KR100782855B1 - Method and apparatus for converting sampled digital signal into natural sampled digital signal - Google Patents

Abstract

The present invention relates to a method and apparatus for converting a sampled digital signal into a naturally sampled digital signal, and the method according to the present invention relates to a method of converting a sampled digital signal into a naturally sampled digital signal. Receiving a signal, and determining a naturally sampled digital signal from the sampled digital signal using an interpolation function, wherein the naturally sampled digital signal is sampled from the sampled digital signal to determine the naturally sampled digital signal. It is characterized in that the step of determining repeatedly to perform a predetermined number of times. This saves resources and maintains good audio quality.

Description

Method and apparatus for converting a sampled digital signal to a natually samplled digital signal

1 is a block diagram of a PWM converter 100 according to an embodiment of the present invention.

2 is a harmonic spectrum at the output terminal of the PWM converter 104.

3 is a configuration diagram of the natural sampling converter 102 of FIG. 1.

4 illustrates the principle of natural sampling conversion.

5 is a conceptual diagram of an interpolation method by iterative operation according to an embodiment of the present invention.

FIG. 6 is a schematic diagram showing the structure of the natural sampling converter 102 of FIG.

7 shows the spectrum of demodulated PWM with uniform sampling.

8 shows the spectrum of demodulated PWM with natural sampling.

9 is a flowchart describing a method for converting a uniformly sampled digital signal into a naturally sampled digital signal in accordance with one embodiment of the present invention.

<Explanation of symbols for the main parts of the drawings>

100: digital audio amplifier

101: Up Sampler

102: natural sampling conversion unit

102a: coefficient calculation unit

102b: Natural Sampler

103: Noise Shaper

104: PWM converter

105: power stage

The present invention relates to a method and apparatus for converting a sampled digital signal into a naturally sampled digital signal, and more particularly, (a) receiving a sampled digital signal; And (b) determining a natural sampled digital signal from the sampled digital signal using an interpolation function, wherein the step (b) is performed a predetermined number of times to determine the natural sampled digital signal. It relates to a method to perform repeatedly.

Pure digital amplifiers for home or mobile applications are becoming a major component of modern audio systems. The main advantages of digital amplification are high efficiency power delivery to the speakers and good audio performance. The amplifier converts the digital audio stream into high and high power pulsed signals that directly drive the speaker without other active circuitry in between. Most speaker fronts have a demodulating L-C filter for the removal of high frequency signal components. Pulse Width Modulation (PWM) is the most common and appropriate technique for creating pulse streams. There is a lot of literature on the design problems and principles of PWM pure digital amplifiers.

On the other hand, conventional Pulsed Coded Modulation (PCM) -PWM converters cause high order harmonic distortion on the resulting output signals, and one method of causing such distortion is using uniform sampling.

An alternative method for uniform sampling to reduce distortion is called natural sampling. Natural sampling is a theoretically ideal technique for converting PCM signals into PWM signals. One prior art approximates natural sampling by performing repeated third order polynomial curve fitting. This method is potentially quite useful, but has not been widely used because the implementation typically requires a significant amount of processing time. That is, "natural sampling" requires an interpolation process that trades off between the accuracy of the results and the computational speed.

SUMMARY OF THE INVENTION The present invention has been made to solve the above problems, and by using an iterative method to solve the third order polynomial interpolation method, an object of the present invention is to provide a method and apparatus for providing a fast conversion rate up to a high frequency input have.

In order to achieve the above object, there is provided a method for converting a sampled digital signal into a naturally sampled digital signal, the method comprising the steps of: a) receiving a sampled digital signal; And (b) determining a natural sampled digital signal from the sampled digital signal using an interpolation function, wherein the step (b) is performed a predetermined number of times to determine the natural sampled digital signal. It is characterized by performing repeatedly.

Advantageously, step (b) comprises determining coefficients of said interpolation function using said sampled digital signal; And determining an intersection of the interpolation function and the reference signal.

Preferably, the interpolation function is a cubic polynomial, the sampled digital signal is a uniformly sampled digital signal, and the reference signal is a sawtooth wave.

According to a second aspect of the present invention, there is provided an apparatus for converting a sampled digital signal into a naturally sampled digital signal, the apparatus comprising: a coefficient calculator for determining a coefficient of an interpolation function using the sampled digital signal; And a natural sampler for determining a naturally sampled digital signal from the sampled digital signal using the interpolation function, wherein the natural sampler performs an iterative operation to determine the natural sampled digital signal. do.

