JP2006050429A - Signal processing apparatus, method and program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a signal processing apparatus, method and program in which frequency characteristics can be adjusted. <P>SOLUTION: The signal processing apparatus is provided with: a discrete data extraction unit 10 for extracting two pieces of preceding and following discrete data existing with a point of interest interposed; a sampling function processing unit 20 for computing a value of a sampling function while defining a distance between the point of interest and each of four pieces of discrete data; a convolution arithmetic unit 30 for performing convolution operation by adding computed values of the sampling function; and a shift amount setting unit 50 for variably setting a shift amount required for determining a form of the sampling function. The sampling function processing unit 20 performs the computation, for a finite basic waveform that can be differentiated at least once or more, using the sampling function determined by shifting and adding an auxiliary waveform forward and backward just for the variable shift amount, the auxiliary waveform resulting from performing polarity inversion and gain adjustment upon said basic waveform. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to a signal processing apparatus, method, and program for performing interpolation processing, oversampling processing, and the like using input digital data. In this specification, the case where the value of a function has a finite value other than 0 in a local region and becomes 0 in other regions is referred to as a “finite platform”. .

Conventionally, when a digital signal is converted into an analog signal and reproduced, a Shannon sampling function derived based on the Shannon sampling theorem has been widely used. However, Shannon's sampling function cannot be realized because its oscillation continues indefinitely. If only a finite range is used, a truncation error will occur, and the reproduced analog signal will be band-limited. There was a problem. In order to avoid such an inconvenience, a sampling function that converges in a finite range has been devised that has no truncation error and can reproduce even higher-order band components (see, for example, Patent Document 1). .) Since this sampling function converges to 0 at two sampling points before and after the origin, it is confirmed that signal reproduction can be performed with a small amount of calculation and that the band has a high frequency.
International Publication No. 99/38090 (page 4-9, Fig. 1-4)

  By the way, by performing oversampling processing or the like by interpolation processing using the sampling function disclosed in Patent Document 1 described above, band components up to a high frequency can be reproduced, and the signal level of this band component is varied. The method is not known, and there is a problem that the frequency characteristics cannot be adjusted. If the interval of the interpolation process is changed, the entire frequency characteristic is greatly changed, which is not preferable, and a method capable of adjusting only a high frequency band component is desired. In particular, considering the case where a digital-to-analog converter for speech is configured using the sampling function described above, it is understood that a high frequency component peculiar to the case where this sampling function is used contributes to the improvement of sound quality. Yes. Therefore, if only the high-frequency component can be adjusted, it is possible to realize optimal audible characteristics for each music listener, and thus it is possible to increase the commercial value of the audio apparatus.

  The present invention has been made in view of such a point, and an object thereof is to provide a signal processing apparatus, method, and program capable of adjusting frequency characteristics.

  In order to solve the above-described problem, a signal processing apparatus according to the present invention includes discrete data extraction means for extracting a total of four discrete data before and after the target point to be interpolated, and discrete data. Sampling function processing means for calculating the value of the sampling function φ (t) with respect to each of the four discrete data extracted by the extracting means, where t is the distance between the point of interest and each discrete data, and sampling function processing means And a convolution operation means for calculating the value of the point of interest by performing the convolution operation by adding the values of the sampling functions corresponding to each of the four discrete data calculated by the The processing means calculates a value corresponding to the point of interest for a basic waveform that can be differentiated at least once, with a local range wider than the sample interval τ being a value other than 0 and a value in the other range being 0. You Basic waveform calculation means, and an auxiliary for calculating the value corresponding to the point of interest for the two auxiliary waveforms before and after the polarity of the basic waveform are inverted and the gain is adjusted, and further shifted by a predetermined shift amount before and after the basic waveform. It further includes a shift amount setting unit that includes a waveform calculation unit and an addition unit that adds the calculation results of the basic waveform calculation unit and the auxiliary waveform calculation unit, and variably sets the shift amount.

  Further, the signal processing method of the present invention includes a discrete data extraction step for extracting a total of four discrete data before and after the target point to be interpolated, and 4 extracted in the discrete data extraction step. A sampling function processing step for calculating the value of the sampling function φ (t), where t is the distance between the point of interest and each discrete data for each of the discrete data, and the four calculated in the sampling function processing step A convolution operation step of calculating a value of the point of interest by performing a convolution operation that adds the values of the sampling functions corresponding to each of the discrete data, and the sampling function processing step is more than the sampling interval τ. A fundamental wave that calculates a value corresponding to a point of interest for a fundamental waveform that can be differentiated at least once with a wide local range other than 0 and a value in the other range of 0. Auxiliary waveform calculation that calculates the value corresponding to the point of interest for the two auxiliary waveforms before and after the shape calculation step, with the polarity of the basic waveform reversed and the gain adjusted, and further shifted by a predetermined shift amount before and after the basic waveform And a shift amount setting step for variably setting the shift amount.

  Further, the signal processing program of the present invention extracts a computer by a discrete data extracting means for extracting a total of four discrete data before and after the target point to be interpolated, and a discrete data extracting means. For each of the four discrete data, the sampling function processing means for calculating the value of the sampling function φ (t), where t is the distance between the point of interest and each discrete data, and the sampling function processing means. A convolution operation for adding the values of the sampling functions corresponding to each of the four discrete data is performed to function as a convolution operation means for calculating the value of the point of interest. Calculates the value corresponding to the point of interest for a basic waveform that can be differentiated at least once, with a local range wider than τ being a value other than 0 and the other range values being 0. Basic waveform calculation means for performing inversion of the polarity of the basic waveform and adjusting the gain, and for calculating the value corresponding to the point of interest for the two auxiliary waveforms before and after the basic waveform shifted by a predetermined shift amount It has waveform calculation means and addition means for adding the calculation results of the basic waveform calculation means and the auxiliary waveform calculation means, and further causes the computer to function as shift amount setting means for variably setting the shift amount.

