Matlab comprehensive exercise: application in signal and system

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MATLAB 2018b

Preface

“ dad , The teacher is very satisfied with the spectrum analysis of time domain signals you sent me yesterday , She left new homework again , Please help me find your employee to help me , I'm not very good at .”
Boss kuchazi , He snorted unhappily ：“ Can't you learn a little by yourself ？ What can you do when you come out in the future ？ Just point to me every day and give you every month 50 Ten thousand pocket money , How can you survive like this ！”
“ Stop nagging , Stinky old man , Bye-bye , I fooled ！”
“ Ah ！“ The boss of kuchazi sighed , Then let the female secretary call Xiao Liu to the office .
” Xiao Liu ！ The homework you did yesterday , I? , I'm really satisfied , In order to continue to exercise your ability , Here are a few more questions , You did it too ！ ah , Not much .“ Kuchazi's boss said with a straight face .
Xiao Liu thought of refusing , When I see the boss's angry face , I dare not open that mouth , Just waxy said ：” well , Boss .“
” The document was sent to you , Write it quickly ！“ The boss kicked Xiao Liu out of the office .
Xiao Liu returned to his desk , Looking at so many questions , Silently opened CSDN Search for ：” How to raise salary with the boss ？“

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One 、 Generate numerical signals

utilize MATLAB Generate signals x(t)=cos(10Πt),y(t)=sin(10Πt²)
, Draw the waveform of the signal respectively , And draw a picture to compare the waveforms of the two signals .

The code is as follows , Shown ：

>> t=linspace(0,8*pi,100);% establish 0 To 4Π Linearly separated numeric vector of t, Element is 100 individual 
>> x=cos(10*pi*t);%x(t) Waveform of ;
>> plot(t,x,'r'),title('x(t) wavy curve '),xlabel('t Numeric vectors ')
>> y=sin(10*pi*t.^2);%y(t) Waveform of ;
>> plot(t,y,'c'),title('y(t) wavy curve '),xlabel('t Numeric vectors ')
>> plot(t,x,'r',t,y,'c')
>> title('x(t) and y(t) Compare ')
>> xlabel('t Numeric vectors ')

1. A separate x Oscillogram of ：

2. A separate y Oscillogram of ：

3.x(t) Signal waveform and y(t) Compare the signal waveform ：

Two 、 The basic operation of the signal

utilize MATLAB Realization signal f1 (t)=sin⁡(πt),f2(t)=sin⁡(10πt) Add and multiply , Try to draw the waveforms of these two signals and their sum and product signals respectively .

The code is as follows , Shown ：

>> t=linspace(0,8*pi,100);% establish 0 To 4Π Linearly separated numeric vector of t, Element is 100 individual 
>> f1=sin(pi*t);%f1 Signal function expression 
>> f2=sin(10*pi*t);%f2 Signal function expression 
>> subplot(1,2,1),plot(t,f1,'m'),title('x(t) The waveform curve of ')
>> subplot(1,2,2),plot(t,f2,'w'),title('y(t) The waveform curve of ')
>> f3=f1+f2;
>> format short,f3;
>> plot(t,f3),title('f3 Is the signal and waveform curve ')
>> f4=f1.*f2;
>> plot(t,f4,'m'),title('f4 Is the waveform curve of signal product ')

1.f1、f2 The waveform curve of ：

2.f3 Waveform curve of the product sum of two signals

3.f4 Waveform curve of the product of two signals

3、 ... and 、 Convolution operation

use MATLAB Draw out the function 3[u(t+1)-u(t-2)] And exponential function 2e^(-2t) Convolution graph .

