[PPT] - ELG3 1 2 5 Signal and System Analysis Lab2: Signal Manipulation PowerPoint Presentation

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School of Information Technology and Engineering (SITE) Lab2: Signal Manipulation and Graphics TA: Jungang Liu ELG3 1 2 5 Signal and System Analysis

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ELG3125 Signal and System Analysis Fall 2010

School of Information Technology and Engineering

Outline

1. Periodic Signals
2. Signal Combination
3. Matlab Graphing

http://www.mathworks.com MATLab Manual

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ELG3125 Signal and System Analysis Fall 2010

School of Information Technology and Engineering

Continuous-Time Sinusoidal Signals Sine signal with period T: Example: T=6; %Period t=0:0.01:60; y=sin(2pi/T.t); plot(t,y),grid;

) 2 sin( t T y π =

10 20 30 40 50 60

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1

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ELG3125 Signal and System Analysis Fall 2010

School of Information Technology and Engineering

Exponential Function Signal

Exponential function Example: t=0:0.01:20;

mega=1;

; y=exp(omega .*t); plot(t,y),grid;

t

e x

ω

=

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 50 100 150

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ELG3125 Signal and System Analysis Fall 2010

School of Information Technology and Engineering

Plot Two Continuous-time Signals in One Graph (Method1)

Use plot function %Sinusoidal 1 T=6; t1=0:0.01:20; y1=sin(2pi/T.t1); %Sinusoidal 2 t2=0:0.01:20; y2=sin(4pi/T.t2); plot(t1,y1,'r',t2,y2,'b'),grid;

2 4 6 8 10 12 14 16 18 20

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1

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ELG3125 Signal and System Analysis Fall 2010

School of Information Technology and Engineering

Plot Two Continuous-time Signals in One Graph (Method2)

Use hold function % Sinusoidal 1 T=6; t1=0:0.01:20; y1=sin(2pi/T.t1); plot(t1,y1,'r‘); hold on %Sinusoidal 2 t2=0:0.01:20; y2=sin(4pi/T.t2); plot(t2,y2,'b'); grid on;

2 4 6 8 10 12 14 16 18 20

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1

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ELG3125 Signal and System Analysis Fall 2010

School of Information Technology and Engineering

Square Wave

Square wave with period T. Example: t=0:0.01:20; T=5; %period y=sign(sin(2pi/T.t)); % or y=mod(t.*1/T,1)>1/2; plot(t,y),grid; axis([0 20 -1.5 1.5]);

2 4 6 8 10 12 14 16 18 20

1.5
1
0.5

0.5 1 1.5

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ELG3125 Signal and System Analysis Fall 2010

School of Information Technology and Engineering

Discrete-Time Sinusoidal Signals

Sine signal with period N: Example: n=0:20; m=1; N=7; %period y=sin(2pim/N.*n); stem(n,y),grid; .

5 10 15 20 25 30

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1

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ELG3125 Signal and System Analysis Fall 2010

School of Information Technology and Engineering

Discrete-Time Sinusoidal Signals (Homework 1-26 b) Cosine signal x[n]=cos(n/8-pi) Code n=0:600; x=cos(n./8-pi); stem(n,x) grid on; Result(next page): Not periodic, and this verifies our analysis in the tutorial class.

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ELG3125 Signal and System Analysis Fall 2010

School of Information Technology and Engineering

X[ n] = cos(n/ 8-pi) Result: NOT periodic

20 40 60 80 100 120 140 160 180 200

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X= 13 Y= 0.054177 X= 63 Y= 0.021017 X= 114 Y= 0.11259 X= 164 Y= 0.079564

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ELG3125 Signal and System Analysis Fall 2010

School of Information Technology and Engineering

Discrete-Time Sinusoidal Signals Homework 1-26 c) x[n]=cos((pi/8)n2) Code n=0:100; x=cos(power(n,2)*pi/8); stem(n,x,’r’),grid; Result: period N=8;

5 10 15 20 25

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0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1

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ELG3125 Signal and System Analysis Fall 2010

School of Information Technology and Engineering

Discrete-Time Exponential Signals

Exponential signal y[n]=e-n Example n=0:10; y=exp(0.5*n); stem(n,y),grid;

1 2 3 4 5 6 7 8 9 10 50 100 150

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ELG3125 Signal and System Analysis Fall 2010

School of Information Technology and Engineering

Combination of Two Continuous-Time Signals t=0:0.01:20; T1=2; T2=4; y1=cos(2pi/T1t); y2=sin(2pi/T2t); y3=y1+y2; plot(t,y3),grid;

2 4 6 8 10 12 14 16 18 20

2
1.5
1
0.5

0.5 1 1.5

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ELG3125 Signal and System Analysis Fall 2010

School of Information Technology and Engineering

Combination of Two Discrete-Time Signals1

-----Addition

Code n=0:60; N1=2; m1=3; N2=4; m2=2; y1=cos(m1/N12pi.n); y2=sin(m2/N22pi.n); y3=y1+y2; stem(n,y3),grid;

10 20 30 40 50 60

1.5
1
0.5

0.5 1 1.5

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ELG3125 Signal and System Analysis Fall 2010

School of Information Technology and Engineering

Combination of Two Discrete-Time Signals2

-----Multiplication

Homework 1.26 d) x[n]=cos[pin/2]cos[pin/4] Code n=-15:15; x= cos(pi.n/2)cos(pi.*n/4) Stem(n,x),grid Result: period N=8 (It verifies our analysis in the tutorial class.)

15
10
5

5 10 15

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0.2 0.4 0.6 0.8 1

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ELG3125 Signal and System Analysis Fall 2010

School of Information Technology and Engineering

3 -D Plotting

3-D analog of plotting function.
Function: plot3(x,y,z)
When x, y and z are three vectors of the same

length, it plots a line in 3-D through the points whose coordinates are the elements of x, y and z.

