how to represent signal

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abdelrahman ibrahiem
回答： Sameer 2025-5-16
#y = sin(2*pi*50*t) + 2*sin(2*pi*120*t);
t = (0:0.001:1)';
y = sin(2*pi*50*t) + 2*sin(2*pi*120*t);
yn = y + 0.5*randn(size(t));% adding white noise
figure
subplot(2,1,1);
plot(t(1:50),y(1:50),'r')
subplot(2,1,2);
plot(t(1:50),yn(1:50),'b')
  • #Draw a stem plot
t = 0:0.01:2; % sample points from 0 to 2 in steps of 0.01
xt = sin(2*pi*t); % Evaluate sin(2 pi t)
n = 0:1:40; % sample index from 0 to 40
xn = sin(0.1*pi*n); % Evaluate sin(0.2 pi n)
Hs = stem(n,xn,'b', 'filled'); % Stem-plot with handle Hs
set(Hs,'markersize',4); % Change circle size
xlabel('n'); ylabel('x(n)'); % Label axis
title('Stem Plot of sin(0.2 pi n)'); % Title plot
figure
plot(t,xt,'b'); hold on; % Create plot with blue line
Hs = stem(n*0.05,xn,'b','filled'); % Stem-plot with handle Hs
set(Hs,'markersize',4); hold off; % Change circle size
#t = 0:0.01:2; % sample points from 0 to 2 in steps of 0.01
xt = sin(2*pi*t); % Evaluate sin(2 pi t)
n = 0:1:40; % sample index from 0 to 20
xn = sin(0.1*pi*n); % Evaluate sin(0.2 pi n)
figure
subplot(2,1,1); % Two rows, one column, first plot
plot(t,xt,'b'); % Create plot with blue line
subplot(2,1,2); % Two rows, one column, second plot
Hs = stem(n,xn,'b','filled'); % Stem-plot with handle Hs
  • Impulse, Step, and Ramp, Quad, square Functions
t = (-1:0.01:1)';
impulse = t==0;
unitstep = t>=0;
ramp = t.*unitstep;
quad = t.^2.*unitstep;
sqwave = 0.81*square(4*pi*t);
figure
subplot(5,1,1); plot(t,impulse,'r'); % impule
subplot(5,1,2); plot(t,unitstep,'b'); % unit step
subplot(5,1,3); plot(t,ramp,'k'); % ramp
subplot(5,1,4); plot(t,quad,'g'); % quad
subplot(5,1,5); plot(t,sqwave,'b')% square
  • Exponential signals
n3 = 0:0.5:10; x3 = (0.9).^n3;
figure
Hs = stem(n3,x3,'b','filled');
complex valued exponential
n4 = 5:0.2:10; x4 = exp((1+8j)*n4);
figure
Hs = stem(n4,x4,'b','filled');
sinusoidal sequence
n5 = 0:0.2:10; x5 = 3*cos(0.1*pi*n5+pi/3) + 2*sin(0.5*pi*n5);
figure
Hs = stem(n5,x5,'b','filled');
Sinc Function
x = linspace(-5,5);
y = sinc(x);
figure
plot(x,y)
grid
signal addition
n1 = 0:20; x1 = (0.9).^n1;
n2 = 5:30; x2 =3*cos(0.1*pi*n2+pi/3)+ 2*sin(0.5*pi*n2);
nn = min(min(n1),min(n2)):max(max(n1),max(n2)); % duration of y(n)
y1 = zeros(1,length(nn)); y2 = y1;
% x1 with duration of y
y1(find((nn>=min(n1))&(nn<=max(n1))==1))=x1;
% x2 with duration of y
y2(find((nn>=min(n2))&(nn<=max(n2))==1))=x2;
y = y1+y2; % sequence addition
figure
subplot(3,1,1); Hs = stem(nn,y1,'r','filled');
subplot(3,1,2); Hs = stem(nn,y2,'g','filled');
subplot(3,1,3); Hs = stem(nn,y,'b','filled');
figure
hold on
Hs = stem(nn,y1,'r','filled');
Hs = stem(nn,y2,'g','filled');
Hs = stem(nn,y,'b','filled');
hold off
signal multiplication
n1 = 0:20; x1 = (0.9).^n1;
n2 = 5:30; x2 =3*cos(0.1*pi*n2+pi/3)+ 2*sin(0.5*pi*n2);