The code is as follows , Shown ：

>> dt=0.01; t=0:dt:5;
>> f1=3*(u.*(t+1)-u.*(t-2)); subplot(1,3,1), plot(t,f1,'g') ,title(' Gate function waveform curve ')
>> f2=2*exp(-2.*t); subplot(1,3,2), plot(t,f2,'r'),title(' Exponential function waveform curve ')
>> y =conv(f1,f2)*dt;% Call convolution conv() function 
>> subplot(1,3,3), plot(dt*([1:length(y)]-1),y,'m'), title(' Convolution curve '),grid  %  Ignorance t The length of , When drawing t Array setting method 

Gate function , Exponential function 、 The convolution waveforms of the two signals are as follows ：

Four 、 Fourier series expansion

utilize MATLAB Set the fundamental frequency to 50Hz The square wave expansion of is Fourier series .

The code is as follows , Shown ：

>> N = 500; % Take item , And the higher the number of items , The less distorted the waveform .
>> T = 0.02;% The period of the square wave is 0.02;
>> fs = 1/T;% The fundamental frequency of square wave is 50Hz;
>> N_point = 150; % Set the number of sampling points per cycle 
>> dt = T/N_point;% step 
>> t=1:dt:100*T-dt;% Value range ,” Shoulds not be too large “
>> ft = zeros(1,length(t));
>> %ft For all 0 matrix 
>> for n=1:N
an = (2*sin(pi*n) - sin(2*pi*n))/(pi*n);
bn = (1-2*cos(n*pi)+cos(2*pi*n))/(pi*n);
ft = ft + an*cos(n*2*pi*fs*t)+bn*(sin(n*2*pi*fs*t));% Fourier expansion series 
end
>> plot(t,ft,'m')
>> title(' The fundamental frequency is 50Hz The square wave expansion of is Fourier series ')

The fundamental frequency is 50Hz The square wave ：

The situation of square wave synthesized by each harmonic ：

5、 ... and 、 Spectrum analysis

use MATLAB Draw H(s)=s²/((s+1)²+1) Zero of 、 Pole distribution diagram , And draw the impulse response of the system h(n) Waveform and frequency response H（jω） The curve of , Judge whether the system is low-pass 、 qualcomm 、 Bandpass 、 Which kind of band stop ？

The code is as follows , Shown ：

>> a = [1 2 2];%  Denominator vector 
>> b = [1]; %  Molecular vector 
>> zs=roots(b)  % Find the zero point of the system 
zs =

   Empty  0×1 double  Column vector 
>> ps=roots(a)  % Find the pole of the system 
ps =

  -1.0000 + 1.0000i
  -1.0000 - 1.0000i
>> plot(real(zs), imag(zs), 'go', real(ps), imag(ps), 'mx', 'markersize', 12);
>> grid; legend(' zero ',' pole ');
>>figure(1); pzmap(sys); %  Draw the zero pole diagram 
>> figure(2);freqs(b, a, w);%  Draw the amplitude frequency characteristic curve and phase frequency characteristic curve 
>> dn=0.1; n=0:dn:6;%n Value range 
>> [r,p,k]=residue( b, a);% Use the pole residue method to find the impact function 
>> H=zeros(1,length(n));
>> for i=1:length(a)-1
H=H+r(i)*exp(p(i)*n);%  Shock function h(n) General formula of 
end
>> plot(n,H); grid; title(' Impulse response H(t)')![ Insert picture description here ](https://img-blog.csdnimg.cn/d25cf9c7d0764f569678bfd9e8288153.png)

>> freqs(b,a,w) % The frequency response of the filter 

1. zero 、 Pole diagram ：

2. Amplitude frequency characteristic curve and phase frequency characteristic curve ：

3. Impulse function H（t）:

4. Frequency response H（jω） The curve of :

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summary

Xiao Liu finally finished these questions , He stretched himself , Look at the time , It's already night 21：35 了 , After looking at the boss' office, the light has gone out , It is estimated that the boss has gone home to sleep , Send it to him tomorrow . Take another look at the office where there are few people around , Shook his head , Make yourself a cup of coffee , Continue to look at the questions this afternoon ：” How to get the boss to give himself a raise ？“