  As a result, when the value of the sampling function is calculated by synthesizing the basic waveform and the auxiliary waveform, the relative shift amount of these waveforms can be shifted. Therefore, data interpolation or the like is performed using this sampling function. The frequency characteristics can be adjusted.

  The basic waveform described above is preferably a waveform corresponding to the third-order B-Prine function. This makes it possible to obtain a sampling function waveform whose signal level changes gently.

  The basic waveform described above is preferably a convex waveform that can be differentiated only once in the entire range. As a result, it is possible to generate a sampling function waveform that smoothly changes and can be approximated to a natural phenomenon.

  The above-mentioned local range is a range corresponding to a width W that is not less than 2 and not more than 3 times the sample interval τ, and the shift amount set by the shift amount setting means (or the shift amount setting step) is ( It is desirable that the time is equal to or less than 4τ−W) / 2. As a result, the value of the sampling function waveform can be converged to 0 in a range that is the same as or narrower than the two sampling positions before and after the central position, and data is obtained using this sampling function. When performing interpolation or the like, it is only necessary to use two (two in total) data before and after the position of interest, and the processing load can be reduced.

  Further, the shift amount setting means (or the shift amount setting step) uses the shift amount setting means (or the shift amount setting step) while maintaining the same relationship between the shift amount of the auxiliary waveform shifted forward with respect to the basic waveform and the shift amount of the auxiliary waveform shifted later. It is desirable that the shift amount is variably set. Further, the shift amount setting means (or the shift amount setting step) maintains the same relationship between the gain adjustment value of the auxiliary waveform shifted forward with respect to the basic waveform and the gain adjustment value of the auxiliary waveform shifted later. It is desirable that the shift amount is variably set by (). As a result, the sampling function waveform can be made symmetrical, and distortion generated in data interpolation or the like using this sampling function can be reduced.

  Further, it is desirable that the above-described gain adjustment value changes according to the shift amount, and the auxiliary waveform calculation means calculates the gain adjustment value according to the shift amount set by the shift amount setting means. Alternatively, the gain adjustment value described above includes a shift amount as a parameter, and the auxiliary waveform calculation step desirably calculates the gain adjustment value according to the shift amount set by the shift amount setting step. As a result, it becomes possible to adjust the shape of the combined waveform when changing the amount of overlap between the basic waveform and the auxiliary waveform by changing the shift amount so as to satisfy the condition as a sampling function.

  Further, it is desirable that the shift amount setting by the shift amount setting means described above is performed by variably setting the value of the shift parameter for adjusting the frequency characteristic of the data output from the adding means. Alternatively, the setting of the shift amount in the shift amount setting step is desirably performed by variably setting the value of the shift parameter that adjusts the frequency characteristic of the data output in the addition step.

  Further, the frequency characteristic of the data output from the adding means can be adjusted by adjusting the gain adjustment value and shift amount of the auxiliary waveform with respect to the basic waveform by the auxiliary waveform calculating means in conjunction with the shift parameter value described above. desirable. Alternatively, the frequency characteristic of the data output in the addition step can be adjusted by adjusting the gain adjustment value and the shift amount of the auxiliary waveform with respect to the basic waveform in the auxiliary waveform calculation step in conjunction with the shift parameter value described above. desirable.

  Moreover, it is desirable to further include an update means (or update step) for updating the above-described distance t at a predetermined time interval. As a result, it is possible to perform an oversampling process that smoothly connects discrete data with a plurality of data.

  Further, the discrete data extracting means described above holds four pieces of discrete data inputted at a period T corresponding to the sample interval τ, outputs the four pieces of discrete data held at the same time, and inputs the discrete data. It is desirable that the combination of the four discrete data to be retained is updated every time the update is performed, and the updating unit updates the distance t at a period of 1 / N of the period T. The discrete data extraction step described above holds four pieces of discrete data input at a period T corresponding to the sample interval τ, outputs the four pieces of discrete data held at the same time, and inputs the discrete data. It is desirable that the combination of four discrete data to be retained is updated each time the update is performed, and the update step updates the distance t at a period of 1 / N of the period T. Thereby, it is possible to perform an oversampling process for increasing the frequency of the input discrete data by N times.

  Further, it is desirable to further include a digital-analog converter that converts the operation result data that is updated at a 1 / N period of the above-described period T and that is output from the convolution operation means into an analog signal and smoothes it. Further, it is desirable to further include a digital-analog conversion step in which the value is updated at a cycle of 1 / N of the above-described cycle T and the calculation result data output from the convolution calculation step is converted into an analog signal and smoothed. This makes it possible to obtain an analog signal that smoothly connects input discrete data.

  Hereinafter, a signal processing apparatus according to an embodiment to which the present invention is applied will be described in detail with reference to the drawings.

(1) Improvement of sampling function The conventional sampling function proposed by the inventor of the present application (hereinafter, this sampling function is referred to as “C-type sampling function”) is defined by the following equation (1): It is derived as a function represented by the equation (2) by linear combination of a function system (a set of functions) obtained by shifting the second-order piecewise polynomial. Here, τ represents the sample interval.

Here, ³ _[c] ψ (t) in the expression (2) needs to satisfy the following conditional expression as a sampling function.

この条件式を解くと、

Solving this conditional expression,

を得る。

Get.

If the frequency characteristic of the C-type sampling function is Ψ (f), Ψ (f) is obtained by Fourier transforming ³ _[c] ψ (t),

として表される。但し、（５）式においてｆ_S＝１／τとしている。

Represented as: However, in the equation (5), f _S = 1 / τ.

