CN105974997B - A kind of Digital Implementation method of sine wave signal - Google Patents

Abstract

The invention relates to a digital realization method of a sine wave signal, specifically: first setting parameters, then calculating the number of sampling points N of a sine wave signal cycle and the angle value θ occupied by a sampling point; and then calculating sin(θ) and the values of cos(θ) and sin(2θ) and cos(2θ); then calculate the discrete point value f ₀ of the sine wave signal; then send the discrete point value f ₀ of the sine wave signal into the DAC conversion circuit to generate a continuous The sine wave current signal; finally, the UA operational amplifier is used to convert the continuous sine wave current signal into a continuous sine wave voltage signal, so as to realize the output of the sine wave signal. The sine wave signal digital implementation method of the present invention simplifies the calculation program, reduces the calculation time of the DSP controller; effectively reduces the cumulative error caused by continuous recursive calculation, and occupies a small storage space and low cost; it can be conveniently Calculate the initial sine function value and cosine function value, and flexibly adjust the frequency of the sine wave signal.

Description

A Digital Realization Method of Sine Wave Signal

technical field

The invention belongs to the field of realization of wave signals, in particular to a digital realization method of sine wave signals.

Background technique

Sine wave signal generators have been widely used in signal processing systems in the fields of communication, instrumentation, and industrial control. There are many digital implementation methods for generating sine wave signals based on DSP controller, the difference mainly lies in the difference of generation algorithm and software. There are three commonly used methods: look-up table method, Taylor series expansion method and iteration method.

The look-up table method is the most direct digital implementation method. The designer can pre-calculate all possible sine function values according to the needs of the operation, and arrange these results into a data table. The function value of . The table look-up method is characterized by fast speed and easy frequency and amplitude modulation, but it needs to occupy a large amount of storage space and has low flexibility.

The Taylor series expansion method is a digital implementation method that uses polynomials to approximate the sine function. The waveform of the sine wave can be regarded as composed of countless points. These points correspond to each angle value θ of the x-axis and can be processed by a DSP processor. The advantages of a large number of repeated calculations (multiplication and addition operations) are used to calculate the value of y corresponding to each point on the x-axis (if N points are taken on the x-axis for approximation, then θ=2π/N). The accuracy of Taylor series calculation depends on the number of expansion items and the angle value θ corresponding to the point: the more the number of expansion items, the higher the accuracy, but the longer the calculation time, the more time it takes for the DSP controller; the smaller the angle value θ corresponding to the point , the higher the accuracy is, but the accuracy will inevitably decrease as the angle value θ corresponding to the point increases.

In order to overcome the above shortcomings, some scholars have improved the Taylor series expansion method considering the fact that the calculation results of the sine function can be reused. First, use the Taylor series expansion method to calculate the sine and cosine values from 0 to π/4, and save the above calculation results; secondly, use the sin(2θ)=2sin(θ)cos(θ) formula to find the sine and cosine values from 0 to π/2 Sine value; finally, the sine value of 0~2π is obtained by copying, and the sine wave can be obtained by repeatedly outputting this value. It can be seen from this that the improved Taylor series expansion method uses the method of combining the Taylor series expansion method and the look-up table method, and overcomes the problem that the point-corresponding angle value θ of the point-corresponding angle value range of the Taylor series expansion method overcomes the The disadvantage that the value of θ increases and the accuracy decreases, but at the same time, it introduces the disadvantage that the look-up table method takes up a large amount of storage space, and it does not change the inherent disadvantage of the Taylor series expansion method that the calculation time is longer due to the more expansion items.

