existing in the vicinity of the output sample point of interest by the first counting unit.
Further, the thinning program selects two adjacent output sample points based on the count value generated by the first count unit by the second count unit, and classifies the selected two output sample points as a section. The integer values in the section are sequentially generated as sample point positions, and the sample point positions are normalized in the time direction to generate normalized coordinates.

Further, the thinning program generates a function value by substituting the normalized coordinate generated by the second coefficient unit into the impulse response waveform used for sub-sampling at equal intervals by the function value generating unit.
The thinning-out program generates a tap coefficient for each section by multiplying the function value generated by the function value generating means according to the section by the reciprocal of the distance between the two output sample points by the section tap coefficient generating means. .

  Then, the thinning-out program generates a tap coefficient list in which tap coefficients for each section are aligned and connected according to a time series of sample point positions that are sequentially generated by the tap coefficient generation unit, so that taps for input sample points are generated. Generate coefficients.

  According to the first, second, and fifth aspects of the invention, it is possible to obtain an appropriate tap coefficient corresponding to the subsampling interval even when the subsampling interval is not uniform. Deterioration of signal quality can be prevented. Furthermore, with a simple method of connecting the tap coefficients generated for each section in accordance with the time series of the sample point positions that are sequentially generated, the sub-sampling intervals are either equal or unequal. Even if it exists, since the production | generation of the appropriate tap coefficient according to an input sample point is realizable, a structure becomes simple and it becomes cheap.

  According to the third and fourth aspects of the present invention, it is possible to suppress aliasing even when the sub-sampling interval is equal or unequal, and when sub-sampling is performed thereafter. Deterioration of signal quality can be prevented.

It is a figure for demonstrating the outline | summary of the thinning filter which concerns on embodiment of this invention, (a) shows typically the impulse response waveform of a thinning filter when performing subsampling at equal intervals, ( b) schematically shows an impulse response waveform of the thinning filter when sub-sampling is performed at unequal intervals. It is a block diagram which shows the structure of the thinning filter which concerns on embodiment of this invention. (A) is a conceptual diagram for explaining how the sample point position is normalized by the normalized coordinate calculation means of the thinning filter according to the embodiment of the present invention, and (b) is the sample point position generation means, It is a conceptual diagram for demonstrating a mode that a point position is produced | generated. It is a figure explaining a mode that the tap coefficient corresponding to an input sample point is generated with the thinning filter concerning the embodiment of the present invention, (a) is a basic function used when generating a tap coefficient, and (b) is Tap coefficients generated by the decimation filter when performing equal interval sub-sampling, and (c) indicate tap coefficients generated by the decimation filter when performing equal interval sub-sampling. It is a flowchart which shows operation | movement of the thinning filter which concerns on embodiment of this invention. It is a block diagram which shows the structure of the subsampling apparatus of the arbitrary intervals to which the thinning filter which concerns on embodiment of this invention is applied. It is a flowchart which shows operation | movement of a subsampling apparatus.

[Outline of decimation filter]
Hereinafter, embodiments of the present invention will be described.
The decimation filter is applied to, for example, the sub-sampling device S shown in FIG. 6, and is applied before sub-sampling when further sampling (sub-sampling) is performed on the input signal z that has already been sampled. is there. The sub-sampling device S will be described later.

Next, an outline of the thinning filter according to the present embodiment will be described with reference to FIG.
As shown in FIGS. 1A and 1B, the thinning filter 1 according to the present embodiment has a predetermined sample point position used for subsampling an input sample point that is a sample point of an input signal. (Y _i ) _{i = 0, 1,..., N−1} (N is a natural number; hereinafter referred to as “output sample point list”) to be noted (n is 0 or more) If you want to find the tap coefficients output sample point P ₁ of the n-1 an integer.), sequentially selected based of the plurality of output sample points, the output sampling point in the vicinity of the n-th output sample point index k Then, the tap coefficients of the thinning filter 1 are obtained by classifying two adjacent output sample points as a section, sampling the input signal for each section to obtain a tap coefficient, and aligning and connecting the tap coefficients obtained for each section. It is said. In FIGS. 1A and 1B, a part of the impulse response waveform and a part by two adjacent sample points are shown by broken lines for easy understanding.