  By the way, as expressed by the equation (2), the C-type sampling function is considered to be realized by setting the shift interval of the second-order piecewise polynomial to 1/2 of the sample interval. However, the generality of the shift interval in equation (2) has not been discussed so far. As shown in equation (5), since the sampling interval can be considered as a parameter related to the frequency characteristics, various frequencies can be obtained by changing the shift interval when forming the sampling function. A sampling function with characteristics can be designed. Therefore, in the following, the sampling function designed by changing the shift interval and its frequency characteristic will be examined.

  If a C-type sampling function that generalizes the shift interval of the piecewise polynomial is expressed as φα (t), φα (t) is expressed as

It can be expressed as. Here, α (0 <α ≦ 1/2) is referred to as a shift parameter. In order for the function φα (t) to be a sampling function, the condition of the expression (3) needs to be satisfied in the same manner as the C-type sampling function described above. That is,

When the expansion coefficient βk (k = -1, 0, 1) in the equation (6) is obtained based on this condition, the following simultaneous equations are established by the equations (6) and (7).

ところで、³ _[c]ψ（ｔ）は以下に示す区分多項式として表すことができる。

By the way, ³ _[c] ψ (t) can be expressed as a piecewise polynomial shown below.

（９）式の値を（８）式に代入することにより、以下の式が得られる。

By substituting the value of equation (9) into equation (8), the following equation is obtained.

これを解くことにより、展開係数が以下のように求められる。

By solving this, the expansion coefficient is obtained as follows.

したがって、シフトパラメータを持つ標本化関数は、

Therefore, a sampling function with a shift parameter is

Can be expressed as Here, 0 <α ≦ ½, but when α = ½, it matches the C-type sampling function described above. That is,

となる。

It becomes.

  If the frequency characteristic of φα (t) is expressed as Φα (f), Φα (f) can be obtained as follows by Fourier-transforming the equation (12).

ここで、ｆ_Sは（５）式と同様にｆ_S＝１／τである。

Here, f _S is f _S = 1 / τ as in the equation (5).

  Next, the frequency characteristic of the sampling function by changing the shift parameter α will be examined. FIG. 1 is a diagram illustrating a waveform of a sampling function when the shift parameter α is changed. FIG. 2 is a diagram showing the frequency characteristics of the sampling function when the shift parameter α is changed. As shown in FIG. 1, in the improved sampling function, the width of the central portion becomes thicker as the shift parameter α becomes smaller than 1/2, but the attenuation becomes steep when it exceeds t = ± 0.5τ. Thus, it can be confirmed that the undershoot after t = ± τ is large. As shown in FIG. 2, the frequency characteristic of the improved sampling function does not change much in the main pole band (main lobe) even if the value of α changes, but when α becomes small, It can be confirmed that the amplitude of the first side lobe is increased and the subpolar descent rate is decreased. From another point of view, even if the shift parameter α is changed, the harmonic component can be adjusted without substantially changing the characteristics of the main lobe.

(2) Signal Processing Device FIG. 3 is a diagram showing a configuration of a signal processing device using the improved sampling function shown in FIG. The signal processing apparatus shown in FIG. 3 performs an interpolation process between values of discrete data based on the input discrete data, and includes a discrete data extraction unit 10, a sampling function processing unit 20, a convolution calculation unit 30, and an interpolation. A position setting unit 40, a shift amount setting unit 50, a D / A (digital-analog) converter 60, and an LPF (low-pass filter) 70 are included.

  The discrete data extraction unit 10 extracts the previous four data from the sequentially input discrete data, and holds the four discrete data until new discrete data is input next. These four discrete data are output to the sampling function processing unit 20 connected to the next stage. When the data interpolation position b is designated, the sampling function processing unit 20 calculates the value of the sampling function based on the distance between the data interpolation position b and each discrete data. The value of the sampling function is calculated for each of the four discrete data output from the discrete data extraction unit 10. The convolution operation unit 30 multiplies each of the values of the four sampling functions calculated by the sampling function processing unit 20 by the values of the discrete data, and adds the results, thereby convolution corresponding to the four discrete data. Perform the operation. A value obtained by this convolution operation is an interpolation value at a predetermined interpolation position between the second discrete data and the third discrete data. The interpolation position setting unit 40 sets the data interpolation position b used for the calculation by the sampling function processing unit 20. The value of the data interpolation position b is updated at a predetermined time interval, specifically, every 1 / N period (= T / N) of the period T corresponding to the input interval of discrete data.

  The shift amount setting unit 50 is for variably setting a shift amount necessary for determining the shape of the sampling function used in the sampling function processing unit 20, and is a shift obtained by normalizing the shift amount with the sampling interval. Set the parameter α. The shift parameter α will be described later. The D / A converter 60 receives interpolation data from the convolution operation unit 30 at a cycle T / N, converts it into a corresponding analog voltage, and outputs it. The LPF 70 performs a smoothing process on the output signal of the D / A converter 60 and outputs a signal whose voltage changes smoothly.

  FIG. 4 is a diagram showing the positional relationship between the four discrete data and the point of interest. For example, a continuous signal that smoothly changes is sampled at a constant time interval, and quantized to obtain discrete data as sample data. In FIG. 4, the values of discrete data d1, d2, d3, and d4 that are sequentially input corresponding to the sample positions t1, t2, t3, and t4 are Y (t1), Y (t2), and Y (t3). , Y (t4), and a case where an interpolation value y corresponding to a predetermined position t0 (distance b from t2) between the sample positions t2 and t3 is obtained.