Preferably, the interpolation function is a cubic polynomial and the sampled digital signal is a uniformly sampled digital signal.

According to a third aspect of the present invention, there is provided a computer-readable recording medium having recorded thereon a program for executing the method by a computer.

Hereinafter, a preferred embodiment of an apparatus and method for converting a sampled digital signal into a naturally sampled digital signal according to the present invention will be described in detail with reference to the accompanying drawings. In adding reference numerals to the components of the drawings, it should be noted that the same components are denoted by the same reference numerals as much as possible even if they are shown in different drawings. In addition, in the following description, many specific details are shown, such as components of a specific circuit, which are provided to help a more general understanding of the present invention, and the present invention may be practiced without these specific details. It is self-evident to those of ordinary knowledge in Esau. In describing the present invention, when it is determined that detailed descriptions of related known functions or configurations may obscure the gist of the present invention, the detailed description thereof will be omitted.

1 is a block diagram of a PWM converter 100 according to an embodiment of the present invention, an upsampler 101, a natural sampling converter 102, a noise shaper 103, a PWM converter 104, and a power stage. 105.

Referring to FIG. 1, the upsampler 101 increases the sampling frequency of the input stream to the sampling frequency of the PWM signal. This step broadens the frequency band and is necessary for proper noise shaper operation.

The natural sampling converter 102 is used to estimate the actual value of the input audio signal placed between given samples by converting the sampled digital signal into a natural sampled digital signal. It can be seen that for uniformly sampled streams it produces an audio band of PWM signals free from unwanted components generated in the digital domain, thus significantly improving system performance.

The noise shaper 103 quantizes the input stream with an acceptable accuracy and shifts the quantization noise from the audible spectral region to the high frequency band. Our model starts with 20-bit precision data quantized into an 8-bit stream.

The PWM converter 104 generates a new 1-bit digital stream (per channel) with 8-bit precision for every sample at the Fc rate. Thus, the minimum conditions for the clock frequency used by the modulator are as follows:

The PWM signal output from the PWM converter 104 is amplified by the power stage 105 and output.

2 is a harmonic spectrum at the output of the PWM converter 104. As can be seen in FIG. 2, the output signal of the PWM modulator has a series of harmonics with a mixture of audio-band signal and noise shaping components. The demodulation filter should suppress everything but audible ones.

3 is a block diagram of the natural sampling converter 102 of FIG. 1 and includes a coefficient calculator 102a and a natural sampler 102b.

The coefficient calculator 102a determines coefficients of the third order polynomial, which are interpolation functions, using the sampled digital signal.

The natural sampler 102b uses an interpolation function to determine the naturally sampled digital signal from the sampled digital signal, and as described below, the natural sampler may determine the period during which the natural sampled digital signal is determined. Perform an iterative operation.

4 illustrates a conversion principle of natural sampling, and FIG. 5 is a conceptual diagram of an interpolation method by iterative operation according to an embodiment of the present invention.

Reference numeral 400 denotes an ideal analog signal, reference numeral 410 denotes a sawtooth wave as a reference signal, reference numeral 510 denotes a polynomial which is an interpolation function, and reference numeral 500 denotes an iterative calculation process.

As shown, the PCM (Pulse Coded Modulated) data at the input of the digital amplifier is typically a series of samples uniformly distributed over time or uniformly sampled series US. A feature of PWM encoding requires a known series of actual signal values, or naturally sampled data NS, at the moments that intersect the sawtooth reference signal. It can easily be obtained in the analog implementation of a PWM encoder, but it is not simple in a digital amplifier. The goal of the natural sampling converter is to find NS values with acceptable resource consumption and maximum possible accuracy that depend only on the available US data.

The problem can be divided into two subtasks: (a) performing interpolation and (b) finding the intersection between the interpolation function and the reference signal. The simplest solution to the first problem is the polynomial interpolation approach. Since our experiments show that linear and quadratic interpolation functions are not satisfactory for harmonic performance, we chose a third-order (ie cubic) polynomial. In that case, the second subtask requires the solution of the cubic algebraic equation. The direct way to this solution is very complicated and not practical. Thus, we used a method of iterations. It is shown here that this method is adequate and provides fast conversion rates up to the highest frequency input.

