CN105974997B - A kind of Digital Implementation method of sine wave signal - Google Patents
A kind of Digital Implementation method of sine wave signal Download PDFInfo
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Abstract
The present invention relates to a kind of Digital Implementation methods of sine wave signal, specially：Then first setup parameter calculates the sampling number N and the occupied angle value θ of a sampled point in a sine wave signal period；The numerical value of sin (θ) and cos (θ) and sin (2 θ) and cos (2 θ) are calculated again；Then the discrete point value f of sine wave signal is calculated0；Again the discrete point value f of sine wave signal0DAC conversion circuits are sent into, continuous sine-wave current signal is generated；Continuous sine-wave current signal is finally converted into continuous sine voltage signal using UA operational amplifiers, to realize the output of sine wave signal.The sine wave signal Digital Implementation method of the present invention simplifies calculation procedure, reduces the calculating time of dsp controller；Accumulated error caused by continuous recurrence calculation is effectively reduced, and the memory space occupied is small, it is at low cost；Initial sine function and cosine function value can be easily calculated, the frequency of sine wave signal is neatly adjusted.
Description
Technical field
The invention belongs to the realization fields of wave signal, more particularly to a kind of Digital Implementation method of sine wave signal.
Background technology
Sine wave signal generator has been widely used at the signals in fields such as communication, instrument and meter and Industry Control
In reason system.Based on dsp controller generate sine wave signal Digital Implementation method it is very much, difference essentially consist in generate algorithm and
The difference of software.There are three ways to common：Look-up table, Taylor series expansion method and iterative method.
Look-up table is a kind of most direct Digital Implementation method, and designer can be according to the precalculated institute of needs of operation
It is possible that the sine function occurred, by these result layouts at tables of data, as long as finding right in table according to input when in use
The functional value answered.The characteristics of look-up table, is that speed is fast, FM amplitude modulation is easy, but needs to occupy a large amount of memory space, and
Flexibility ratio is low.
Taylor series expansion method is a kind of Digital Implementation method using approximation by polynomi-als SIN function, the waveform of sine wave
It is considered as being made of numerous points, these points are corresponding with each angle value θ of x-axis, dsp processor can be utilized to handle big
Amount computes repeatedly the advantage of (multiply-add operation) to calculate the value of the corresponding y of x-axis every bit (if taking N number of point to be forced in x-axis
Closely, then θ=2 π/N).The precision of taylor series computation depends on expansion item number and point corresponding angles angle value θ：It is more smart that item number is unfolded
Degree is higher, but the calculating time is longer, and the time for occupying dsp controller is more；Point corresponding angles angle value θ is smaller, and precision is higher, but
With an increase of corresponding angles angle value θ, precision also necessarily declines.
In order to overcome disadvantage mentioned above, considers the characteristics of result of calculation of SIN function can be multiplexed, have scholar to Taylor's grade
The number method of development is improved.First, the sine and cosine value of 0~π/4 are calculated with Taylor series expansion method, preserve above calculate
As a result；Secondly, the sine value of 0~pi/2 is found out using sin (2 θ)=2sin (θ) cos (θ) formula；Finally, by replicate obtain 0~
The sine value of 2 π, repetition export the value and can be obtained by sine wave.It will thus be seen that improved Taylor series expansion method utilizes Thailand
The method that Series Expansion Method is combined with look-up table is strangled, Taylor series are overcome by the value range of diminution point corresponding angles angle value θ
The method of development increases with a corresponding angles angle value θ the shortcomings that accuracy decline, but introduces look-up table simultaneously and occupies a large amount of storages
The shortcomings that space, and cause to calculate time longer intrinsic since expansion item number without changing Taylor series expansion method
Disadvantage.