  The sampling function φα (t) used in this embodiment converges at t = ± (3/2 + α) τ. Here, since 0 <α ≦ 1/2, this sampling function φα (t) has only a value other than 0 within the range of t = ± 2τ at the maximum, and up to t = ± 2τ. Discrete data may be taken into account. Therefore, when the interpolation value y shown in FIG. 4 is obtained, the respective values Y (t1), Y (t2), Y (4) of the four discrete data d1 to d4 corresponding to t = t1, t2, t3, t4. Only t3) and Y (t4) need be considered, and the amount of processing can be reduced. Moreover, each discrete data of t = ± 3τ or more should be considered originally, but it is not ignored in consideration of the processing amount, accuracy, etc. There is no error.

  FIG. 5 is a diagram showing an outline of data interpolation processing using a sampling function by the signal processing apparatus of the present embodiment. As the contents of the data interpolation processing, as shown in FIGS. 5A to 5D, for each sample position, the peak at t = 0 (center position) of the sampling function φα (t) shown in FIG. The heights are matched, and the value of each sampling function φα (t) at the interpolation position t0 at this time is obtained.

  Focusing on the value Y (t1) of the discrete data d1 at t1 shown in FIG. 5A, the distance between the interpolation position t0 and the sample position t1 is τ + b. Therefore, the value of the sampling function at the interpolation position t0 when the center position of the sampling function φα (t) is aligned with the sample position t1 is φα (τ + b). Actually, in order to match the peak height at the center position of the sampling function φα (t) so as to match the value Y (t1) of the discrete data, a value φα obtained by multiplying the above-mentioned φα (τ + b) by Y (t1). (Τ + b) · Y (t1) is a desired value. φα (τ + b) is calculated by the sampling function processing unit 20, and calculation for multiplying φα (τ + b) by Y (t 1) is performed by the convolution operation unit 30.

  Similarly, focusing on the value Y (t2) of the discrete data d2 at t2 shown in FIG. 5B, the distance between the interpolation position t0 and the sample position t2 is b. Therefore, the value of the sampling function at the interpolation position t0 when the center position of the sampling function φα (t) is aligned with the sampling position t2 is φα (b). Actually, in order to match the peak height at the center position of the sampling function φα (t) so as to match the value Y (t2) of the discrete data, a value φα obtained by multiplying the above-mentioned φα (b) by Y (t2). (B) · Y (t2) is a desired value. φα (b) is calculated by the sampling function processing unit 20, and calculation for multiplying φα (b) by Y (t 2) is performed by the convolution operation unit 30.

  Focusing on the value Y (t3) of the discrete data d3 at t3 shown in FIG. 5C, the distance between the interpolation position t0 and the sample position t3 is τ−b. Therefore, the value of the sampling function at the interpolation position t0 when the center position of the sampling function φα (t) is aligned with the sample position t3 is φα (−τ + b). Actually, a value obtained by multiplying the above-mentioned φα (−τ + b) by Y (t3) in order to match the peak height at the center position of the sampling function φα (t) so as to coincide with the value Y (t3) of the discrete data. φα (−τ + b) · Y (t3) is a desired value. φα (−τ + b) is calculated by the sampling function processing unit 20, and calculation for multiplying φα (−τ + b) by Y (t 3) is performed by the convolution operation unit 30.

  Focusing on the value Y (t4) of the discrete data d4 at t4 shown in FIG. 5D, the distance between the interpolation position t0 and the sample position t4 is 2τ−b. Therefore, the value of the sampling function at the interpolation position t0 when the center position of the sampling function φα (t) is aligned with the sampling position t4 is φα (−2τ + b). Actually, in order to match the peak height at the center position of the sampling function φα (−2t + b) so as to match the value Y (t4) of the discrete data, the above φα (−2τ + b) is multiplied by Y (t4). The value φα (−2τ + b) · Y (t4) is a desired value. φα (−2τ + b) is calculated by the sampling function processing unit 20, and calculation to multiply φα (−2τ + b) by Y (t 4) is performed by the convolution operation unit 30.

  In this way, the four values φα (τ + b) · Y (t1), φα (b) · Y (t2), φα (−τ + b) · Y (t3) obtained corresponding to the point of interest at the interpolation position t0. ), [Phi] [alpha] (-2 [tau] + b) .Y (t4) is added by the convolution operation unit 30 to calculate the interpolation value y corresponding to the point of interest.

  Next, details of the sampling function processing unit 20 will be described. FIG. 6 is a diagram illustrating a detailed configuration of the sampling function processing unit 20. As shown in FIG. 6, the sampling function processing unit 20 includes four sampling function calculation units 22, 24, 26, and 28. The sampling function calculator 22 corresponds to the first discrete data (discrete data d1 shown in FIG. 4) among the four discrete data extracted by the discrete data extractor 10, and the basic waveform calculator 22 -1, auxiliary waveform calculators 22-2 and 22-3, and an adder 22-4. Similarly, the sampling function calculator 24 corresponds to the second discrete data d2, the sampling function calculator 26 corresponds to the third discrete data d3, and the sampling function calculator 28 corresponds to the fourth discrete data d4. ing. Each of the sampling function calculators 24, 26, and 28 has basically the same configuration as the sampling function calculator 22, and the detailed operation of the sampling function calculator 22 will be described below representatively. To do.

  In the sampling function calculation unit 22, when the center of the sampling function is aligned with the position of the discrete data d1 as shown in FIG. Processing to calculate the value of the corresponding sampling function is performed.