  FIG. 1A shows tap coefficients generated by the thinning filter 1 when the intervals between the output sample points are uniform (equal intervals), and FIG. 1B shows the case where the intervals between the output sample points are not uniform. The tap coefficients generated by the thinning filter 1 are shown in FIG. That is, the thinning filter 1 according to the present embodiment classifies adjacent output sampling points and obtains a tap coefficient for each classification. Therefore, not only when the interval between the output sampling points is uniform, Even in the case of non-uniformity, an appropriate tap coefficient corresponding to each interval can be obtained. Thus, the thinning filter 1 according to the present embodiment can perform appropriate subsampling in accordance with the nature of the input signal. Note that the conventional thinning filter can generate tap coefficients of the output sample points of interest only when the intervals between the output sample points are equal (the state shown in FIG. 1A).

[Thinning filter configuration]
Next, the configuration of the thinning filter 1 according to the present embodiment will be described with reference to FIG.
As shown in FIG. 2, the decimation filter 1 includes first counting means 10, second counting means 20, function value generation means 30, piecewise tap coefficient generation means 40, and tap coefficient generation means 50. ing.

The first counting means 10 (scaling means) generates an index k (count value) in which integers from −W to W−1 are sequentially increased or decreased. The index k, of the output sampling point in the vicinity of the output sample point P ₁ of interest, is intended to define the scope of the output sampling point used to determine the tap coefficient of the output sample point P ₁ of interest. Here, W is a natural number that determines the domain of the basic function of the thinning filter 1, and the larger the W, the better the filter characteristics, but the more the calculation amount. In other words, W defines the range of how many output sample points before and after the tap coefficient of the output sample point P1 of interest is used. Here, it is assumed that the first counting means 10 has a preset definition area and W = 3.

Accordingly, decimation filter 1, when an output sample point P ₁ of interest is n-th output sample point y _n, n-3-th output sample point y _{n-3, n-2-th} output sample point y _{Using the (n−2)} , (n−1) th output sample point y _n−1 , the nth output sample point y _n , the (n + 1) th output sample point y _{n + 1} , and the (n + 2) th output sample point y _{n + 2} , the n th thereby obtaining the tap coefficients of the output sample point y _n. The index k generated by the first counting means 10 is output to the second counting means 20.

  The second counting means 20 (scaling means) selects two adjacent output sample points based on the index k generated by the first counting means 10 and classifies the selected two output sample points as a section. The integer values in the sections are sequentially generated as sample point positions, and the sample point positions are normalized in the time direction to generate normalized coordinates. The second counting unit 20 includes an output sample point selection unit 21, a sample point position generation unit 22, a normalized coordinate calculation unit 23, and a normalization coefficient calculation unit 24.

The output sample point selection means 21 determines the division for generating the tap coefficient h (x). When the index k generated by the first counting unit 10 is input, the output sample point selection unit 21 receives an output sample point list (y _i ) _{i = 0, 1,.} during from and to select the n + k + 1 th output sample point _{y n + k + 1} adjacent to the target to n + k-th output sample point _{y n + k} and the output sampling point _{y n + k.} This output sample point y _{n + k} and the output sample point y _{n + k + 1} are _defined as a segment.
The output sample point selection unit 21 outputs the selected output sample points y _{n + k} and y _{n + k + 1} to the sample point position generation unit 22.

The sample point position generation unit 22 sequentially generates an integer value satisfying y _{n + k} <x ≦ y _{n + k + 1} as the sample point position x in the section selected by the output sample point selection unit 21.

The sample point position x generated by the sample point position generation unit 22 is sequentially output to the normalized coordinate calculation unit 23 and the tap coefficient generation unit 50. The section may be replaced by y _{n + k} ≦ x <y _{n + k + 1} instead of y _{n + k} <x ≦ y _{n + k + 1. When} the basic function f takes a value of 0 at both ends of each section k, y _{n + k} <x <y _It may be _{n + k + 1} .

The normalized coordinate calculation means 23 calculates a normalized coordinate v that serves as a reference for expanding and contracting the basic function f (x) in the time direction. The normalized coordinate calculation means 23 converts the sample point position x sequentially generated by the sample point position generation means 22 for each section according to the following equation (1), thereby converting the sample point position x into FIG. As shown in a), a normalization coordinate v is obtained by performing an operation of normalizing between _k and _{k + 1} in accordance with the interval between the two output sample points y _{n + k} and y _{n + k + 1} .