Iterative method is to generate the Digital Implementation method of sine wave by iterative algorithm using digital oscillator, its key is
Recurrence relation between functional value, that is, the difference equation of system or system function model.If a discrete-time system
System function there is no a zero, only a pair of be on unit circle grips pole altogether, then its unit impulse response is that permanent amplitude is shaken
It swings, that is, produces sinusoidal signal.The SIN function recurrence formula of iterative algorithm is：Sin (n θ)=2cos (θ) sin [(n-1) θ]-
sin[(n-2)θ].In formula, θ=2 π/N, N=fs/ f is in a sine wave period using points, fsFor sample frequency, f is
Sine wave freuqency, n are the serial number of sampled point.As long as the numerical value of iterative method preset first sin (θ) and cos (θ), so that it may to calculate
Go out below all sin (n θ), and is sent into DAC conversion circuits and produces continuous sine wave signal.Iterative method is due to being real
Shi Shengcheng generates the discrete point value of sine wave, thus the memory space occupied is relatively fewer, and operation time is short and then occupies DSP
The time of controller is also shorter.But since new numerical value generates the functional value before being utilized, accumulated error is will produce,
Especially in the latter half of sine wave, accumulated error can be increasing, and when sampling number N is not sufficiently large,
The accumulation of error can further increase.Simultaneously as recurrence formula calculating before will preset first sin (θ) and cos (θ) number
Value, thus cause sampling number N immutable, in sample frequency fsIn the case of fixed, the flexible tune of sine wave freuqency f is influenced
Section.
Invention content
In order to overcome the deficiencies of the prior art, the present invention proposes a kind of Digital Implementation method of sine wave signal, effectively subtracts
Accumulated error caused by small continuous recurrence calculation, and the memory space occupied is small, it is at low cost；It can easily calculate just
The sine function and cosine function value of beginning neatly adjusts the frequency of sine wave signal.
The object of the invention to solve the technical problems is realized using following technical scheme.
A kind of Digital Implementation method of the sine wave signal proposed according to the present invention comprising following steps：
(1), setup parameter specifically includes：Set the frequency f and amplitude A of sine wave signal, setting sample frequency fs；
(2), the sampling number N in a sine wave signal period is calculated；
(3), the occupied angle value θ of a sampled point is calculated；
(4), when angle value θ is between [- 0.2 ,+0.2], according to the proximal line of angle value θ and SIN function sin (θ)
Sexual intercourse calculates the numerical value of sin (θ) and cos (θ)；
(5), the numerical value of sin (2 θ) and cos (2 θ) are calculated；
(6), according to the difference in section where sampled point n, the recurrence formula sin of SIN function and cosine function is used alternatingly
(n θ)=2cos (θ) sin [(n-1) θ]-sin [(n-2) θ] and cos (n θ)=2cos (θ) cos [(n-1) θ]-cos [(n-2) θ]
The discrete point value f of sine wave signal is calculated in real time0；
(7), using dsp controller the discrete point value f of calculated sine wave signal0It is sent into DAC by interface circuit
Conversion circuit generates continuous sine-wave current signal；
(8), continuous sine-wave current signal is finally converted into continuous sine voltage using UA operational amplifiers
Signal, to realize the output of sine wave signal.
The object of the invention to solve the technical problems also can be used following technical measures and further realize.
The Digital Implementation method of a kind of sine wave signal above-mentioned, wherein the calculation formula used in step (2) is N=fs/
f。
A kind of Digital Implementation method of sine wave signal above-mentioned, wherein calculation formula used in step (3) be the π of θ=2/
N。
The Digital Implementation method of a kind of sine wave signal above-mentioned, wherein step (4) is calculated using formula sin (θ) ≈ θ
The numerical value of sin (θ), utilizes formulaCalculate the numerical value of cos (θ).
The Digital Implementation method of a kind of sine wave signal above-mentioned, wherein step (5) utilizes formula sin (2 θ)=2sin (θ)
Cos (θ) calculates the numerical value of sin (2 θ), is calculated using formula cos (2 θ)=[cos (θ)+sin (θ)] [cos (θ)-sin (θ)]
The numerical value of cos (2 θ).