  The basic waveform calculation unit 22-1 uses a basic waveform that can be differentiated at least once, in which the local range wider than the sampling interval τ corresponding to the sampling function is a value other than 0 and becomes 0 in other ranges. The value corresponding to the point of interest is calculated. On the other hand, the auxiliary waveform calculation unit 22-2 reverses the polarity of the basic waveform, adjusts the gain, and corresponds to the point of interest for the first auxiliary waveform that is shifted to the front side of the basic waveform by a predetermined shift amount. Calculate the value. The other auxiliary waveform calculation unit 22-3 inverts the polarity of the basic waveform, adjusts the gain, and further corresponds to the point of interest for the second auxiliary waveform shifted to the rear side of the basic waveform by a predetermined shift amount. Calculate the value to be.

FIG. 7 is a diagram showing the relationship between the basic waveform used in the basic waveform calculator 22-1 and the first and second auxiliary waveforms used in the auxiliary waveform calculators 22-2 and 22-3. In FIG. 7, A shows the basic waveform, B shows the first auxiliary waveform, and C shows the second auxiliary waveform.
The basic waveform A is a waveform of a function corresponding to the second term on the right side of the above-described equation (12), and (1 + 4α ² ) τ / (4α ² ) is added to the third-order B-spline function ³ _[b] ψ (t). Obtained by multiplication. Note that this third-order B-spline function ³ _[b] ψ (t) is defined by the equation (9), and is a value other than 0 within a local range of −3τ / 2 ≦ t ≦ + 3τ / 2. It is a waveform that can be differentiated only by the first order that becomes 0 in the range other than.

The first auxiliary waveform B is a waveform of a function corresponding to the first term on the right side of the equation (12), and the third-order B-spline function ³ _[b] ψ (t) is multiplied by −τ / (8α ² ). Can be obtained. The second auxiliary waveform B is a waveform of a function corresponding to the third term on the right side of the expression (12), and the third-order B-spline function ³ _[b] ψ (t) is multiplied by −τ / (8α ² ). Can be obtained. Each of the first auxiliary waveform B and the second auxiliary waveform C is a waveform obtained by inverting the polarity of the basic waveform A and adjusting the gain, and further shifting it forward or backward by a predetermined shift amount. The shift amount at this time can be expressed by ατ as apparent from the first term on the right side and the third term on the right side of the equation (12), and is normalized by the sample interval τ (the sample interval τ is set to 1). It can be specified by the parameter α. Since 0 <α ≦ 1/2, the maximum shift amount is τ / 2.

The basic waveform calculator 22-1 calculates a value corresponding to the position t0 of the point of interest for the basic waveform A corresponding to the discrete data d1. Since the sampling function φα (t) of the present embodiment is generated by synthesizing the basic waveform A and the two auxiliary waveforms B and C, the center position of the sampling function is matched with the position of the discrete data d1 The positional relationship between the basic waveform A and the point of interest position t0 is as shown in FIG. Therefore, the basic waveform calculator 22-1 calculates ((1 + 4α ² ) τ / (4α ² )) · ³ _[b] ψ (τ + b) using the second term on the right side of the equation (12). Thus, for the basic waveform A, a value corresponding to the position t0 of the point of interest is calculated.

Similarly, one auxiliary waveform calculator 22-2 calculates (−τ / (8α ² )) · ³ _[b] ψ (τ + b + ατ) using the first term on the right side of equation (12). Thus, a value corresponding to the position t0 of the point of interest is calculated for the auxiliary waveform B. As can be seen from FIG. 7, this value is zero. The other auxiliary waveform calculator 22-3 calculates (−τ / (8α ² )) · ³ _[b] ψ (τ + b−ατ) by using the third term on the right side of equation (12). Then, a value corresponding to the position t0 of the point of interest is calculated for the auxiliary waveform C.

  The adding unit 22-4 adds values corresponding to the points of interest calculated by the basic waveform calculating unit 22-1, the auxiliary waveform calculating units 22-2, and 22-3. In this way, the sampling function calculation unit 22 calculates the sampling function value φα (τ + b) corresponding to the point of interest for the discrete data d1.

  Similarly, the sampling function calculation unit 24 calculates the sampling function value φα (b) corresponding to the point of interest for the discrete data d2. The sampling function calculation unit 26 calculates the sampling function value φα (−τ + b) corresponding to the point of interest for the discrete data d3. The sampling function calculation unit 28 calculates the sampling function value φα (−2τ + b) corresponding to the point of interest for the discrete data d4.

  The discrete data extraction unit 10 described above is a discrete data extraction unit, the sampling function calculation unit 20 is a sampling function processing unit, the convolution calculation unit 30 is a convolution calculation unit, and the basic waveform calculation unit 22-1 is a basic waveform calculation unit. The auxiliary waveform calculators 22-2 and 22-3 are auxiliary waveform calculators, the adder 22-4 is an adder, the shift amount setting unit 50 is a shift amount setting unit, and the interpolation position setting unit 40 is an update unit. Further, the D / A converter 60 and the LPF 70 correspond to digital-analog conversion means, respectively.

  Next, the overall operation of the signal processing apparatus of this embodiment will be described. FIG. 8 is a flowchart showing the overall operation of the signal processing apparatus of this embodiment.

  First, the shift amount is set by the shift amount setting unit 50 (step 100). As a setting method, a case where the shift parameter α is selected by a user's operation from a plurality of selection candidates can be considered. For example, as shown in FIG. 1 and FIG. 2, four types of 1/2, 1/4, 1/8, and 1/16 are prepared as selection candidates in advance as the value of the shift parameter α, and one selection is made. Let the user select a candidate. Alternatively, as another setting method, a case where the user directly inputs the value of the shift parameter α within a range of 0 <α ≦ 1/2 can be considered.