  The normalized coordinate v calculated by the normalized coordinate calculation unit 23 is output to the function value generation unit 30.

The normalization coefficient calculation means 24 calculates a normalization coefficient a for normalizing the amplitude value for each section of the basic function f (x) according to the expansion / contraction ratio in the x direction. The normalization coefficient calculation unit 24 calculates the distance between the two output sample points y _{n + k} and y _{n + k + 1} selected by the output sample point selection unit 21, that is, the basic function f in the section, as shown in the following equation (2). The reciprocal of the time direction expansion / contraction ratio (width shown in FIG. 3A) of (x) is calculated to obtain a normalization coefficient a that serves as a reference for expanding and contracting the basic function f (x) in the amplitude direction.

  The normalization coefficient a calculated by the normalization coefficient calculation unit 24 is output to the segment tap coefficient generation unit 40.

If there is no integer value satisfying y _n−1 <x ≦ y _{n + 1} between the two selected output sample points y _{n + k} and y _{n + k + 1} , the sample point position generation means 22 performs the following (3) The numerical value shown in the equation is output to the normalized coordinate calculation means 23 and the tap coefficient generation means 50 only once.

Here, the function R (y) is an operation for rounding the argument y to an integer, and can be performed by arbitrary rounding such as rounding off, rounding down after the decimal point, rounding up after the decimal point. For example, as shown in FIG. 3B, the output sample point y _{n + k} selected by the output sample point selection means 21 is “10.2”, the output sample point y _{n + k + 1} is “10.4”, If there is no integer value in the section, the closest integer outside the section (here, “10”) is output to the normalized coordinate calculation means 23 and the tap coefficient generation means 50 as the sample point position x.

  The function value generation means 30 (scaling means) obtains a function value f (v) by substituting the normalized coordinates v input from the normalized coordinate calculation means 23 into the basic function f (x). The function value generating unit 30 may have the basic function f (x) in advance, or may be generated when the normalized coordinate v is input from the normalized coordinate calculating unit 23.

  Here, the basic function f (x) is an impulse response of a decimation filter to be applied when sampling at equal intervals with the interval between output sampling points being “1”. The design of the basic function f (x) is arbitrary. For example, a sinc function as shown in the following equation (4) or a sinc function with a limited domain can be used.

  Here, the sinc function is defined by the following equation (5).

  As described above, since W = 3, FIG. 4A shows a sinc function in which the domain is limited to -3 or more and 3 or less.

  As the basic function f (x), for example, as shown in the following equation (6), a product of two sinc functions or a product of two sinc functions with a limited domain can be used.

  Here, L is a real constant other than zero. For example, when L = 3 and the domain is limited to -3 or more and 3 or less, this corresponds to Lanczos-3 interpolation in equidistant sampling. For example, when L = 4 and the domain is limited to -4 or more and 4 or less, this corresponds to Lanczos-4 interpolation in equidistant sampling.

Here, the basic function f (x) is divided into sections [k, k + 1) or (k, k + 1) (k is an integer. Hereinafter, simply referred to as “section k”), and the interval between output sample points for each section k. The impulse response h of a decimation filter applied when sampling at equal intervals is performed in the y direction by multiplying by a normalization coefficient a that is the reciprocal of the expansion ratio in the x direction. (X).
That is, the function value generating means 30 defines the impulse response h (x) of the thinning filter 1 by the following equation (7).

  Thus, the operation as the thinning filter 1 is obtained by convolving the impulse response waveform h (x) obtained by the equation (7) with the input signal z (x).

  For example, when sub-sampling at equal intervals is performed, an impulse response h (x) as shown in FIG. When the sinc function is used as the basic function f (x), the impulse response h (x) is a sinc function with the coefficients truncated in the middle, and therefore corresponds to the decimation filter 1 used when performing equal-interval subsampling. To be.

  On the other hand, when sub-sampling at unequal intervals is performed, an impulse response as shown in FIG. 4C is obtained, and a gentle impulse response is convoluted as the output sample point interval is coarser. That is, as the output sample point interval is larger, the impulse response waveform of the basic function f (x) is expanded in the time direction and reduced in the amplitude direction. On the other hand, as the output sample point interval is smaller, the impulse response waveform of the basic function f (x) is reduced in the time direction and expanded in the amplitude direction.