3rd order polynomial interpolation CUBIC POLINOMIAL INTERPOLATION )

Consider some interval of an audio signal limited by four consecutive samples of US data. For simplicity we assume that the time intervals between successive samples are x (n + 1)-x (n) = 1 and choose as the counting origin at the left point of the interpolated region. Therefore, the interval of four points will be defined as {Y _-1 , Y ₀ , Y ₁ , Y ₂ } (see FIG. 5). Then set Yn ∈ [-1: 1]. Third-order interpolation polynomials and boundary conditions have the form

Where a, b, c, d are unknown variables and P ₀ , P ₁ are estimated derivatives of the analog signal at the boundaries.

Equation (3) is a 3-point formula for differential value estimation.

Solving Equation (3), it can be seen that the variables of the cubic polynomial are very simple functions of boundary conditions, as in Equation (4).

In the next step, we must find the intersection between the reference function g (x) and the function 2 having the following equation (5) during the considered interval (see FIG. 5).

In the following, there is only one intersection point in the interval, and it can be seen that it is clearly the solution of the following algebraic equation.

Suppose Equation (6) has more than one solution over a period. This means that the absolute value of the left derivative must be less than 1 at the intersection and otherwise greater than 1. Under the conditions of our system, we will prove that the latter statement is not true. If Q is the oversampling factor (Q = 8 in our system), and the input signal is the worst case 1. -1, 1, -2, ..., then the derivative of the left part of (6) is D ( The absolute value of x) can be upper estimated by the following inequality.

The last value is less than 1 for Q> 1, so | D (x) | <1/16 << 1 for Q = 8. Therefore, only one intersection point may exist in the interpolation interval, and the last problem is how to solve the equation (6) and find the intersection point.

Iterative Solving Algorithm ( ITERATIVE SOLVING ALGORITHM )

Since it is unnecessary to find the correct value, the direct solution of equation (6) is obviously not practical. Instead, an algorithm can be provided that can provide a trade-off between computational complexity and speed. There are many ways to such a problem.

Considering that the PWM amplifier uses clock frequencies higher than the sampling frequency of the audio stream (to operate in PWM modulators and other blocks), a time-sharing method that results from a simpler architecture instead of using a slower but more complex scheme. It is reasonable to use a time sharing method.

Iteration methods simply follow such data. The method produces a continuous method for the solution by iteration of the next map.

의 값으로부터 나온다. 첫 번째 초기 조건은 구간 [0;1]의 어떤 값으로도 세팅될 수 있는데, 그 이유는 스킴의 동작에 영향을 미치지 않기 때문이다. N은 하나의 구간에 대한 반복 횟수이며, 연산 정확성 및 속도 간의 필요한 트레이드-오프를 설정하기 위해 쉽게 변할 수 있다. Where X _n is the nth approach to the solution and X ₀ is the initial condition, which is an estimate of the intersection of the previous interval

Comes from the value of. The first initial condition can be set to any value in the interval [0; 1] because it does not affect the behavior of the scheme. N is the number of iterations for one interval and can easily be changed to set the required trade-off between computational accuracy and speed.

Equation (8) is a stable and unique solution according to equation (7) and is a well known stability theorem. The convergence rate of equation (8) is determined by | D (x) | and can be estimated more quickly by π / 2Q. Therefore, the worst case of the estimation error is as follows.

는 이전의 구간 추정 및 정확한 솔루션 거리(exact solution distance)이다. 이전의 교점 추정은 다음 구간에서의 교점에 대한 훌륭한 예측이기 때문에,

라는 점은 명백하다. 예를 들면, 만약 Q=8 및 N=8, R(N)<10^-6, 그리고 N=16, R(N)<10^-12이라면, 실제 값에 대한 근접한 근사화에 대한 매우 훌륭한 근사화를 제공할 것이다.here,

Is the previous interval estimation and the exact solution distance. Because the previous intersection estimate is a good prediction of the intersection in the next interval,

It is obvious. For example, if Q = 8 and N = 8, R (N) <10 ⁻⁶ , and N = 16, R (N) <10 ⁻¹² , they provide a very good approximation of close approximation to the actual value. something to do.

6 illustrates the structure of the natural sampling converter 102 of FIG.

