how to represent signal

#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');

Answer 1

[Sameer]

Hi @abdelrahman ibrahiem

Please go through the following MathWorks documnetation links to know about signal representations:

https://www.mathworks.com/help/signal/signal-generation-analysis-and-preprocessing.html

https://www.mathworks.com/help/signal/ug/signal-generation-and-visualization.html

Hope this helps!