  As described above, the thinning filter 1 can deal with the case where the sampling intervals of the sub-sampling are equal intervals or unequal intervals with one equation (7). That is, the thinning filter 1 can be applied when subsampling is performed at unequal intervals while maintaining compatibility with a thinning filter that should be applied when subsampling is performed at equal intervals. The function value f (v) generated by the function value generation unit 30 is output to the segment tap coefficient generation unit 40.

The section tap coefficient generation means 40 (scaling means) generates a tap coefficient h (x) for each section selected by the sample point position generation means 22.
As shown in the following equation (8), the section tap coefficient generation unit 40 includes the normalization coefficient a input from the normalization coefficient calculation unit 24 and the impulse response waveform (function value) input from the function value generation unit 30. ) Multiply f (v) to calculate the tap coefficient h (x) for each section.

  That is, the function value f (v) for each section input from the function value generating means 30 is a result of reflecting the expansion / contraction ratio in the x direction (time direction) for each corresponding section of the basic function f (x). Therefore, the division tap coefficient generation means 40 multiplies the expansion / contraction ratio in the y direction (amplitude direction) for each corresponding section of the basic function f (x) calculated by the normalization coefficient calculation means 24, thereby obtaining In addition, it is possible to generate a tap coefficient h (x) serving as a reference for expanding and contracting the basic function f (x) in the x direction and the y direction. The tap coefficients h (x) generated by the divided tap coefficient generation means 40 are sequentially output to the tap coefficient generation means 50.

The tap coefficient generation means 50 arranges and connects the tap coefficients for each section generated by the section tap coefficient generation means 40 according to the time series of the sample point positions (x) that are sequentially generated ([x _j , h _j ]) _{j = 0, 1,..., M−1} to generate a tap coefficient h (x) for the input sample point. This tap coefficient h (x) is a coefficient to be convoluted with the input signal in the sub-sampling device described later.

The tap coefficient generation means 50 has a tap coefficient list ([x _j , h _j ]) _{j = 0, 1,..., M−1} are M sample point positions x sequentially input from the sample point position generation means 22. And the tap coefficient list ([x _j , h _j ]) _{j = 0, 1} by listing the correspondence with the tap coefficient h (x) for each section sequentially input from the section tap coefficient generation means 40. _{,..., M−1} are generated.
The tap coefficient list ([x _j , h _j ]) _{j = 0, 1,..., M−1} generated by the tap coefficient generation means 50 is output to the outside.

Further, the tap coefficient generation unit 50 sequentially inputs the divisions sequentially input from the division tap coefficient generation unit 40 prior to the output of the tap coefficient list ([x _j , h _j ]) _{j = 0, 1,..., M−1.} Is calculated by dividing the coefficient component (h _j ) _{j = 0, 1,..., M−1} by H and then normalizing the tap coefficient list ([x _j , h _j ]) _{j = 0, 1,..., M−1} may be output.

[Thinning filter operation]
Next, the operation of the thinning filter 1 will be described with reference to FIG.
The thinning filter 1 uses the first counting unit 10 to generate an index in which integers from −W to W−1 are sequentially set in ascending or descending order. The thinning filter 1 outputs the index k generated by the first counting unit 10 to the second counting unit 20 (step S101).

The decimation filter 1 includes an index k input from the first counting means 10 and an output sample point list (y _i ) _{i = 0,1} input from the outside by the output sampling point selection means 21 of the second counting means 20. _{,..., N−1} , the n + k-th and n + k + 1-th two output sample points y _{n + k} and y _{n + k + 1} are selected (step S102).

The decimation filter 1 sets y _{n + k} <x ≦ y _{n + k + 1} between the two output sample points y _{n + k} and y _{n + k + 1} selected by the output sample point selection unit 21 by the sample point position generation unit 22 of the second counting unit 20. It is searched whether there is an integer value that satisfies (step S103). When the sampling point position generation unit 22 of the second counting unit 20 determines that an integer value exists (Yes in step S103), the thinning filter 1 taps the normalized coordinate calculation unit 23 with the integer value as the sample point position x. The data are sequentially output to the coefficient generation means 50 (step S104).