The Digital Implementation method of a kind of sine wave signal above-mentioned, wherein the specific algorithm of step (6) is：
Enable f1s=sin (θ), f1c=cos (θ), f2s=sin (2 θ), f2c=cos (2 θ)；N=1；
1. sampled point n enables i=n at [1, N/4] section：
If i=1, f3=f1s, f0=Af3, f1=f1s；
If i=2, f3=f2s, f0=Af3, f2=f2s；
If i >=3, f3=2f1cf2-f1, f0=Af3, f1=f2, f2=f3；
N=n+1 simultaneously；
If n≤N/4, repeat 1., is otherwise transferred to 2.；
2. sampled point n (N/4, N/2] section when, enable j=n-N/4：
If j=1, f6=f1c, f0=Af6, f4=f1c；
If j=2, f6=f2c, f0=Af6, f5=f2c；
If j >=3, f6=2f1cf5-f4, f0=Af6, f4=f5, f5=f6；
N=n+1 simultaneously；
If n≤N/2, repeat 2., is otherwise transferred to 3.；
3. sampled point n (N/2,3N/4] section when, enable i=n-N/2：
If i=1, f3=-f1s, f0=Af3, f1=-f1s；
If i=2, f3=-f2s, f0=Af3, f2=-f2s；
If i >=3, f3=2f1cf2-f1, f0=Af3, f1=f2, f2=f3；
N=n+1 simultaneously；
If n≤3N/4, repeat 3., is otherwise transferred to 4.；
4. sampled point n (3N/4, N] section when, enable j=n-3N/4：
If j=1, f6=-f1c, f0=Af6, f4=-f1c；
If j=2, f6=-f2c, f0=Af6, f5=-f2c；
If j >=3, f6=2f1cf5-f4, f0=Af6, f4=f5, f5=f6；
N=n+1 simultaneously；
If n≤N, repeat 4., otherwise, enable n=1, be transferred to 1., starts next sine wave signal period.
The Digital Implementation method of a kind of sine wave signal above-mentioned, wherein the method is by generating sine wave signal
Circuit system realizes that the circuit system includes：Keyboard input circuit, dsp controller, interface circuit, DAC conversion circuits and UA fortune
Calculate amplifier；Wherein, the output end of keyboard input circuit is connect with dsp controller, the output end and interface circuit of dsp controller
Connection, the output end of interface circuit are connect with DAC conversion circuits, and the output end of DAC conversion circuits is connect with UA operational amplifiers,
UA operational amplifiers export sine wave signal.
The interface circuit is the speed difference buffered between dsp controller and DAC conversion circuits, to ensure sine wave signal
Discrete point value be accurately and reliably sent into a kind of circuits of DAC conversion circuits.
The DAC conversion circuits are the discrete point numerical value conversion of the sine wave signal being sent by interface circuit at continuous
Sine-wave current signal.
Continuous sine-wave current signal is converted into continuous sine voltage signal by the UA operational amplifiers.
The present invention has clear advantage and advantageous effect compared with prior art, by above-mentioned technical proposal, the present invention
A kind of Digital Implementation method of sine wave signal can reach comparable technological progress and practicability, and with extensive in industry
Utility value at least has following advantages：
(1), the present invention utilizes the linear approximate relationship of angle value θ and SIN function sin (θ), rather than utilizes Taylor's grade
Number expansion formula, calculates initial sine function and cosine function value, simplifies calculation procedure, to reduce DSP controls
The calculating time of device processed；
(2), the present invention is according to the difference in section where sampled point n, and SIN function and remaining is used alternatingly using dsp controller
The recurrence formula of string function calculates the discrete point value of sine wave signal in real time, and SIN function is only used like that rather than iterative method
Recurrence formula, to reduce recurrence formula accumulated error caused by continuous recurrence calculation, and due to calculating in real time just
The discrete point value of string wave signal, does not occupy memory space largely also like look-up table, to reduce to dsp controller memory space
Occupancy, reduce cost；
(3), the present invention, need not picture due to can easily calculate initial sine function and cosine function value
Iterative method wants preset initial sine function and cosine function value like that, and sampling number N is changeable, thus even if in sampling frequency
Rate fsIn the case of fixed, the frequency of sine wave signal still can be neatly adjusted.
