JP2019016002A - Data interpolation apparatus and data interpolation method - Google Patents

Abstract

To interpolate digital data.SOLUTION: A data interpolation apparatus 100 includes interpolation means for interpolating a section between two consecutive sample points of inputted digital data using a spline function, and output means for converting an interpolation result by the interpolation means of an interpolation target section into analog data and outputting the analog data. The interpolation means calculates a coefficient of the spline function with respect to the interpolation target section, a predetermined number of sections on a past side than the interpolation target section, and a predetermined number of sections on a future side than the interpolation target section, defines the spline function using the calculated coefficient, and interpolates the interpolation target section.SELECTED DRAWING: Figure 1

Description

  The present invention relates to a data interpolation device and a data interpolation method.

  The following digital-analog converters are known. In this digital-analog converter, a sampling function H (t), which is a quadratic piecewise polynomial using a third-order B-spline function F (t), is used to interpolate digital data (for example, a patent) Reference 1).

Japanese Patent No. 3992849

  When performing interpolation using spline functions on continuous digital data, if the coefficients of the spline function can be obtained for each section between sample points of the digital data, high-accuracy interpolation according to the input digital data is possible. It becomes possible. However, the conventional digital-analog converter uses a sampling function which is a quadratic piecewise polynomial, but does not perform a process of obtaining a coefficient by solving the polynomial for each section, and the coefficient of the polynomial is set in advance. Therefore, interpolation cannot be performed by setting a coefficient suitable for the input digital data.

A data interpolating apparatus according to the present invention includes an interpolation means for interpolating a section between two consecutive sample points of input continuous digital data using a spline function, and an interpolation by an interpolation means for an interpolation target section. Output means for converting the result into analog data and outputting, and the interpolation means includes an interpolation target section, a predetermined number of sections on the past side of the interpolation target section, and a predetermined number of sections on the future side of the interpolation target section. A coefficient of a spline function is calculated with respect to a section, a spline function is defined using the calculated coefficient, and an interpolation target section is interpolated.
A data interpolation method according to the present invention is a data interpolation method for converting input digital data into analog data, and a spline between two consecutive sample points of the input digital data is splined. In order to cause the arithmetic unit to execute an interpolation procedure for performing interpolation using a function and an output procedure for converting the interpolation result of the interpolation procedure of the interpolation target section into analog data and outputting the result, the interpolation procedure includes an interpolation target section, an interpolation The spline function coefficient is calculated for a predetermined number of sections on the past side of the target section and a predetermined number of sections on the future side of the interpolation target section, and the spline function is defined using the calculated coefficients. The interpolation target section is interpolated.

  According to the present invention, the coefficient of the spline function is calculated for the interpolation target section, the predetermined number of sample points on the past side of the interpolation target section, and the predetermined number of sample points on the future side of the interpolation target section. Since the spline function is defined using the calculated coefficient and the interpolation target section is interpolated, the coefficient of the spline function can be obtained for each section between the sample points of the digital data, and the input digital data Highly accurate interpolation can be performed according to the above.

1 is a block diagram showing a configuration of an embodiment of a data conversion apparatus 100. FIG. It is the figure which showed typically the spline function defined with respect to the area between the sample points of digital data. It is the figure which showed typically an example of the start point and end point in a finite area. It is the figure which showed typically an example of the area in the data which continues infinitely. It is the figure which showed typically the specific example at the time of clipping the calculation result of a spline function. It is the figure which showed typically the comparative example of the output result of the DAC apparatus using a general digital filter, and the output result by the data converter. 4 is a flowchart of processing executed by a data interpolation circuit 102. FIG.

  In the present embodiment, data that realizes 32 times supersampling by interpolating between 31 sample points on a spline curve using a spline function between sample points of CD or TV digital data. The interpolation device will be described.

  FIG. 1 is a block diagram showing a configuration of an embodiment when the data interpolation apparatus according to the present embodiment is applied to a data conversion apparatus 100 for interpolating digital audio data and then converting it into analog audio data. is there. The data conversion apparatus 100 includes an input interface 101, a data interpolation circuit 102, and a D / A converter 103.