On the other hand, when the thinning filter 1 determines by the sample point position generation unit 22 of the second counting unit 20 that there is no integer value satisfying y _{n + k} <x ≦ y _{n + k + 1} in the section (No in step S103), The integer value at the nearest position outside the section is output only once to the normalized coordinate calculation means 23 and the tap coefficient generation means 50 as the sample point position x (step S105).

  The decimation filter 1 converts the sample point position x input from the first counting means 10 by the normalized coordinate calculation means 23 of the second counting means 20 according to the above-described equation (1), so that it is A normalization coordinate v is obtained by performing normalization by expanding and contracting in the x direction according to the interval between the output sample points. The normalized coordinate calculation unit 23 outputs the normalized coordinate v to the function value generation unit 30 (step S106).

The thinning filter 1 uses the above-described equation (2) for the two output sample points y _{n + k} and y _{n + k + 1} selected by the sample point position generation unit 22 by the normalization coefficient calculation unit 24 of the second counting unit 20. The reciprocal of the expansion / contraction ratio in the x direction is calculated in the amplitude direction (y direction) of the basic function f (x) to obtain a normalization coefficient a. The normalization coefficient calculation unit 24 outputs the normalization coefficient a to the segment tap coefficient generation unit 40 (step S107).

  The decimation filter 1 uses the function value generation means 30 to substitute the normalized coordinates v input from the second counting means 20 into the basic function f, and generates a function value f (v). The function value generation unit 30 outputs the generated function value f (v) to the tap coefficient generation unit 50 (step S108).

  The decimation filter 1 includes a normalization coefficient a input from the normalization coefficient calculation means 24 by the piecewise tap coefficient generation means 40, an impulse response waveform (function value) f (v) input from the function value generation means 30, and the like. To calculate a tap coefficient h (x) for each section. The section tap coefficient generation unit 40 sequentially outputs the calculated tap coefficient h (x) for each section to the tap coefficient generation unit 50 (step S109).

The decimation filter 1 includes M sample point positions x sequentially input from the sample point position generation unit 22 by the tap coefficient generation unit 50 and tap coefficients h (for each section sequentially input from the section tap coefficient generation unit 40. A tap coefficient list ([x _j , h _j ]) _{j = 0, 1,..., M−1} is generated by listing the associations with x). The thinning filter 1 outputs the tap coefficient list ([x _j , h _j ]) _{j = 0, 1,..., M−1} to the outside by the tap coefficient generation means 50 (step S110).

According to the thinning filter 1 described above, the following effects can be obtained.
According to the decimation filter 1, by dividing the input signal into sections, generating tap coefficients for each section, and connecting the tap coefficients generated for each section, not only in the case of equally spaced subsampling, but also unequal It can also be applied to the case of interval sub-sampling.

  The decimation filter 1 has a decimation program for causing the computer to function as the first counting unit 10, the second counting unit 20, the function value generating unit 30, the segmented tap coefficient generating unit 40, and the tap coefficient generating unit 50. It may be realized by being executed by the Central Processing Unit.

As mentioned above, although one Embodiment of this invention was described, this invention is not limited to this, Of course, it can change in the range which does not deviate from the meaning of this invention.
For example, in the above-described embodiment, the domain of the basic function is defined as W = 3. However, the domain is not limited to this, and the domain may not be defined.

[Outline of sub-sampling device]
Next, a subsampling apparatus to which the thinning filter 1 described in the above embodiment is applied will be described with reference to FIGS. 4 and 5. FIG.
Here, the sub-sampling device S further samples the sampled input signal. Sampling intervals in the sub-sampling device S may be equal intervals or unequal intervals. The minimum sampling interval in the sub-sampling device S is preferably not narrower than the sampling interval of the input signal.

[Configuration of sub-sampling device]
As shown in FIG. 4, the sub-sampling device S includes a thinning filter 1, a third counting unit 2, an input buffer 3, a convolution unit 4, and an output buffer 5. In addition, since the structure of the thinning filter 1 is as described in the above-described embodiment, the detailed description will be omitted with reference to FIG. 1 as appropriate.

  The third counting means 2 generates an index n (index of interest) for identifying an output sample point of interest among a plurality of output sample points. The generated index n is output to the thinning filter 1.