The iterative method is a digital implementation method that uses a digital oscillator to generate a sine wave through an iterative algorithm. Its key is the recursive relationship between function values, that is, the differential equation of the system or the system function model. If the system function of a discrete-time system has no zero point, but only a pair of conjugate poles on the unit circle, its unit impulse response is a constant amplitude oscillation, that is, a sinusoidal signal is generated. The sine function recursion formula of the iterative algorithm is: sin(nθ)=2cos(θ)sin[(n-1)θ]-sin[(n-2)θ]. In the formula, θ=2π/N, N=f _s /f is the number of points used in a sine wave cycle, f _s is the sampling frequency, f is the frequency of the sine wave, and n is the serial number of the sampling point. In the iterative method, as long as the values of sin(θ) and cos(θ) are preset first, all subsequent sin(nθ) can be calculated and sent to the DAC conversion circuit to generate a continuous sine wave signal. Since the iterative method is to generate the discrete point value of the sine wave in real time, it occupies relatively less storage space, and the operation time is short, which in turn occupies the shorter time of the DSP controller. However, since the new value is generated using the previous function value, there will be cumulative error, especially in the second half of the sine wave, the cumulative error will become larger and larger, and when the number of sampling points N is not large enough, the cumulative error will be will increase further. At the same time, since the values of sin(θ) and cos(θ) must be preset before the calculation of the recursive formula, the number of sampling points N cannot be changed, which affects the flexibility of the sine wave frequency f when the sampling frequency f _s is fixed adjust.

Contents of the invention

In order to overcome the deficiencies of the prior art, the present invention proposes a digital realization method of a sine wave signal, which effectively reduces the cumulative error caused by continuous recursive calculation, and occupies a small storage space and low cost; it can be easily calculated Output the initial sine function value and cosine function value, and flexibly adjust the frequency of the sine wave signal.

The purpose of the present invention and the solution to its technical problems are achieved by adopting the following technical solutions.

According to the digital realization method of a kind of sine wave signal proposed by the present invention, it comprises the following steps:

(1), setting parameters specifically include: setting frequency f and amplitude A of sine wave signal, setting sampling frequency f _s ;

(2), calculate the number of sampling points N of a sine wave signal cycle;

(3), calculate the angle value θ that a sampling point occupies;

(4), when the angle value θ is between [-0.2,+0.2], calculate the numerical value of sin (θ) and cos (θ) according to the approximate linear relationship between the angle value θ and the sine function sin (θ);

(5) Calculate the values of sin(2θ) and cos(2θ);

(6), according to the difference in the interval where the sampling point n is located, alternately use the recursive formula sin(nθ)=2cos(θ)sin[(n-1)θ]-sin[(n-2) of the sine function and the cosine function θ] and cos(nθ)=2cos(θ)cos[(n-1)θ]-cos[(n-2)θ] calculate the discrete point value f ₀ of the sine wave signal in real time;

(7), utilize the DSP controller to send the calculated sine wave signal discrete point value f ₀ into the DAC conversion circuit through the interface circuit to generate a continuous sine wave current signal;

(8) Finally, the UA operational amplifier is used to convert the continuous sine wave current signal into a continuous sine wave voltage signal, thereby realizing the output of the sine wave signal.

The purpose of the present invention and its technical problems can also be further realized by adopting the following technical measures.

The aforementioned digital implementation method of a sine wave signal, wherein the calculation formula used in step (2) is N=f _s /f.

In the above-mentioned digital realization method of a sine wave signal, the calculation formula used in step (3) is θ=2π/N.

The digital implementation method of the aforesaid sine wave signal, wherein, step (4) uses the formula sin(θ)≈θ to calculate the value of sin(θ), and uses the formula Calculate the value of cos(θ).

The digital realization method of a kind of aforementioned sine wave signal, wherein, step (5) utilizes formula sin(2θ)=2sin(θ)cos(θ) to calculate the numerical value of sin(2θ), utilizes formula cos(2θ)=[ cos(θ)+sin(θ)][cos(θ)-sin(θ)] calculates the value of cos(2θ).