  Next, the discrete data extraction unit 10 extracts, holds, and outputs four discrete data d1 to d4 from the discrete data input in order at a predetermined interval T (step 101). Further, the interpolation position setting unit 40 sets an interpolation position t0 (step 102). Next, the sampling function processing unit 20 calculates the values of the basic waveform A and the auxiliary waveforms B and C corresponding to the point of interest at the interpolation position t0 for each of the four discrete data d1 to d4 (step 103, 104) These are added for each discrete data to calculate the basic waveform sampling function values φα (τ + b), φα (b), φα (−τ + b), φα (−2τ + b) (step 105). Next, the convolution calculation unit 30 calculates the sampling function values φα (τ + b), φα (b), φα (−τ + b), φα (−2τ + b) calculated for each discrete data by the sampling function calculation unit 20. And a convolution operation using the values Y (t1), Y (t2), Y (t3), and Y (t4) of each discrete data (Y (t1) · φα (τ + b) + Y (t2) · φα (b) + Y (T3) * [phi] [alpha] (-[tau] + b) + Y (t4) * [phi] [alpha] (-2 [tau] + b)) is performed to output the interpolation data corresponding to the point of interest (step 106).

  The D / A converter 60 generates an analog voltage corresponding to the value of the interpolation data (interpolation value y) (step 107), and passes the analog voltage through the LPF 70 to output an analog signal that changes smoothly. (Step 108).

  Further, the interpolation position setting unit 40 determines whether or not the interpolation position t0 and the position of the discrete data match (step 109). If they do not match, a negative determination is made, and then the process returns to step 102. Update the interpolation position. Thereafter, the processing after step 103 is repeated. On the other hand, when the interpolation position matches the position of the discrete data, an affirmative determination is made, and the process returns to step 101 to extract new discrete data with the updated combination.

  Step 100 described above is a shift amount setting step, step 101 is a discrete data extraction step, step 102 is an update step, steps 103 to 105 are sampling function processing steps, step 103 is a basic waveform calculation step, step 104 Corresponds to the auxiliary waveform calculation step, step 105 corresponds to the addition step, step 106 corresponds to the convolution operation step, and steps 107 and 108 correspond to the digital-analog conversion step.

  As described above, in the signal processing apparatus according to the present embodiment, when the basic waveform A and the auxiliary waveforms B and C are combined to calculate the value of the sampling function, the relative shift amount (ατ) of these waveforms is shifted. Therefore, it is possible to adjust the frequency characteristics when performing data interpolation or the like using this sampling function.

  Further, as the basic waveform A, a convex waveform that can be differentiated only once in the entire range, specifically, a waveform corresponding to the third-order B-Prine function is considered to be able to sufficiently approximate a natural phenomenon. Thus, it is possible to obtain a sampling function waveform whose value changes.

  A local range W where the value of the basic waveform A to be synthesized is other than 0 is a range corresponding to a width W that is not less than 2 times and not more than 3 times the sample interval τ, and shifts of the auxiliary waveforms B and C are performed. The amount is set to be equal to or less than (4τ−W) / 2. As a result, the value of the sampling function waveform can be converged to 0 in a range that is the same as or narrower than the two sampling positions before and after the central position, and data is obtained using this sampling function. When performing interpolation or the like, it is only necessary to use two (two in total) data before and after the position of interest, and the processing load can be reduced. In the basic waveform A of the present embodiment, the local range W is set to 3τ, and the shift amounts of the auxiliary waveforms B and C are set to ± ατ, which satisfies the above relationship. The range of the basic waveform A may be set to be less than 3τ.

Further, in the present embodiment, the shift amount setting unit 50 maintains the same relationship between the shift amount of the auxiliary waveform B shifted forward with respect to the basic waveform A and the shift amount of the auxiliary waveform C shifted later. The shift amount is variably set. Furthermore, the gain adjustment values of auxiliary waveform B which is shifted forward with respect to the fundamental wave ^{A (-τ / (8α 2)} ) and the gain adjustment value of the auxiliary waveform C which is shifted after (-τ / (8α ²⁾ The shift amount is set variably by the shift amount setting unit 50 while maintaining the same relationship. As a result, the sampling function waveform can be made symmetrical, and distortion generated in data interpolation or the like using this sampling function can be reduced.

  The gain adjustment value described above changes depending on the shift amount, and the auxiliary waveform calculation units 22-2 and 22-3 calculate the gain adjustment value according to the shift amount set by the shift amount setting unit 50. is doing. As a result, it is possible to adjust the shape of the combined waveform when changing the degree of overlap between the basic waveform A and the auxiliary waveform B by changing the shift amount so as to satisfy the conditions as a sampling function. Become.

  Further, in the signal processing apparatus of the present embodiment, the distance to the point of interest is updated by the interpolation position setting unit 40 at a predetermined time interval T / N, and oversampling in which discrete data is smoothly connected with a plurality of data. Processing can be performed. Furthermore, in the signal processing apparatus of the present embodiment, the D / A for smoothing the conversion of the calculation result data (interpolation data) output from the convolution calculation unit 30 with the value updated at the cycle of T / N into an analog signal. The converter 60 and the LPF 70 are provided, and an analog signal that smoothly connects the input discrete data can be obtained.

  In addition, this invention is not limited to the said embodiment, A various deformation | transformation implementation is possible within the range of the summary of this invention. For example, in the above-described embodiment, the signal processing device that operates as a digital-analog converter that outputs an analog signal corresponding to discrete data input in order has been described. However, interpolation data obtained by calculation of the convolution operation unit 30 is described. May be output from the signal processing device. The signal processing device in this case operates as an oversampling processing device.

  Further, instead of using discrete data input in order, four discrete data to be processed may be read out from discrete data already recorded in a memory or the like, and the same processing may be performed.

  Further, the operation of the signal processing apparatus according to the above-described embodiment may be performed by a computer including a CPU, a ROM, a RAM, and the like. In this case, a signal processing program (each step shown in FIG. 8) stored in ROM, RAM, or other storage device (hard disk device or the like) is executed, or before the D / A converter 60 shown in FIG. A program for realizing the function of each unit may be executed by the CPU.