Here, the decimation filter 1 refers to the index n generated by the third counting unit 2, and the tap coefficient list ([x _j , h _j ]) generated by the tap coefficient generation unit 50 _{j = 0, 1,. , M−1} are divided into coordinate components (x _j ) _{j = 0, 1,..., M−1} and coefficient components (h _j ) _{j = 0, 1,. j} ) _{j = 0, 1,..., M−1} are output to the input buffer 3 and coefficient components (h _j ) _{j = 0, 1,..., M−1} are output to the convolution means 4. .

The input buffer 3 is a storage means for storing a classification necessary for sub-sampling among the input signal z input from the outside.
The input buffer 3 receives the tap coefficient list ([x _j , h _j ]) _{j = 0, 1,..., M−1} coordinate components (x _j ) _{j = 0, 1,.} The input signal value at each coordinate is output to the convolution means 4 with reference to _M-1 . The signal sequence output from the input buffer 3 to the convolution means 4 is (z (x _j )) _{j = 0, 1,..., M−1} .

The convolution means 4 applies the tap coefficient list ([x _j ,) inputted from the decimation filter 1 to the signal sequence (z (x _j )) _{j = 0, 1,..., M−1} outputted from the input buffer 3. h _j ]) _{j = 0, 1,..., M−1} coefficient components (h _j ) _{j = 0, 1} ,.

Note that the tap coefficient h (x) for the input sample point generated by the thinning filter 1 is defined for the sample point position x in a certain closed section in the input signal z, that is, for the input signal z, Perform convolution with a finite tap length. In the following description, the tap length of the output tap coefficient group is M (M is a natural number), the j-th tap position (j is an integer not less than 0 and not more than M−1) (sample point position) is x _j , Let the tap coefficient be h _j .

The convolution means 4 uses the tap coefficient list ([x _j , h _j ]) _{j = 0, 1,..., M−1} coefficient components (h _j ) _{j = 0, 1,.} When normalized by the sum, the output signal value s (n) is normalized by the following equation (9).

On the other hand, when tap coefficient list ([x _j , h _j ]) _{j = 0, 1,..., M−1} coefficient components (h _j ) _{j = 0, 1,.} In the convolution, the convolution means 4 uses the following equation (10) to calculate the coefficient components (h _j ) _{j = 0} of the tap coefficient list ([x _j , h _j ]) _{j = 0, 1,. , 1,..., M−1} is normalized by the sum.
The result of the convolution by the convolution means 4 is output to the output buffer 5 as the output signal value s (n).

  The output buffer 5 is storage means for accumulating and storing the output signal value s (n) at an address corresponding to the index n generated by the third counting means 2, and holds a signal series to be output. . The accumulated output signal value s (n) is sequentially output to the outside as the output signal s.

  The input buffer 3 and the output buffer 5 are realized by, for example, a RAM (Random Access Memory), a hard disk, or the like.

[Operation of sub-sampling device]
Next, the operation of the sub-sampling device S will be described with reference to FIG.
In step S201, the sub-sampling device S generates an index n for scanning the sampling points of the output signal of the number of sub-sampling when the third counting unit 2 receives an input of an operation command from the outside. Then, the sub-sampling device S outputs the generated index n to the thinning filter 1 by the third counting unit 2. In step S201, the sub-sampling device S may generate the index n by the third counting means 2 when the input signal z is input by the input buffer 3.

In step S202, when the sub-sampling device S receives the input of the output sample point list (y _i ) _{i = 0, 1,..., N−1} from the outside by the thinning filter 1, the sub-sampling device S ([x _j , h _j ]) _{j = 0, 1,..., M−1} .

In step S203, the sub-sampling device S uses the thinning filter 1 to generate the tap coefficient list ([x _j , h _j ]) _{j = 0, 1,..., M−1} as coordinate components (x _j ) _{j = 0. , 1,..., M−1} and coefficient components (h _j ) _{j = 0, 1} ,. Then, the sub-sampling device S outputs the coordinate components (x _j ) _{j = 0, 1,..., M−1} to the input buffer 3 by the thinning filter 1, and the coefficient components (h _j ) _{j = 0, 1, ..., M-1} is output to the convolution means 4.

In step S204, the sub-sampling device S convolves the input signal value at each coordinate with the input buffer 3 based on the coordinate component (x _j ) _{j = 0, 1,..., M−1} input from the decimation filter 1. Output to means 4.