The digital realization method of aforesaid a kind of sine wave signal, wherein, the concrete algorithm of step (6) is:

Let f _1s =sin(θ), f _1c =cos(θ), f _2s =sin(2θ), f _2c =cos(2θ); n=1;

①When the sampling point n is in the [1,N/4] interval, let i=n:

If i=1, then f ₃ =f _1s , f ₀ =Af ₃ , f ₁ =f _1s ;

If i=2, then f ₃ =f _2s , f ₀ =Af ₃ , f ₂ =f _2s ;

If i≥3, then f ₃ =2f _1c f ₂ −f ₁ , f ₀ =Af ₃ , f ₁ =f ₂ , f ₂ =f ₃ ;

At the same time n=n+1;

If n≤N/4, repeat ①, otherwise transfer to ②;

②When the sampling point n is in the interval (N/4,N/2], set j=n-N/4:

If j=1, then f ₆ =f _1c , f ₀ =Af ₆ , f ₄ =f _1c ;

If j=2, then f ₆ =f _2c , f ₀ =Af ₆ , f ₅ =f _2c ;

If j≥3, then f ₆ =2f _1c f ₅ −f ₄ , f ₀ =Af ₆ , f ₄ =f ₅ , f ₅ =f ₆ ;

At the same time n=n+1;

If n≤N/2, repeat ②, otherwise transfer to ③;

③ When the sampling point n is in the interval (N/2, 3N/4], let i=n-N/2:

If i=1, then f ₃ =-f _1s , f ₀ =Af ₃ , f ₁ =-f _1s ;

If i=2, then f ₃ =-f _2s , f ₀ =Af ₃ , f ₂ =-f _2s ;

If i≥3, then f ₃ =2f _1c f ₂ −f ₁ , f ₀ =Af ₃ , f ₁ =f ₂ , f ₂ =f ₃ ;

At the same time n=n+1;

If n≤3N/4, repeat ③, otherwise transfer to ④;

④ When the sampling point n is in the (3N/4,N] interval, set j=n-3N/4:

If j=1, then f ₆ =-f _1c , f ₀ =Af ₆ , f ₄ =-f _1c ;

If j=2, then f ₆ =-f _2c , f ₀ =Af ₆ , f ₅ =-f _2c ;

If j≥3, then f ₆ =2f _1c f ₅ −f ₄ , f ₀ =Af ₆ , f ₄ =f ₅ , f ₅ =f ₆ ;

At the same time n=n+1;

If n≤N, execute ④ repeatedly, otherwise, set n=1, turn to ①, and start the next cycle of the sine wave signal.

The digital realization method of a kind of aforementioned sine wave signal, wherein, described method is realized by the circuit system that generates sine wave signal, and this circuit system comprises: keyboard input circuit, DSP controller, interface circuit, DAC conversion circuit and UA operational amplifier ; Wherein, the output end of the keyboard input circuit is connected with the DSP controller, the output end of the DSP controller is connected with the interface circuit, the output end of the interface circuit is connected with the DAC conversion circuit, the output end of the DAC conversion circuit is connected with the UA operational amplifier, and the UA The operational amplifier outputs a sine wave signal.

The interface circuit is a circuit that buffers the speed difference between the DSP controller and the DAC conversion circuit to ensure that the discrete point values of the sine wave signal are accurately and reliably sent to the DAC conversion circuit.

The DAC conversion circuit converts the discrete point value of the sine wave signal input through the interface circuit into a continuous sine wave current signal.

The UA operational amplifier converts a continuous sinusoidal current signal into a continuous sinusoidal voltage signal.