  The input interface 101 is an interface for inputting digital data. For example, a USB-I2S conversion board is used. Digital data input via the input interface 101 is output to the data interpolation circuit 102.

  The data interpolation circuit 102 is an arithmetic unit for interpolating between sample points of digital data by performing interpolation processing described later on digital data continuously input from an input interface. This corresponds to the data interpolation apparatus in the present invention. The digital data processed by the data interpolation circuit 102 is output to the D / A converter 103.

  The D / A converter 103 is a digital-analog conversion circuit for converting digital data input from the data interpolation circuit 102 into analog data, and for example, a 16-bit 2-channel DAC is used. The D / A converter 103 outputs the converted analog data.

  In the data conversion apparatus 100 according to the present embodiment, the data interpolation circuit 102 sets a section between two consecutive sample points of the digital data input from the input interface 101 as one section, Interpolation target sections, a predetermined number of sections on the past side of the interpolation target section, and a predetermined number of sections on the future side of the interpolation target section. A spline function is defined so that the differential value and the secondary differential value are continuous, and the interpolation target section is interpolated.

  In general, when digital data is converted to analog data, quantization noise and aliasing noise are generated, and in order to remove these noises, a conventional DAC device for converting digital data to analog data requires oversampling. Oversampling that inserts an intermediate value between data is performed using a digital filter. In this oversampling, a method of dispersing quantization noise over a wide band and removing the high frequency of the noise with a low-pass filter is used. However, there has been a problem that the sound quality of the output digital data is greatly influenced by the performance of the digital filter used for oversampling.

  In the data conversion apparatus 100 according to the present embodiment, the data interpolation circuit 102 performs a digital filter that affects sound quality by performing interpolation processing using a spline function on input digital data as will be described later. Music reproduction with reduced quantization noise is realized without using it. Details of processing executed by the data interpolation circuit 102 will be described below.

The spline function is defined by a cubic function represented by the following equation (1).

In the present embodiment, the spline function defined by Expression (1) is defined for each interval, with one interval from the sample point of the input digital data to the next sample point. That is, if the interval changes, the coefficient is recalculated and a new spline function is defined. In equation (1), x is a variable that takes a value of 0 ≦ x ≦ 1. Also, _dj is a sample point value and is known. On the other hand, a _j , b _j and c _j are coefficients of a spline function and are unknown numbers.

  FIG. 2 shows the equation (1) for each of the interval between P and Q, the interval between Q and R, and the interval between R and S at four sample points P, Q, R, and S. An example of defining the spline function shown in FIG. In FIG. 2, the spline function shown in Equation (1) is defined as the current section j in which the section between Q and R is the interpolation target, and the section between Q and R is the previous one on the past side. The section j−1, the section between R and S defines the spline function shown in the equation (1) as the section j + 1 that is the next one on the future side.

  Here, since the both ends of all sections are determined as shown in FIG. 3, the spline function of the finite section can be determined by a boundary condition in which the secondary differential value of the start point 3a and the end point 3b is zero. it can. However, since digital data such as a music signal is approximated as a signal that continues indefinitely from the past to the future as shown in FIG. 4, it is impossible to specify both ends of the entire section, and the above boundary The spline function cannot be solved using conditions. For this reason, in the present embodiment, the current section to be interpolated, a predetermined number of sections on the past side of the interpolation target section, and a predetermined number of sections on the future side of the interpolation target section are targeted. Spline interpolation is performed by solving the spline function with all the combined sections as an infinite series.