nn = min(min(n1),min(n2)):max(max(n1),max(n2)); % duration of y(n)
y1 = zeros(1,length(nn)); y2 = y1;
% x1 with duration of y
y1(find((nn>=min(n1))&(nn<=max(n1))==1))=x1;
% x2 with duration of y
y2(find((nn>=min(n2))&(nn<=max(n2))==1))=x2;
y = y1.*y2; % sequence multiplication
signal shifting
n4 = 5:30;
x4=3*cos(0.1*pi*n4+pi/3)+ 2*sin(0.5*pi*n4);
k=5; m=n4+k;% shift
x4_new =3*cos(0.1*pi*m+pi/3)+ 2*sin(0.5*pi*m);
figure
subplot(2,1,1); Hs = stem(n4,x4,'r','filled');
subplot(2,1,2); Hs = stem(m,x4_new,'g','filled');
figure
hold on
Hs = stem(n4,x4,'b','filled');
Hs = stem(m,x4_new,'g','filled'); hold off
signal folding
n = 5:0.2:20;
x=3*cos(0.1*pi*n+pi/3)+ 2*sin(0.5*pi*n);
y = fliplr(x);
figure
subplot(2,1,1);
Hs = stem(n,x,'r','filled');
subplot(2,1,2);
Hs = stem(n,y,'b','filled');
signal energy
n = 5:0.2:20;
x=3*cos(0.1*pi*n+pi/3)+ 2*sin(0.5*pi*n);
% the value of the signal energy
Ex = sum(abs(x) .^ 2);
Signal convolution
x = [3, 11, 7, 0, -1, 4, 2]; nx = [-3:3];
h = [2, 3, 0, -5, 2, 1]; nh = [-1:4];
nyb = nx(1)+nh(1);
nye = nx(length(x)) + nh(length(h));
ny = [nyb:nye];
y = conv(x,h);% without above 3 lines it will make convolution but can't draw result
figure
subplot(2,2,1); stem( nx,x); title('first sequence')
xlabel('n'); ylabel('x(n)');
subplot(2,2,2); stem(nh,h); title('second sequence')
xlabel('n'); ylabel('h(n)');
subplot(2,2,4); stem(ny,y); title('convolution result')
xlabel('n'); ylabel('y(n)');
Periodogram power spectral density estimate
Fs = 1000; t = 0:1/Fs:1;
x = cos(2*pi*100*t)+randn(size(t));
[Pxx,F] = periodogram(x,[],length(x),Fs);
figure
subplot(3,1,1); plot(t,x);
xlabel('Time');ylabel('x(t)');
title('Original signal')
subplot(3,1,2); plot(F,Pxx)
xlabel('Frequency');
ylabel('Power Spectrum Magnitude');
title('Power spectral Density')
subplot(3,1,3); plot(F,10*log10(Pxx))
xlabel('Frequency');
ylabel(' 'Power Spectrum Magnitude(dB)');
title('Power spectral Density')
Recording an audio signal
Fs=8000;
recObj = audiorecorder
disp('Start speaking.')
recordblocking(recObj, 5);
disp('End of Recording.');
play(recObj);
x = getaudiodata(recObj);
[Pxx,F] = periodogram(x,[],length(x),Fs);
figure
subplot(3,1,1); plot(x);xlabel('Time');ylabel('x(t)');
title('Original sound signal')
subplot(3,1,2); plot(F,Pxx);xlabel('Frequency'); ylabel('PSM');title('Power spectral Density')
subplot(3,1,3); plot(F,10*log10(Pxx))
xlabel('Frequency');ylabel('PSM (dB)');
title('Power spectral Density')
m2
Fs=8000;
recObj = audiorecorder
disp('Start speaking.')
recordblocking(recObj, 5);
disp('End of Recording.');
play(recObj); % or sound
x = getaudiodata(recObj);
filename = 's1.wav';
audiowrite(filename,x,Fs);
[y,Fs] = audioread(filename);
soundsc(y,Fs);% Scale data and play as sound
•Use the audioread function to read the file, handel.wav. The audioread function can support WAVE, OGG, FLAC, AU, MP3, and MPEG-4 AAC files.