Compared with the prior art, the present invention has obvious advantages and beneficial effects. With the above-mentioned technical scheme, a digital realization method of a sine wave signal in the present invention can achieve considerable technical advancement and practicability, and has wide industrial application Utilization value, which has at least the following advantages:

(1), the present invention utilizes the approximate linear relationship of angle value θ and sine function sin (θ), rather than utilizing Taylor series expansion formula, calculates initial sine function value and cosine function value, simplifies calculation program, thereby reduces The calculation time of the DSP controller is reduced;

(2), the present invention calculates the discrete point value of sine wave signal in real time by using the recursive formula of sine function and cosine function alternately by DSP controller according to the difference in the interval of sampling point n, instead of only using sine like iterative method The function recursive formula reduces the cumulative error caused by the continuous recursive calculation of the recursive formula, and because the discrete point value of the sine wave signal is calculated in real time, it does not occupy a large amount of storage space like the look-up table method, thereby reducing the need for DSP The occupancy of the controller storage space reduces the cost;

(3), the present invention owing to can calculate initial sine function value and cosine function value easily, does not need to preset initial sine function value and cosine function value like iterative method, sampling point number N can change, thus even if When the sampling frequency f _s is fixed, the frequency of the sine wave signal can still be adjusted flexibly.

To sum up, the digital realization method of a sine wave signal of the present invention has significant technical progress, and has obvious positive effects. It is a novel, progressive and practical new design.

The above description is only an overview of the technical solution of the present invention. In order to better understand the technical means of the present invention, it can be implemented according to the contents of the description, and in order to make the above and other purposes, features and advantages of the present invention more obvious and understandable , the following preferred embodiments are specifically cited below, and are described in detail as follows in conjunction with the accompanying drawings.

Description of drawings

Fig. 1 is a circuit system diagram of the digital realization method of the sine wave signal of the present invention.

Fig. 2 is an approximate linear relationship diagram between the angle value θ and the sine function sin(θ) in the present invention.

Detailed ways

In order to further explain the technical means and effects that the present invention adopts to achieve the intended purpose of the invention, below in conjunction with the accompanying drawings and preferred embodiments, a digital implementation method for a sine wave signal proposed according to the present invention, its specific implementation, Structure, characteristic and effect thereof are as follows in detail.

The digital implementation method of a kind of sine wave signal of the present invention, in conjunction with shown in Fig. 1, on hardware circuit structure, comprise: keyboard input circuit, DSP controller, interface circuit, DAC conversion circuit and UA operational amplifier; On software structure Including the angle value θ and the sine function sin(θ). Among them: the main purpose of the keyboard input circuit is to set the frequency and amplitude of the sine wave signal, as well as the sampling frequency. The DSP controller calculates the discrete point value of the sine wave signal according to the frequency, amplitude and sampling frequency of the sine wave signal set by the keyboard input circuit, and at the same time sends the discrete point value to the DAC conversion circuit through the interface circuit. The interface circuit is used to buffer the speed difference between the DSP controller and the DAC conversion circuit, so as to ensure that the discrete point value of the sine wave signal is accurately and reliably sent to the DAC conversion circuit. The DAC conversion circuit is mainly used to convert the discrete point value of the sine wave signal sent through the interface circuit into a continuous sine wave current signal. If the required sine wave signal is a voltage signal, it is necessary to use the UA operational amplifier to convert the continuous sine wave current signal into a continuous sine wave voltage signal.

A kind of digital realization method of sine wave signal is to realize the system by above-mentioned sine wave number, at first calculate the sampling point number N of a sine wave signal period according to the ratio of sampling frequency f _s and sine wave frequency f, utilize formula θ=2π/ N calculates the angle value θ occupied by one sampling point. Use the approximate linear relationship between the angle value θ and the sine function sin(θ) to calculate the value of the sine function sin(θ), and use the formula cos(θ)≈1-0.5θ ² to calculate the value of the cosine function cos(θ). Then, utilize DSP controller, in the interval of sampling point n=[1, N/4], use the recursive formula of sine function to calculate the discrete point value of sine wave signal; At sampling point n=(N/4, N/ 2] interval, use the recursive formula of the cosine function to calculate the discrete point value of the sine wave signal; in the sampling point n=(N/2, 3N/4] interval, use the recursive formula of the sine function to calculate the value of the sine wave signal Discrete point value; in the sampling point n=(3N/4, N] interval, use the recursive formula of the cosine function to calculate the discrete point value of the sine wave signal. Finally, the discrete point value of the sine wave signal is converted into Continuous sine wave signal, so as to realize the output of sine wave signal. The circuit block diagram of the sine wave signal digital realization system is shown in Figure 1.

