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Continuous and Discrete Time

Signals

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0 20 40 60 80 100

-10

0

10

t (ms)

0 10 20 30 40 50-10

0

10

n (samples)

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Plot and step functions

plot (x,y) stem (x,y)

Where: x - horizontal axis (vector)

y

vertical axis (vector)***x and y must have the same length

t n

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square(t,duty)

>> t = 1:100;

>> y = square(t,80);

>> plot(t,y)

2*pi

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Fs = 20000;

F = 1000;

f = F/Fs;

dc = 50;Amp = 1;

t = 0:1/Fs:0.005;

x = Amp*square(2*pi*F*t,dc)

plot(t,x);

T = 1/1000

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sawtooth(t) generates a sawtooth wave with

period 2pi for the elements of time vector t.

t = -10:0.1:10;A = 1;

y = A*sawtooth(t);

plot(t,y);

2*pi

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t = -10:0.1:10;

A = 1;w = xx ;

y = A*sawtooth(t,w);

plot(t,y);

sawtooth(t, width)

W = 0 W = 0.5

W = 1

2*pi 2*pi

2*pi

If no w is included it

will use a default w =1

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Fs = 20000;

F = 1000;

f = F/Fs;

Amp = 1;

t = 0:1/Fs:0.005;

x = sawtooth(2*pi*F*t)

plot(t,x);

T = 1/1000

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tripults(t,w)

t = -5:0.1:5;

w = 4;

y = tripuls(t,w);

plot(t,y);

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sinc(t) sinc(t) = sin(pi*t)/(pi*t)

t = -5:.01:5;

plot(t,sinc(t))

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The square wave contains a fundamental and a

series of ODD HARMONICS that is harmonics which

are odd number multiples of the fundamental (x3

x5 x7 etc.) These are called the 3rd harmonic, 5th

harmonic etc.

SQUARE WAVE

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TRIANGULAR WAVE

The triangular wave also contains a fundamental

and a series of ODD HARMONICS, but in this case,

each successive harmonic component starts off in

the opposite PHASE to the previous one. i.e. the 3rd

harmonic starts by going positive the 5th harmonic

begins by going negative, the 7thpositive and so on.

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SAWTOOTH WAVE

The sawtooth wave contains a fundamental

and both ODD and EVEN HARMONICS.

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Fs = 20000;

F = 1000;

f = F/Fs;

t = 0:99;

Amp = 5;

x = Amp*sin(2*pi*f*t);stem(t,x);

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Fs = 20000;

F = 1000;f = F/Fs;

n = 0:99;

Amp =5;

wnoise = 1.5 + sqrt(0.5)*randn(size(n));

x = Amp*sin(2*pi*f*n);

y = wnoise+x;subplot(3,1,1);stem(n,x);

subplot(3,1,2);stem(n,wnoise);

subplot(3,1,3);stem(n,y);

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Fs = 20000;

F1 = 1000;

F2 = 3000;

F3 = 5000;

n = 0:99;

wnoise = sqrt(0.2)*randn(size(n));

x1 = sin(2*pi*n*F1/Fs);

x2 = sin(2*pi*n*F2/Fs);

x3 = sin(2*pi*n*F3/Fs);x4 = sin(2*pi*n*F3/Fs);

s= x1 + x2 + x3 + wnoise;

sf = fft(s,512);

w = (0:255)/255*(Fs/2);

plot(w,abs(sf(1:256)));

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Fs = 20000;

F1 = 1000;

F2 = 3000;

F3 = 5000;

n = 0:99;

wnoise = sqrt(0.2)*randn(size(n));

x1 = sin(2*pi*n*F1/Fs);

x2 = sin(2*pi*n*F2/Fs);

x3 = sin(2*pi*n*F3/Fs);x4 = sin(2*pi*n*F3/Fs);

s= x1 + x2 + x3 + wnoise;

sf = fft(s,512);

w = (-255:255)/255*(Fs/2);

plot(w,abs(sf(1:511)));

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Fs = 20000;

F = 1000;f = F/Fs;

t = 0:1/Fs:0.005;

Amp = 5;

x = Amp*sin(2*pi*F*t);

plot(t,x)