[y,Fs] = audioread('handel.wav');
•Play the audio.
sound(y,Fs)
Discriminating two sounds based on energy
Fs=8000;
recObj = audiorecorder;
disp('Start speaking1.')
recordblocking(recObj, 3);
disp('End of Recording1.');
x = getaudiodata(recObj);
filename = 's1.wav'; audiowrite(filename,x,Fs);
[y1,Fs] = audioread(filename);
Ey1 = sum(abs(y1) .^ 2);
disp('Start speaking2.') % second signal
recordblocking(recObj, 3);
disp('End of Recording2.');
x2 = getaudiodata(recObj);
filename = 's2.wav'; audiowrite(filename,x2,Fs);
[y2,Fs] = audioread(filename);
Ey2 = sum(abs(y2) .^ 2);
soundsc(y2,Fs);
Filter design (lowpass)
[x,fs] = wavread('s1.wav'); % load audio file
[Pxx1,F1] = periodogram(x,[],length(x),Fs);
% design window based FIR filter stages=200,CF=300
b = fir1(200,300/(fs/2));
y = filter(b,1,x); % filter the signal
[Pxx2,F2] = periodogram(y,[],length(y),Fs);
figure
subplot(4,1,1);plot(x)
subplot(4,1,2); plot(F1,Pxx1)
subplot(4,1,3);plot(y)
subplot(4,1,4); plot(F2,Pxx2)
Filter design (hightpass)
[x,fs] = wavread('s1.wav'); % load audio file
[Pxx1,F1] = periodogram(x,[],length(x),Fs);
% design window based FIR filter stages=200,CF=300
b = fir1(200,300/(fs/2),'high');
[Pxx2,F2] = periodogram(y,[],length(y),Fs);
figure
subplot(4,1,1);plot(x)
subplot(4,1,2); plot(F1,Pxx1)
subplot(4,1,3);plot(y)
subplot(4,1,4); plot(F2,Pxx2)
Comparing lowpass and highpass
FS=1000;t = 0:1/Fs:1;
x=cos(2*pi*100*t)+cos(2*pi*500*t)+randn(size(t));
[Pxx,F] = periodogram(x,[],length(x),Fs);
b1 = fir1(200,300/(FS/2));
y1 = filter(b1,1,x); % lowpass filter
[Pxx1,F1] = periodogram(y1,[],length(y1),Fs);
b2 = fir1(200,300/(FS/2),'high');
y2 = filter(b2,1,x); % highpass filter
[Pxx2,F2] = periodogram(y2,[],length(y2),Fs);
figure
subplot(3,1,1);plot(t,x);
xlabel('time');ylabel('x(t)');title('original signal in time domain');
subplot(3,1,2);plot(t,y1);
xlabel('time');ylabel('y1(t)');title('signal in time domain after removing high freq. complnents');
subplot(3,1,3);plot(t,y2)
xlabel('time');ylabel('y2(t)');title('signal in time domain after removing low freq. complnents');
figure
subplot(3,1,1);plot(F,Pxx);
xlabel('frequency');ylabel('PSM');title('Power Spectral Density of original signal');
subplot(3,1,2); plot(F1,Pxx1);
xlabel('frequency');ylabel('PSM');title('Power Spectral Density of signal after lowpass filter');
subplot(3,1,3); plot(F2,Pxx2);
xlabel('frequency');ylabel('PSM');title('Power Spectral Density of original signal after highpass filter');

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Sameer
Sameer 2025-5-16

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