The Taylor series expansion method is to use the Taylor series expansion formula to calculate the value of the sine function sin(θ) and the cosine function cos(θ), which requires multiple multiplication and addition operations of the DSP controller to complete the sine function sin(θ) and Calculation of the cosine function cos(θ); Although the iterative method can preset the values of the sine function sin(θ) and the cosine function cos(θ), the flexibility of changing the frequency of the sine wave signal is limited.

In general, the relationship between the angle value θ and the sine function sin(θ) is nonlinear. But when the angle value θ is between [-0.2,+0.2], the relationship between the angle value θ and the sine function sin(θ) is almost linear, and Figure 2 reflects the relationship between the angle value θ and the sine function sin(θ) Approximate linear relationship. It can be seen from Figure 2 that when the angle value θ is relatively small, the relationship between the angle value θ and the sinusoidal function sin(θ) is approximately linear. Therefore, in the case of ensuring that the angle value θ is relatively small, the approximate linear relationship sin(θ)≈θ between the angle value θ and the sine function sin(θ) can be used to directly obtain the value of the sine function sin(θ) as θ, The value of the sine function sin(θ) can be directly obtained without calculation, which simplifies the calculation procedure and reduces the burden on the DSP controller; while the cosine function cos(θ) only needs three multiplications and one subtraction, and can be passed The formula cos(θ)≈1-0.5θ ² is calculated, which is much smaller than the amount of calculation used by the Taylor series expansion formula. Therefore, the digital implementation method of this sine wave signal not only overcomes the shortcomings of the large amount of calculation of the Taylor series expansion method, but also overcomes the shortage of the look-up table method taking up a large amount of storage space, and has a sine wave signal frequency that the iterative method does not have. Adjustment flexibility.

The above description is only a preferred embodiment of the present invention, and does not limit the present invention in any form. Although the present invention has been disclosed as above with preferred embodiments, it is not intended to limit the present invention. Anyone familiar with this field Those skilled in the art, without departing from the scope of the technical solution of the present invention, can use the technical content disclosed above to make some changes or modify equivalent embodiments with equivalent changes. Any simple modifications, equivalent changes and modifications made to the above embodiments by the technical essence still belong to the scope of the technical solution of the present invention.

Claims (7)