  In the present embodiment, the predetermined number of sections on the past side of the interpolation target section is a section of the past side of the interpolation target section, which is a number obtained by adding 1 to half the number of bits of the input data. Also, the predetermined number of sections on the future side is a section of the future side with respect to the interpolation target section plus one half of the number of bits of the input data. For example, when the input digital data is 16 bits, 20 sample points including both ends of 19 sections including the current section are targeted by targeting 9 sections on both the past and future sides. Then, the interpolation target section is interpolated by solving the spline function. In addition, when the input digital data is 24 bits, by targeting 13 sections on both the past side and the future side, 28 sample points including both ends of 27 sections including the current section are targeted. Then, the interpolation target section is interpolated by solving the spline function. When the input digital data is 32 bits, by targeting 17 sections on both the past side and the future side, 36 sample points including both ends of 35 sections including the current section are targeted. The interpolation target section is interpolated by solving the spline function. Thus, since each section is divided by sample points, the number of sample points required for calculation is one greater than the number of sections.

Hereinafter, with respect to the method of obtaining the spline function coefficients a _j , b _j , c _j and the digital data approximated as infinite from the past to the future, the input data on the past side of the interpolation target section If we target the number of sections with 1 added to half the number of bits and the section with 1 added to half the number of bits of input data on the future side of the interpolation target section, The reason why the defined spline function can be solved with high accuracy will be described.

As shown in FIG. 2, since digital data is data that is continuously input, the function value is continuous at the sample points in the adjacent sections, and the primary differential value and the secondary differential value are also continuous. To do. For this reason, the relationship of following Formula (2)-(4) is formed. That is, in the adjacent sections j and j + 1, since the values are continuous, the following equation (2) is satisfied, and since the primary differential values are continuous, the following equation (3) is satisfied and the secondary differential values are continuous. Therefore, the following equation (4) is established.

If the equations (2) to (4) can be solved, the coefficients a _j , b _j , and c _j of the spline function shown in the equation (1) can be obtained, so that the interpolation target section j can be interpolated. .

Where: d _j-8 d _j-7 d _j-6 d _j-5 d _j-4 d _j-3 d _j-2 d _j-1 d _j d _{j + 1} d _{j + 2} d _{j + 3} d _{j + 4} d _{j + 5} Two infinite series shown in the following equations (5) and (6) are defined for the data string d _{j + 6} d _{j + 7} . In the following expressions (5) and (6), α is a constant represented by the following expression (7).

In the formula (5), _{e j} is obtained by compilation the influence of the data in the past side than the current interval j, in this embodiment, referred to as Back Impulse. Incidentally, _{e j} satisfies the recurrence formula represented by the following expression (8).

In Expression (6), f _j is a summation of the influence of data on the future side from the current section j, and in the present embodiment, this is referred to as “Front Impulse”. Note that f _j satisfies the recurrence formula shown in the following formula (9).

これにより、式（１１）に示すように、まず係数ｂ_ｊを求めることができる。 Then, the coefficients a _j , b _j and c _j can be obtained as shown in the following equations (10) to (12).

Thereby, as shown in the equation (11), the coefficient b _j can be obtained first.

これにより、式（１１）で求めた係数ｂ_ｊにより、式（１３）、（１４）を用いて、係数ａ_ｊとｃ_ｊを簡単な数式で求めることできる。 Here, the relational expressions shown in the following expressions (13) and (14) hold between the coefficients a _j , b _j and c _j .

Thus, the coefficients a _j and c _j can be obtained by a simple mathematical expression using the expressions (13) and (14) based on the coefficient b _j obtained by the expression (11).

The above-described Back Impulse and Front Impulse are defined as infinite series, but since these converge quickly, the calculation can be terminated in the vicinity of n a predetermined number of times. The truncation error when the computation is terminated in the vicinity of n is obtained by the following equations (15) and (16).

Since the infinite series converges when the truncation error is less than half of the minimum resolution of _dj , in this embodiment, when the number of bits of digital data is D bits, the following equation (17) is satisfied. Suppose that _the truncation error of _dj has converged.

そうすると、デジタルデータのビット数がそれぞれ１６ビット、２４ビット、３２ビットの場合は、次式（２０）〜（２２）に示すように、ｎの値はデータのビット数の半分に１を加えた数と概算することができる。

Here, when the logarithm of 2 on both sides of equation (17) is taken, the following equation (18) is obtained. To summarize this, the relationship between n and D is as shown in the following equation (19).