In conclusion a kind of Digital Implementation method of sine wave signal of the present invention technically has significant progress, and have
There is apparent good effect, is really a new and innovative, progressive, practical new design.
Above description is only the general introduction of technical solution of the present invention, in order to better understand the technical means of the present invention,
And can be implemented in accordance with the contents of the specification, and in order to allow the above and other objects, features and advantages of the present invention can
It is clearer and more comprehensible, it is special below to lift preferred embodiment, and coordinate attached drawing, detailed description are as follows.
Description of the drawings
Fig. 1 is the circuit system figure of the sine wave signal Digital Implementation method of the present invention.
Fig. 2 is the linear approximate relationship figure of the angle value θ and SIN function sin (θ) of the present invention.
Specific implementation mode
It is of the invention to reach the technological means and effect that predetermined goal of the invention is taken further to illustrate, below in conjunction with
Attached drawing and preferred embodiment, the Digital Implementation method to a kind of sine wave signal proposed according to the present invention, specific embodiment party
Formula, structure, feature and its effect are described in detail as after.
A kind of Digital Implementation method of sine wave signal of the present invention, in conjunction with shown in Fig. 1, on hardware circuit, packet
It includes：Keyboard input circuit, dsp controller, interface circuit, DAC conversion circuits and UA operational amplifiers；Include on software configuration
Angle value θ and SIN function sin (θ).Wherein：The main purpose of keyboard input circuit is to set the frequency and width of sine wave signal
Value and sample frequency.Sine wave signal frequency, amplitude and the sample frequency that dsp controller is set according to keyboard input circuit,
The discrete point value of sine wave signal is calculated, while discrete point value is sent into DAC conversion circuits by interface circuit.Interface electricity
Road is used to buffer the speed difference of dsp controller and DAC conversion circuits, to ensure that the discrete point value of sine wave signal accurately may be used
It is sent into DAC conversion circuits by ground.DAC conversion circuits are mainly used for the discrete point the sine wave signal being sent by interface circuit
Numerical value conversion is at continuous sine-wave current signal.Sine wave signal if necessary is voltage signal, then needs to transport using UA
It calculates amplifier and continuous sine-wave current signal is converted into continuous sine voltage signal.
A kind of Digital Implementation method of sine wave signal is by above-mentioned sine wave Digital Implementation system, first according to adopting
Sample frequency fsThe sampling number N that a sine wave signal period is calculated with the radiometer of sine wave freuqency f, utilizes formula θ=2 π/N
Calculate the occupied angle value θ of a sampling number.Utilize the linear approximate relationship meter of angle value θ and SIN function sin (θ)
The numerical value for calculating SIN function sin (θ), utilizes formula cos (θ) ≈ 1-0.5 θ2Calculate the numerical value of cosine function cos (θ).So
Afterwards, it using dsp controller, in sampled point n=[1, N/4] section, calculates sine wave using the recurrence formula of SIN function and believes
Number discrete point value；Sampled point n=(N/4, N/2] section, using the recurrence formula of cosine function calculate sine wave believe
Number discrete point value；Sampled point n=(N/2,3N/4] section, using the recurrence formula of SIN function calculate sine wave believe
Number discrete point value；Sampled point n=(3N/4, N] section, calculate sine wave signal using the recurrence formula of cosine function
Discrete point value.The discrete point numerical value conversion of sine wave signal is believed at continuous sine wave finally by DAC conversion circuits
Number, to realize the output of sine wave signal.The circuit block diagram of sine wave signal Digital Implementation system is as shown in Figure 1.
Taylor series expansion method is to calculate SIN function sin (θ) and cosine function cos using series expansion formula is strangled
The numerical value of (θ) needs the multiple multiply-add operation of dsp controller to complete SIN function sin's (θ) and cosine function cos (θ)
It calculates；Although iterative method can change sine wave signal with the numerical value of preset SIN function sin (θ) and cosine function cos (θ)
The flexibility of frequency is restricted.