Referring to FIG. 6, the natural sampling transforming unit 102 includes a polynomial coefficient calculating unit, a cubic polynomial block (Cubic_eq) 600, and an iterative feedback loop. The polynomial coefficient calculating unit corresponds to a left portion of the cubic polynomial block (Cubic_eq) 600 and may be configured from Equation (4). Meanwhile, the cubic polynomial block (Cubic_eq) 600 and the iterative feedback loop may be constructed from Equations (5) and (8).

The feedback and polynomial blocks have clock frequencies N times faster than the rest of the subsystem. The converter has a number of advantages, all of which are very simple 2 or 1/2 for hardware implementation, have only 4 memory cells and include only 5 multipliers, not dividers. Multiplication operations can be easily done by a Final State Machine (FSM) architecture using only one shared hardware multiplier.

The model described herein was implemented in hardware using an evaluation board based on Xlinx FPGA-based digital subsystems and proprietary power stages. It was also thoroughly verified by simulation.

7 shows the spectrum of 3 kHz harmonic input amplification for US PWM. It can be seen that strong harmonics have been created which greatly degrade audio quality.

8 shows the spectrum of demodulated PWM with natural sampling.

In Fig. 8 we can see the result of the natural sampling transform by our algorithm. The cubic interpolator significantly reduces the harmonics caused by uniformly sampled data, allowing THD + N <0.01% for practical applications.

The parasitic harmonic levels generated by the algorithm are shown in Table 1, where we can see the maximum harmonic levels. The results demonstrate the high stability and performance of the algorithm even for high-pitched tones.

Frequency, kHz H ² Lever, dB 3 -115 6 -100 9 -90 11 -85

9 is a flowchart describing a method for converting a sampled digital signal into a naturally sampled digital signal in accordance with an embodiment of the present invention.

Referring to FIG. 9, a digital signal sampled at step 1000 is received.

Step 1001 uses cubic polynomial interpolation to determine the naturally sampled digital signal. That is, the coefficients of the third-order polynomial, which is an interpolation function, are determined using a uniformly sampled digital signal, and the intersection point of the interpolation function and the reference signal is determined.

In step 1002, step 1001 is repeatedly performed a predetermined number of times.

Thereafter, the natural sampled signal in step 1003 generates a PWM signal through the noise shaper 103 and the PWM converter 104.

Although the preferred embodiments of the present invention have been described in detail above, those of ordinary skill in the art to which the present invention pertains may make various changes without departing from the spirit and scope of the present invention as defined in the appended claims. It will be appreciated that modifications or variations may be made. Therefore, changes in the future embodiments of the present invention will not be able to escape the technology of the present invention.

As described above, by using an iterative method to solve an iterative cubic polynomial interpolation method, it is possible to provide a method and apparatus for providing a fast conversion speed up to a high frequency input.

In addition, the natural sampling transform proposed in this specification allows the converter to operate while maintaining excellent audio quality while saving processing resources. In addition, the proposed architecture of the natural sampler proposed herein provides an acceptable and robust solution.

Claims (9)

A method of converting a sampled digital signal into a naturally sampled digital signal, (a) receiving a sampled digital signal; And (b) determining a naturally sampled digital signal from the sampled digital signal using an interpolation function; And repeatedly performing the step (b) a predetermined number of times to determine the natural sampled digital signal. The method of claim 1, wherein step (b) Determining coefficients of the interpolation function using the sampled digital signals; And Determining an intersection of the interpolation function and a reference signal. The method of claim 1, wherein the interpolation function A third order polynomial. The method of claim 1, wherein the sampled digital signal is And a digitally sampled digital signal. The method of claim 2, wherein the reference signal is A sawtooth wave. An apparatus for converting a sampled digital signal into a naturally sampled digital signal, A coefficient calculator which determines coefficients of an interpolation function using the sampled digital signals; And A natural sampler for determining a naturally sampled digital signal from the sampled digital signal using the interpolation function, The natural sampler And perform an iterative operation to determine the naturally sampled digital signal. The method of claim 1, wherein the interpolation function And a third order polynomial. The method of claim 1, wherein the sampled digital signal is And a digitally sampled digital signal. A computer-readable recording medium having recorded thereon a program for executing the method of any one of claims 1 to 5 by a computer.

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