Then, when the number of bits of the digital data is 16 bits, 24 bits, and 32 bits, respectively, as shown in the following equations (20) to (22), the value of n adds 1 to half the number of bits of the data Can be approximated with a number.

This is the front and rear guard areas necessary for calculating Back Impulse and Front Impulse. That is, for digital data that is approximated to continue indefinitely from the past to the future, for Back Impulse on the past side of the interpolation target interval, the number of intervals obtained by adding 1 to half the number of bits of the input data is If the target is a section of the front side of the interpolation target section with a number obtained by adding 1 to half the number of bits of the input data, the spline function defined for the interpolation target section The coefficients a _j , b _j , and c _j can be obtained with high accuracy, and the interpolation target section can be interpolated.

これは積和算器の中間出力Ｂ（ｘ）、Ｃ（ｘ）を次式（２４）、（２５）のように定義し、積和算器を３つ並べて順次計算することにより、式（２６）に示すようにＳ_ｊ（ｘ）を求めることができる。

If the coefficients a _j , b _j , and c _j can be obtained, the data of the interpolation target section can be interpolated by executing the spline function. In order to execute the spline function, three product-sum calculators are required. Here, the spline function is modified as shown in the following equation (23).

This is because the intermediate outputs B (x) and C (x) of the product-sum calculator are defined as in the following formulas (24) and (25), and three product-sum calculators are arranged side by side and sequentially calculated. S _j (x) can be obtained as shown in FIG.

The calculation of B (x) can be performed in the difference format shown in the following equation (27). This is because B (x) changes linearly from b _j to 2 / 3b _j + 1 / 3b _{j + 1} because of the relationship shown in equation (13).

Since C (x) and S _j (x) do not have a linear relationship as in the above B (x), they are calculated by multiply-add. In this way, it is possible to reduce the hardware size by replacing a part of the product-sum operation with the accumulator method. In this embodiment, the data interpolation circuit 102 sets a spline curve based on the calculated S _j (x) for the interval between sample points, and interpolates at 31 points on the spline curve. By doing so, 32 times supersampling is realized with respect to the input digital data. As a result, the digital data sample points can be interpolated by connecting them with a smooth curve.

The data interpolation circuit 102 clips the value of S _j (x) to 1 when the calculated value of the spline function exceeds 1. For example, FIG. 5 shows an example in which the value of S _j (x) is clipped to 1 for the sections 5 a and 5 b where the value of S _j (x) exceeds 1. This is because there is generally no digital data that would overflow the DAC. If it becomes necessary to handle digital data that intentionally overflows the DAC, it is necessary to expand the dynamic range of the DAC.

  FIG. 6 is a diagram schematically showing a comparative example of the output result of the DAC device using a general digital filter and the output result of the data conversion device 100 in the present embodiment. The digital filter tries to express a square wave by combining continuous sine waves, but the expression of the square wave cannot be expressed because harmonics up to infinite dimensions are required. At this time, harmonics that cannot be expressed cover the square wave as distortion. This appears as a pre-echo 6a and a post-echo 6b shown in FIG. On the other hand, in the data conversion apparatus 100 according to the present embodiment, since interpolation is performed using a three-dimensional spline function, the problem that has occurred in the digital filter is solved, as shown in FIG. 6B. In addition, high sound quality can be achieved without generating noise such as pre-echo and post-echo.

  FIG. 7 is a flowchart of processing executed by the data interpolation circuit 102 in order to perform interpolation processing on input digital data. The process shown in FIG. 7 is executed by the data interpolation circuit 102 when digital data is input from the input interface 101. In the present embodiment, it is assumed that the input digital data is stereo digital data including two left and right channels. Further, the process shown in FIG. 7 is repeatedly executed for each section until the input of digital data is completed.

In step S10, as described above, the data interpolation circuit 102 calculates Back Impulse and Front Impulse as shown in the equations (20) to (22) according to the number of bits of the input digital data circuit. Back and front guard areas necessary for the above are specified, and Back Impulse (e _j ) and Front Impulse (f _j ) are calculated using the expressions (5) and (6) for the specified guard area. Then, it progresses to step S20.