Under normal circumstances, the relationship of angle value θ and SIN function sin (θ) are nonlinear.But when angle value θ [-
When between 0.2 ,+0.2], the relationship of angle value θ and SIN function sin (θ) are almost linear, and Fig. 2 reflections are exactly angle value
The linear approximate relationship of θ and SIN function sin (θ).Figure it is seen that in the case where angle value θ is smaller, angle value θ
With SIN function sin (θ) linear approximate relationship.As a result, in the case where ensureing that angle value θ is smaller, angle value θ can be utilized
With linear approximate relationship sin (θ) ≈ θ of SIN function sin (θ), the numerical value for directly obtaining SIN function sin (θ) is θ, is not required to
It calculates, you can the numerical value for directly obtaining SIN function sin (θ) simplifies calculation procedure, alleviates the burden of dsp controller；
And cosine function cos (θ), it is only necessary to multiplication and a subtraction three times, so that it may to pass through formula cos (θ) ≈ 1-0.5 θ2It calculates
Out, the calculation amount more than Taylor series expansion formula is small.Therefore, the Digital Implementation method of this sine wave signal overcomes
The computationally intensive disadvantage of Taylor series expansion method, also overcomes look-up table and occupies the deficiency of a large amount of memory spaces, and possess
The flexibility that sine wave signal frequency not available for iterative method is adjusted.
The above described is only a preferred embodiment of the present invention, be not intended to limit the present invention in any form, though
So the present invention has been disclosed as a preferred embodiment, and however, it is not intended to limit the invention, any technology people for being familiar with this profession
Member, without departing from the scope of the present invention, when the technology contents using the disclosure above make a little change or modification
For the equivalent embodiment of equivalent variations, as long as being the content without departing from technical solution of the present invention, according to the technical essence of the invention
To any simple modification, equivalent change and modification made by above example, in the range of still falling within technical solution of the present invention.
Claims (7)
1. a kind of Digital Implementation method of sine wave signal, it is characterised in that it includes the following steps：
(1), setup parameter specifically includes：Set the frequency f and amplitude A of sine wave signal, setting sample frequency fs；
(2), the sampling number N in a sine wave signal period is calculated；
(3), the occupied angle value θ of a sampled point is calculated；
(4), it when angle value θ is between [- 0.2 ,+0.2], is closed according to the approximately linear of angle value θ and SIN function sin (θ)
System, calculates the numerical value of sin (θ) and cos (θ), specially：
Sin (θ) ≈ θ,
(5), the numerical value of sin (2 θ) and cos (2 θ) are calculated, wherein sin (2 θ)=2sin (θ) cos (θ), cos (2 θ)=[cos
(θ)+sin(θ)][cos(θ)-sin(θ)]；
(6), according to the difference in section where sampled point n, the recurrence formula sin (n θ) of SIN function and cosine function is used alternatingly
=2cos (θ) sin [(n-1) θ]-sin [(n-2) θ] and cos (n θ)=2cos (θ) cos [(n-1) θ]-cos [(n-2) θ] is real-time
Calculate the discrete point value f of sine wave signal0；Its specific algorithm is：
Enable f1s=sin (θ), f1c=cos (θ), f2s=sin (2 θ), f2c=cos (2 θ)；N=1；
1. sampled point n enables i=n at [1, N/4] section：
If i=1, f3=f1s, f0=Af3, f1=f1s；
If i=2, f3=f2s, f0=Af3, f2=f2s；
If i >=3, f3=2f1cf2-f1, f0=Af3, f1=f2, f2=f3；
N=n+1 simultaneously；
If n≤N/4, repeat 1., is otherwise transferred to 2.；
2. sampled point n (N/4, N/2] section when, enable j=n-N/4：
If j=1, f6=f1c, f0=Af6, f4=f1c；
If j=2, f6=f2c, f0=Af6, f5=f2c；
If j >=3, f6=2f1cf5-f4, f0=Af6, f4=f5, f5=f6；
N=n+1 simultaneously；
If n≤N/2, repeat 2., is otherwise transferred to 3.；
3. sampled point n (N/2,3N/4] section when, enable i=n-N/2：
If i=1, f3=-f1s, f0=Af3, f1=-f1s；
If i=2, f3=-f2s, f0=Af3, f2=-f2s；
If i >=3, f3=2f1cf2-f1, f0=Af3, f1=f2, f2=f3；
N=n+1 simultaneously；
If n≤3N/4, repeat 3., is otherwise transferred to 4.；
4. sampled point n (3N/4, N] section when, enable j=n-3N/4：
If j=1, f6=-f1c, f0=Af6, f4=-f1c；
If j=2, f6=-f2c, f0=Af6, f5=-f2c；
If j >=3, f6=2f1cf5-f4, f0=Af6, f4=f5, f5=f6；
N=n+1 simultaneously；
If n≤N, repeat 4., otherwise, enable n=1, be transferred to 1., starts next sine wave signal period；
(7), using dsp controller the discrete point value f of calculated sine wave signal0It is sent into DAC conversion electricity by interface circuit
Road generates continuous sine-wave current signal；
(8), continuous sine-wave current signal is finally converted into continuous sine voltage signal using UA operational amplifiers,
To realize the output of sine wave signal.