1. A digital realization method of a sine wave signal, characterized in that it comprises the following steps: (1), setting parameters specifically include: setting frequency f and amplitude A of sine wave signal, setting sampling frequency f _s ; (2), calculate the number of sampling points N of a sine wave signal period; (3), calculate the angle value θ that a sampling point occupies; (4), when the angle value θ is between [-0.2,+0.2], calculate the values of sin(θ) and cos(θ) according to the approximate linear relationship between the angle value θ and the sine function sin(θ), Specifically: sin(θ)≈θ, (5), calculate the value of sin(2θ) and cos(2θ), wherein, sin(2θ)=2sin(θ)cos(θ), cos(2θ)=[cos(θ)+sin(θ)][ cos(θ)-sin(θ)]; (6), according to the difference in the interval where the sampling point n is located, alternately use the recursive formula sin(nθ)=2cos(θ)sin[(n-1)θ]-sin[(n-2) of the sine function and the cosine function θ] and cos(nθ)=2cos(θ)cos[(n-1)θ]-cos[(n-2)θ] calculate the discrete point value f ₀ of the sine wave signal in real time; its specific algorithm is: Let f _1s =sin(θ), f _1c =cos(θ), f _2s =sin(2θ), f _2c =cos(2θ); n=1; ①When the sampling point n is in the [1,N/4] interval, let i=n: If i=1, then f ₃ =f _1s , f ₀ =Af ₃ , f ₁ =f _1s ; If i=2, then f ₃ =f _2s , f ₀ =Af ₃ , f ₂ =f _2s ; If i≥3, then f ₃ =2f _1c f ₂ −f ₁ , f ₀ =Af ₃ , f ₁ =f ₂ , f ₂ =f ₃ ; At the same time n=n+1; If n≤N/4, repeat ①, otherwise transfer to ②; ②When the sampling point n is in the interval (N/4,N/2], set j=n-N/4: If j=1, then f ₆ =f _1c , f ₀ =Af ₆ , f ₄ =f _1c ; If j=2, then f ₆ =f _2c , f ₀ =Af ₆ , f ₅ =f _2c ; If j≥3, then f ₆ =2f _1c f ₅ −f ₄ , f ₀ =Af ₆ , f ₄ =f ₅ , f ₅ =f ₆ ; At the same time n=n+1; If n≤N/2, repeat ②, otherwise transfer to ③; ③ When the sampling point n is in the interval (N/2, 3N/4], let i=n-N/2: If i=1, then f ₃ =-f _1s , f ₀ =Af ₃ , f ₁ =-f _1s ; If i=2, then f ₃ =-f _2s , f ₀ =Af ₃ , f ₂ =-f _2s ; If i≥3, then f ₃ =2f _1c f ₂ −f ₁ , f ₀ =Af ₃ , f ₁ =f ₂ , f ₂ =f ₃ ; At the same time n=n+1; If n≤3N/4, repeat ③, otherwise transfer to ④; ④ When the sampling point n is in the (3N/4,N] interval, set j=n-3N/4: If j=1, then f ₆ =-f _1c , f ₀ =Af ₆ , f ₄ =-f _1c ; If j=2, then f ₆ =-f _2c , f ₀ =Af ₆ , f ₅ =-f _2c ; If j≥3, then f ₆ =2f _1c f ₅ −f ₄ , f ₀ =Af ₆ , f ₄ =f ₅ , f ₅ =f ₆ ; At the same time n=n+1; If n≤N, repeat ④, otherwise, set n=1, turn to ①, and start the next sine wave signal cycle; (7), utilize the DSP controller to send the calculated sine wave signal discrete point value f ₀ into the DAC conversion circuit through the interface circuit to generate a continuous sine wave current signal; (8) Finally, the UA operational amplifier is used to convert the continuous sine wave current signal into a continuous sine wave voltage signal, thereby realizing the output of the sine wave signal. 2. The method according to claim 1, characterized in that the calculation formula used in step (2) is N=f _s /f. 3. The method according to claim 1, characterized in that the calculation formula used in step (3) is θ=2π/N. 4. The method according to claim 1, characterized in that said method is realized by generating a circuit system of sine wave signal, which circuit system comprises: keyboard input circuit, DSP controller, interface circuit, DAC conversion circuit and UA operational amplifier ; Wherein, the output end of the keyboard input circuit is connected with the DSP controller, the output end of the DSP controller is connected with the interface circuit, the output end of the interface circuit is connected with the DAC conversion circuit, the output end of the DAC conversion circuit is connected with the UA operational amplifier, and the UA The operational amplifier outputs a sine wave signal. 5. The method according to claim 4, characterized in that the interface circuit in the circuit system is to buffer the speed difference between the DSP controller and the DAC conversion circuit, so as to ensure that the discrete point value of the sine wave signal is accurately and reliably sent A circuit that enters the DAC conversion circuit. 6. The method according to claim 4, characterized in that the DAC conversion circuit in the circuit system converts the discrete point value of the sine wave signal sent in through the interface circuit into a continuous sine wave current signal. 7. The method of claim 4, wherein the UA operational amplifier in the circuit system converts the continuous sinusoidal current signal into a continuous sinusoidal voltage signal.