In step S20, the data interpolation circuit 102 calculates the spline function coefficients a _j , b _j , and c _j as shown in the above-described equations (10) to (14). Then, it progresses to step S30.

In step S30, the data interpolation circuit 102 uses the calculation formulas shown in the equations (23) to (27) for each of the right channel and the left channel of the input digital data, and uses the spline function S _j (x ) Is calculated. Thereafter, the process proceeds to step S40.

In step S40, the data interpolation circuit 102 sets a spline curve based on S _j (x) calculated in step S30 for the section between the sample points, and sets 31 points on the spline curve. Interpolate with. Thereafter, the process proceeds to step S50.

In step S50, the data interpolation circuit 102 clips to 1 when S _j (x) calculated in step S30 exceeds 1. Thereafter, the process proceeds to step S60.

  In step S <b> 60, the data interpolation circuit 102 outputs the interpolated digital data to the D / A converter 103. Thereafter, the process ends.

According to the present embodiment described above, the following operational effects can be obtained.
(1) The data interpolation circuit 102 interpolates a section between two consecutive sample points of the input digital data using a spline function, and the D / A converter 103 interpolates the section to be interpolated. The result is converted to analog data and output. At this time, the data interpolation circuit 102 sets the coefficient of the spline function for the interpolation target section, a predetermined number of sections on the past side of the interpolation target section, and a predetermined number of sections on the future side of the interpolation target section. The spline function is defined using the calculated coefficient, and the interpolation target section is interpolated. Thereby, the coefficient of the spline function can be obtained for each section between the sample points of the digital data, and highly accurate interpolation can be performed according to the input digital data.

(2) The spline function is a spline function defined by a cubic function, and the data interpolation circuit 102 has a function value, a first derivative value, and a second derivative value at sample points in adjacent sections. The coefficient of the spline function is calculated using a formula that takes into account the continuity. Thus, by defining a spline function used for interpolation with a cubic function and solving the spline function so that the function value, the first derivative value, and the second derivative value in adjacent sections are continuous, higher accuracy is achieved. Interpolation can be possible.

(3) The data interpolation circuit 102 sets the number of past sections from the interpolation target section and the number of future sections from the interpolation target section according to the number of bits of the input digital data. The number of sections on the past side of the interpolation target section is a number obtained by adding 1 to half the number of bits of the input data on the past side of the interpolation target section, and the number of sections on the future side of the interpolation target section. Is a number obtained by adding 1 to half of the number of bits of input data on the future side of the interpolation target section. As a result, as described above, with respect to Back Impulse and Front Impulse defined by an infinite series, the calculation can be terminated at a finite number of times that the calculation result converges, and the three-dimensional spline function can be solved.

-Modification-
The data conversion apparatus 100 according to the above-described embodiment can be modified as follows.

(1) In the above-described embodiment, an example in which digital data is interpolated at 31 points on a spline curve set for each section will be described, but the number of interpolation points is not limited to this.

(2) In the above-described embodiment, the example in which the spline function is defined in three dimensions has been described. However, it is also possible to perform interpolation by lowering the order of the spline function. For example, in the case of a quadratic expression, the following expressions (28) to (30) are obtained. In this case, the value of b _j is determined so as to hit the next d _{j + 1} by using the value of C _j (= the slope of the function) when the coefficient of the spline function is calculated as it is.

Further, as shown in the following equations (31) and (32), if the sample points and the sample points are connected by a straight line, the primary interpolation is performed. In the case of linear interpolation, the front and rear guard areas are not necessary, and the sound becomes rough but becomes a good sound.

(3) In the above-described embodiment, the description has been made on the assumption that the D / A converter having the same number of bits as the number of bits of the digital audio data is used. However, by using the sigma delta technique, Can also be applied to a D / A converter with a reduced number of bits.

(4) In the above-described embodiment, the example of performing DA conversion on digital audio data has been described. However, the present invention can be applied not only to digital audio data but also to general DA conversion.