2. the method as described in claim 1, it is characterised in that the calculation formula used in step (2) is N=fs/f。
3. the method as described in claim 1, it is characterised in that the calculation formula used in step (3) is θ=2 π/N.
4. the method as described in claim 1, it is characterised in that the method is real by the circuit system for generating sine wave signal
Existing, which includes：Keyboard input circuit, dsp controller, interface circuit, DAC conversion circuits and UA operational amplifiers；
Wherein, the output end of keyboard input circuit is connect with dsp controller, and the output end of dsp controller is connect with interface circuit, interface
The output end of circuit is connect with DAC conversion circuits, and the output end of DAC conversion circuits is connect with UA operational amplifiers, and UA operations are put
Big device exports sine wave signal.
5. method as claimed in claim 4, it is characterised in that the interface circuit in the circuit system is buffering dsp controller
With the speed difference between DAC conversion circuits, electricity is converted to ensure that the discrete point value of sine wave signal is accurately and reliably sent into DAC
A kind of circuit on road.
6. method as claimed in claim 4, it is characterised in that the DAC conversion circuits in the circuit system are electric interface is passed through
The discrete point numerical value conversion for the sine wave signal that road is sent into is at continuous sine-wave current signal.
7. method as claimed in claim 4, it is characterised in that the UA operational amplifier handles in the circuit system are continuous just
String signal wave current is converted into continuous sine voltage signal.
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| CN106569541B (en) * | 2016-10-17 | 2019-09-17 | 深圳市科陆精密仪器有限公司 | Sine wave generation method and device |
| CN108010537A (en) * | 2017-12-30 | 2018-05-08 | 长沙迪普美医疗科技有限公司 | A kind of audible alarm processing method, device, system |
| CN109115533B (en) * | 2018-09-07 | 2020-10-27 | 天津福云天翼科技有限公司 | Real-time accurate reproduction method of sine wave |
| TWI718625B (en) * | 2019-08-16 | 2021-02-11 | 瑞昱半導體股份有限公司 | Computation circuit used in dct, dst, idct and idst |
| TWI799302B (en) * | 2022-06-24 | 2023-04-11 | 瑞昱半導體股份有限公司 | Computation circuit used in dct, dst, idct and idst |
| CN118192755A (en) * | 2024-05-15 | 2024-06-14 | 南京丰道电力科技有限公司 | Method and system for generating slip waveform based on fixed time interval |
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| CN1666407A (en) * | 2002-07-08 | 2005-09-07 | 索尼株式会社 | Waveform generating device and method, and decoder |
| CN103065039A (en) * | 2012-12-10 | 2013-04-24 | 北京航空航天大学 | High-precision sine/cosine function computing method based on Euler's formula |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN1666407A (en) * | 2002-07-08 | 2005-09-07 | 索尼株式会社 | Waveform generating device and method, and decoder |
| CN103065039A (en) * | 2012-12-10 | 2013-04-24 | 北京航空航天大学 | High-precision sine/cosine function computing method based on Euler's formula |
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