It is a figure which shows the waveform of the sampling function at the time of changing the shift parameter (alpha). It is a figure which shows the frequency characteristic of the sampling function at the time of changing the shift parameter (alpha). It is a figure which shows the structure of the signal processing apparatus using the improved sampling function shown in FIG. It is a figure which shows the positional relationship of four discrete data and an attention point. It is a figure which shows the outline of the data interpolation process using the sampling function by the signal processing apparatus of this embodiment. It is a figure which shows the detailed structure of a sampling function process part. It is a figure which shows the relationship between the basic waveform used in a basic waveform calculation part, and the auxiliary waveform used in an auxiliary waveform calculation part. It is a flowchart which shows the whole operation | movement of the signal processing apparatus of this embodiment.

Explanation of symbols

DESCRIPTION OF SYMBOLS 10 Discrete data extraction part 20 Sampling function processing part 22, 24, 26, 28 Sampling function calculation part 22-1 Basic waveform calculation part 22-2, 22-3 Auxiliary waveform calculation part 22-4 Addition part 30 Convolution calculation part 40 Interpolation position setting section 50 Shift amount setting section 60 D / A (digital-analog) converter 70 LPF (low pass filter)

Claims (35)

Discrete data extraction means for extracting a total of four discrete data before and after the target point to be interpolated, and each of the four discrete data extracted by the discrete data extraction means Sampling function processing means for calculating the value of the sampling function φ (t), where t is the distance between the point of interest and each discrete data, and each of the four discrete data calculated by the sampling function processing means In a signal processing apparatus having a convolution operation means for calculating the value of the point of interest by performing a convolution operation by adding the values of the corresponding sampling functions,
The sampling function processing means includes:
A basic waveform for calculating a value corresponding to the point of interest for a basic waveform that can be differentiated at least once, in which a local range wider than the sample interval τ is a value other than 0 and a value in the other range is 0. A calculation means;
Auxiliary waveform calculation means for inverting the polarity of the basic waveform, adjusting the gain, and calculating a value corresponding to the point of interest for two auxiliary waveforms before and after the basic waveform shifted by a predetermined shift amount; ,
Adding means for adding the calculation results of the basic waveform calculation means and the auxiliary waveform calculation means,
The signal processing apparatus further comprising a shift amount setting means for variably setting the shift amount. In claim 1,
The signal processing apparatus according to claim 1, wherein the basic waveform is a waveform corresponding to a third-order B-Prine function. In claim 1,
The signal processing device according to claim 1, wherein the basic waveform is a convex waveform that can be differentiated only once in the entire range. In any one of Claims 1-3,
The local range is a range corresponding to a width W that is not less than 2 times and not more than 3 times the sample interval τ,
The signal processing apparatus characterized in that the shift amount set by the shift amount setting means is equal to or less than (4τ−W) / 2. In any one of Claims 1-4,
The shift amount setting means variably sets the shift amount while maintaining the same relationship between the shift amount of the auxiliary waveform shifted forward with respect to the basic waveform and the shift amount of the auxiliary waveform shifted later. A signal processing apparatus that is performed. In any one of Claims 1-4,
The shift amount setting means variably sets the shift amount while maintaining the same relationship between the gain adjustment value of the auxiliary waveform shifted forward with respect to the basic waveform and the gain adjustment value of the auxiliary waveform shifted later. Is performed. In claim 6,
The gain adjustment value changes according to the shift amount,
The auxiliary waveform calculation means calculates the gain adjustment value according to the shift amount set by the shift amount setting means. In any one of Claims 1-7,
The signal processing apparatus according to claim 1, wherein the shift amount is set by the shift amount setting means by variably setting a shift parameter value for adjusting a frequency characteristic of data output from the adding means. In claim 8,
Adjusting the frequency characteristic of the data output from the adding means by adjusting the gain adjustment value and the shift amount of the auxiliary waveform with respect to the basic waveform by the auxiliary waveform calculating means in conjunction with the value of the shift parameter; A signal processing device. In any one of Claims 1-9,
The signal processing apparatus further comprising an updating unit that updates the distance t at a predetermined time interval. In claim 10,
The discrete data extraction means holds four pieces of the discrete data input at a period T corresponding to the sample interval τ, outputs the four pieces of discrete data held simultaneously, and the discrete data is Each time it is input, the combination of the four discrete data to be retained is updated,
The signal processing apparatus, wherein the updating means updates the distance t at a period of 1 / N of the period T. In claim 11,
Signal processing further comprising digital-analog conversion means for converting and smoothing the calculation result data output from the convolution calculation means and having a value updated at a period of 1 / N of the period T into an analog signal apparatus. For each of the discrete data extraction step for extracting a total of four discrete data before and after the target point to be interpolated, and for each of the four discrete data extracted in the discrete data extraction step A sampling function processing step for calculating the value of the sampling function φ (t) with the distance between the point of interest and each discrete data as t, and each of the four discrete data calculated in the sampling function processing step. In a signal processing method including a convolution operation step of calculating a value of the point of interest by performing a convolution operation by adding the values of the corresponding sampling functions,
In the sampling function processing step, the basic waveform that can be differentiated at least once when the local range wider than the sampling interval τ is a value other than 0 and the value of the other range is 0 is set as the point of interest. A basic waveform calculation step for calculating a corresponding value; and two auxiliary waveforms before and after the polarity of the basic waveform is inverted and gain adjusted, and further shifted by a predetermined shift amount before and after the basic waveform An auxiliary waveform calculation step for calculating a value corresponding to the above, and an addition step for adding the calculation results of the basic waveform calculation step and the auxiliary waveform calculation step,
A signal processing method further comprising a shift amount setting step of variably setting the shift amount. In claim 13,