(5) In the above-described embodiment, the data interpolation circuit 102 determines the number of sections in the past from the interpolation target section and the section in the future from the interpolation target section according to the number of bits of the input digital data. The number of sections on the past side of the interpolation target section is a number obtained by adding 1 to half the number of bits of the input data on the past side of the interpolation target section. In addition, the number of sections on the future side is set to the number obtained by adding 1 to half the number of bits of the input data on the future side with respect to the interpolation target section. However, it is necessary and sufficient that the number of the sections on the past side of the interpolation target section and the number of the sections on the future side of the interpolation target section are set to the number obtained by adding 1 to half the number of bits. It is possible to make it more than this. If the accuracy is not lowered, it can be simplified to a number smaller than this.

(6) In the embodiment described above, α in the infinite series defined by the equations (5) and (6) is assumed to be a constant represented by the equation (7). However, the circuit shown in Equation (7) can be simplified by approximating α = −1 / 4, for example.

  Note that the present invention is not limited to the configurations in the above-described embodiments as long as the characteristic functions of the present invention are not impaired. Moreover, it is good also as a structure which combined the above-mentioned embodiment and a some modification.

DESCRIPTION OF SYMBOLS 100 Data converter 101 Input interface 102 Data interpolation circuit 103 D / A converter

Claims (8)

A data interpolation device for interpolating input digital data,
Interpolation means for interpolating a section between two consecutive sample points of the input digital data using a spline function;
Output means for outputting an interpolation result by the interpolation means of the interpolation target section,
The interpolation means calculates the coefficient of the spline function for an interpolation target section, a predetermined number of sections on the past side of the interpolation target section, and a predetermined number of sections on the future side of the interpolation target section. And defining the spline function using the calculated coefficient and interpolating the interpolation target section. The data interpolation device according to claim 1, wherein
The spline function is a spline function defined by a cubic function,
The interpolation means calculates the coefficient of the spline function using a calculation formula that takes into account that the function value, the primary differential value, and the secondary differential value are continuous at sample points in adjacent sections. A data interpolation device characterized by the above. The data interpolation device according to claim 1 or 2,
The interpolation means sets the number of sections on the past side of the interpolation target section and the number of sections on the future side of the interpolation target section according to the number of bits of the input digital data. A data interpolation device. The data interpolation apparatus according to claim 3, wherein
The number of sections on the past side of the interpolation target section is a number obtained by adding 1 to half the number of bits of input data on the past side of the interpolation target section, and a section on the future side of the interpolation target section. Is a number obtained by adding 1 to half of the number of bits of input data on the future side of the interpolation target section. A data interpolation method for interpolating input digital data,
An interpolation procedure for interpolating a section between two consecutive sample points of the input digital data using a spline function;
Causing the arithmetic unit to execute an output procedure for outputting an interpolation result by the interpolation procedure of the interpolation target section;
The interpolation procedure calculates the coefficient of the spline function for an interpolation target section, a predetermined number of sections on the past side of the interpolation target section, and a predetermined number of sections on the future side of the interpolation target section. And defining the spline function using the calculated coefficient to interpolate the interpolation target section. The data interpolation method according to claim 5, wherein
The spline function is a spline function defined by a cubic function,
In the interpolation procedure, the coefficient of the spline function is calculated using a calculation formula that takes into account that the function value, the primary differential value, and the secondary differential value continue at sample points in adjacent sections. A data interpolation method characterized by the above. The data interpolation method according to claim 5 or 6,
The interpolation procedure sets the number of sections on the past side of the interpolation target section and the number of sections on the future side of the interpolation target section according to the number of bits of the input digital data. Data interpolation method. The data interpolation method according to claim 7, wherein
The number of sections on the past side of the interpolation target section is a number obtained by adding 1 to half the number of bits of input data on the past side of the interpolation target section, and a section on the future side of the interpolation target section. Is a number obtained by adding 1 to half of the number of bits of input data on the future side of the interpolation target section.

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