In step S205, the sub-sampling device S inputs the signal sequence (z (x _j )) _{j = 0, 1,..., M−1} output from the input buffer 3 from the decimation filter 1 by the convolution means 4. _{.., M−1} are convolved with the coefficient component (h _j ) _{j = 0, 1} ,. Then, the sub-sampling device S outputs the output signal value s (n) to the output buffer 5 by the convolution means 4 as a result of the convolution.

  In step S206, when the output signal value s (n) is input from the convolution unit 4 by the output buffer 5, the sub-sampling device S refers to the index n of the output sample point input from the third counting unit 2. The output signal s corresponding to the index n is output to the outside.

The sub-sampling device S operates as described above.
According to the subsampling apparatus S described above, subsampling of the input signal can be performed at an arbitrary sampling interval.

  The thinning filter according to the present invention can reduce aliasing distortion, for example, when adaptive sampling is performed at irregular intervals according to the density of the local waveform of the input signal. Further, for example, by sequentially applying the thinning filter according to the present invention in the horizontal and vertical directions of an image, it can be used as a filter for preventing aliasing distortion in image warping and morphing.

1 decimation filter 10 first counting means (scaling means)
20 Second counting means (scaling means)
30 Function value generation means (scaling means)
40 Piecewise tap coefficient generation means (scaling means)
50 Tap coefficient generation means S Sub-sampling device 2 Third counting means 3 Input buffer 4 Convolution means 5 Output buffer

Claims (5)

An output sample point list that is a list of predetermined output sample point positions indicating sample point positions used for sub-sampling the input sample points that are the sample points of the input signal, and attention in the output sample point list A decimation filter that generates a tap coefficient for the input sample point based on an index of interest identifying an output sample point;
First counting means for generating a count value for sequentially selecting the plurality of output sample points existing in the vicinity of the target output sample point;
Based on the count value generated by the first counting means, two adjacent output sample points are selected, and an interval between the selected two output sample points is set as a section, and an integer value in this section is set as a sample point position. A second counting means for generating the normalized coordinates by further normalizing the sample point positions in the time direction;
A function value generating means for generating a function value by substituting the normalized coordinates generated by the second coefficient means into an impulse response waveform used for sub-sampling at equal intervals;
Section tap coefficient generation means for generating a tap coefficient for each section by multiplying the function value generated by the function value generation means according to the section by the inverse of the distance between the two output sample points;
Tap coefficient generating means for generating a tap coefficient for the input sample point by generating a tap coefficient list in which the tap coefficients for each section are aligned and connected in accordance with the time points of the sequentially generated sample point positions; ,
A thinning filter comprising:   Impulse response waveforms used for subsampling at equal intervals are classified into adjacent output sample points that are sample point positions used for subsampling the input sample points that are the sample points of the input signal. And scaling means for generating a tap coefficient corresponding to the scaled impulse response waveform for each section, performing scaling according to the interval between the adjacent output sample points, and connecting the tap coefficient for each section And a tap coefficient generating means for generating a tap coefficient for the input sample point.   The thinning filter according to claim 1 or 2, wherein a sinc function or a sinc function with a limited domain is used as the impulse response waveform.   The thinning filter according to claim 1 or 2, wherein a product of two sinc functions or a product of two sinc functions with a limited domain is used as the impulse response waveform. An output sample point list that is a list of predetermined output sample point positions indicating sample point positions used for sub-sampling the input sample points that are the sample points of the input signal, and attention in the output sample point list In order to generate a tap coefficient for the input sample point based on an index of interest identifying an output sample point,
Computer
First counting means for generating a count value for sequentially selecting the plurality of output sample points existing in the vicinity of the target output sample point;
Based on the count value generated by the first counting means, two adjacent output sample points are selected, and an interval between the selected two output sample points is set as a section, and an integer value in this section is set as a sample point position. A second counting means for generating the normalized coordinates by further normalizing the sample point positions in the time direction,
A function value generating means for generating a function value by substituting the normalized coordinate generated by the second coefficient means into an impulse response waveform used for sub-sampling at equal intervals;
Section tap coefficient generation means for generating a tap coefficient for each section by multiplying the function value generated by the function value generation means according to the section by the inverse of the distance between the two output sample points;
A tap coefficient generation means for generating a tap coefficient for the input sample point by generating a tap coefficient list in which the tap coefficients for each section are arranged and connected according to the time series of the sample point positions generated sequentially,
Thinning program to function as.

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