The signal processing method according to claim 1, wherein the basic waveform is a waveform corresponding to a third-order B-Prine function. In claim 13,
The signal processing method according to claim 1, wherein the basic waveform is a convex waveform that can be differentiated only once in the entire range. In any one of Claims 13-15,
The local range is a range corresponding to a width W that is not less than 2 times and not more than 3 times the sample interval τ,
The signal processing method characterized in that the shift amount set in the shift amount setting step is equal to or less than (4τ−W) / 2. In any one of Claims 13-16,
The shift amount can be variably set by the shift amount setting step while maintaining the same relationship between the shift amount of the auxiliary waveform shifted forward with respect to the basic waveform and the shift amount of the auxiliary waveform shifted later. A signal processing method characterized by being performed. In any one of Claims 13-16,
The variable amount of the shift amount is set by the shift amount setting step while maintaining the same relationship between the gain adjustment value of the auxiliary waveform shifted forward with respect to the basic waveform and the gain adjustment value of the auxiliary waveform shifted later. A signal processing method characterized in that is performed. In claim 18,
The gain adjustment value changes according to the shift amount,
The signal processing method characterized in that the auxiliary waveform calculation step calculates the gain adjustment value according to the shift amount set by the shift amount setting step. In any one of Claims 13-19,
The signal processing method according to claim 1, wherein the setting of the shift amount in the shift amount setting step is performed by variably setting a value of a shift parameter for adjusting a frequency characteristic of data output in the addition step. In claim 20,
Adjusting the frequency characteristic of the data output in the adding step by adjusting the gain adjustment value and the shift amount of the auxiliary waveform with respect to the basic waveform in the auxiliary waveform calculating step in conjunction with the value of the shift parameter; A signal processing method characterized by the above. In any one of Claims 13-21,
And a updating step of updating the distance t at a predetermined time interval. In claim 22,
The discrete data extraction step holds four pieces of discrete data input at a period T corresponding to the sample interval τ, outputs the four pieces of discrete data held simultaneously, and the discrete data Each time it is input, the combination of the four discrete data to be retained is updated,
In the signal processing method, the updating step updates the distance t at a period of 1 / N of the period T. In claim 23,
A signal processing further comprising a digital-analog conversion step in which a value is updated at a cycle of 1 / N of the cycle T and the calculation result data output from the convolution calculation step is converted into an analog signal and smoothed. Method. The computer is configured to extract a total of four discrete data before and after the target point to be interpolated, and to extract the four discrete data extracted by the discrete data extraction means. Sampling function processing means for calculating the value of the sampling function φ (t), where t is the distance between the point of interest and each discrete data, and the four discrete data calculated by the sampling function processing means. In the signal processing program that functions as a convolution operation means for calculating the value of the point of interest by performing a convolution operation by adding the values of the sampling functions corresponding to each of
The sampling function processing means includes:
A basic waveform for calculating a value corresponding to the point of interest for a basic waveform that can be differentiated at least once, in which a local range wider than the sample interval τ is a value other than 0 and a value in the other range is 0. A calculation means;
Auxiliary waveform calculation means for inverting the polarity of the basic waveform, adjusting the gain, and calculating a value corresponding to the point of interest for two auxiliary waveforms before and after the basic waveform shifted by a predetermined shift amount; ,
Adding means for adding the calculation results of the basic waveform calculation means and the auxiliary waveform calculation means,
A signal processing program for causing a computer to further function as shift amount setting means for variably setting the shift amount. In claim 25,
The signal processing program characterized in that the basic waveform is a waveform corresponding to a third-order B-prine function. In claim 25,
The signal processing program characterized in that the basic waveform is a convex waveform that can be differentiated only once in the entire range. In any one of Claims 25-27,
The local range is a range corresponding to a width W that is not less than 2 times and not more than 3 times the sample interval τ,
A signal processing program characterized in that the shift amount set by the shift amount setting means is equal to or less than (4τ−W) / 2. In any one of Claims 25-28,
The shift amount setting means variably sets the shift amount while maintaining the same relationship between the shift amount of the auxiliary waveform shifted forward with respect to the basic waveform and the shift amount of the auxiliary waveform shifted later. A signal processing program that is executed. In any one of Claims 25-28,
The shift amount setting means variably sets the shift amount while maintaining the same relationship between the gain adjustment value of the auxiliary waveform shifted forward with respect to the basic waveform and the gain adjustment value of the auxiliary waveform shifted later. Is a signal processing program. In claim 30,
The gain adjustment value changes according to the shift amount,
The signal processing program characterized in that the auxiliary waveform calculation means calculates the gain adjustment value according to the shift amount set by the shift amount setting means. 32. In any of claims 25-31.
The signal processing program characterized in that the setting of the shift amount by the shift amount setting means is performed by variably setting a value of a shift parameter for adjusting a frequency characteristic of data output from the adding means. In claim 32,
Adjusting the frequency characteristic of the data output from the adding means by adjusting the gain adjustment value and the shift amount of the auxiliary waveform with respect to the basic waveform by the auxiliary waveform calculating means in conjunction with the value of the shift parameter; A signal processing program. 34. In any of claims 25-33.
A signal processing program for causing a computer to further function as update means for updating the distance t at a predetermined time interval. In claim 34,
The discrete data extraction means holds four pieces of the discrete data input at a period T corresponding to the sample interval τ, outputs the four pieces of discrete data held simultaneously, and the discrete data is Each time it is input, the combination of the four discrete data to be retained is updated,
The update means updates the distance t at a period of 1 / N of the period T.

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