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ELG3125 Signal and System Analysis Fall 2010

School of Information Technology and Engineering

View

3-D graph viewpoint specification.
Used together with plot3.
Function: view(AZ,EL)
AZ: Azimuth rotation in degree, which revolves

z-axis, with positive values indicating counter- clockwise rotation of the viewpoint.

EL: Elevation in degree, with positive values

corresponding to moving above the object.

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ELG3125 Signal and System Analysis Fall 2010

School of Information Technology and Engineering

Axis

By default, Matlab finds the maximum and minimum of

data to choose the axis limits.

Axis is used to control axis scaling and appearance.
Function: axis([xmin xmax ymin ymax]) for 2-D plot.

axis([xmin xmax ymin ymax zmin zmax]) for 3-D plot.

axis auto returns the axis scaling to its default.

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ELG3125 Signal and System Analysis Fall 2010

School of Information Technology and Engineering

3D Plotting Example

y = ej (2 pi / T)t with period T. (Euler’s formula: ejx = cos(x) + j sin(x)) Code T=6; t=0:0.01:10; y=exp(j2pi/T.*t); figure(1); plot3(t,real(y),imag(y)); grid on; axis square;

10 20 30

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0.5 1

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0.5 1

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ELG3125 Signal and System Analysis Fall 2010

School of Information Technology and Engineering

School of Information Technology and Engineering (SITE) Lab2: Signal Manipulation and Graphics TA: Jungang Liu ELG3 1 2 5 Signal and System Analysis

Outline

http://www.mathworks.com MATLab Manual

Continuous-Time Sinusoidal Signals Sine signal with period T: Example: T=6; %Period t=0:0.01:60; y=sin(2*pi/T.*t); plot(t,y),grid;

) 2 sin( t T y π =

Exponential Function Signal

Exponential function Example: t=0:0.01:20;

; y=exp(omega .*t); plot(t,y),grid;

t

e x

ω

=

Plot Two Continuous-time Signals in One Graph (Method1)

Use plot function %Sinusoidal 1 T=6; t1=0:0.01:20; y1=sin(2*pi/T.*t1); %Sinusoidal 2 t2=0:0.01:20; y2=sin(4*pi/T.*t2); plot(t1,y1,'r',t2,y2,'b'),grid;

Plot Two Continuous-time Signals in One Graph (Method2)

Use hold function % Sinusoidal 1 T=6; t1=0:0.01:20; y1=sin(2*pi/T.*t1); plot(t1,y1,'r‘); hold on %Sinusoidal 2 t2=0:0.01:20; y2=sin(4*pi/T.*t2); plot(t2,y2,'b'); grid on;

Square Wave

Square wave with period T. Example: t=0:0.01:20; T=5; %period y=sign(sin(2*pi/T.*t)); % or y=mod(t.*1/T,1)>1/2; plot(t,y),grid; axis([0 20 -1.5 1.5]);

Discrete-Time Sinusoidal Signals

Sine signal with period N: Example: n=0:20; m=1; N=7; %period y=sin(2*pi*m/N.*n); stem(n,y),grid; .

Discrete-Time Sinusoidal Signals (Homework 1-26 b) Cosine signal x[n]=cos(n/8-pi) Code n=0:600; x=cos(n./8-pi); stem(n,x) grid on; Result(next page): Not periodic, and this verifies our analysis in the tutorial class.

X[ n] = cos(n/ 8-pi) Result: NOT periodic

Discrete-Time Sinusoidal Signals Homework 1-26 c) x[n]=cos((pi/8)n2) Code n=0:100; x=cos(power(n,2)*pi/8); stem(n,x,’r’),grid; Result: period N=8;

Discrete-Time Exponential Signals

Exponential signal y[n]=e-n Example n=0:10; y=exp(0.5*n); stem(n,y),grid;

Combination of Two Continuous-Time Signals t=0:0.01:20; T1=2; T2=4; y1=cos(2*pi/T1*t); y2=sin(2*pi/T2*t); y3=y1+y2; plot(t,y3),grid;

Combination of Two Discrete-Time Signals1

Code n=0:60; N1=2; m1=3; N2=4; m2=2; y1=cos(m1/N1*2*pi.*n); y2=sin(m2/N2*2*pi.*n); y3=y1+y2; stem(n,y3),grid;

Combination of Two Discrete-Time Signals2

Homework 1.26 d) x[n]=cos[pi*n/2]cos[pi*n/4] Code n=-15:15; x= cos(pi.*n/2)*cos(pi.*n/4) Stem(n,x),grid Result: period N=8 (It verifies our analysis in the tutorial class.)

3 -D Plotting

length, it plots a line in 3-D through the points whose coordinates are the elements of x, y and z.

View

z-axis, with positive values indicating counter- clockwise rotation of the viewpoint.

corresponding to moving above the object.

Axis

data to choose the axis limits.

axis([xmin xmax ymin ymax zmin zmax]) for 3-D plot.

3D Plotting Example

y = ej (2 pi / T)t with period T. (Euler’s formula: ejx = cos(x) + j sin(x)) Code T=6; t=0:0.01:10; y=exp(j*2*pi/T.*t); figure(1); plot3(t,real(y),imag(y)); grid on; axis square;

Enjoy signal……

Continuous-Time Sinusoidal Signals Sine signal with period T: Example: T=6; %Period t=0:0.01:60; y=sin(2pi/T.t); plot(t,y),grid;

Use plot function %Sinusoidal 1 T=6; t1=0:0.01:20; y1=sin(2pi/T.t1); %Sinusoidal 2 t2=0:0.01:20; y2=sin(4pi/T.t2); plot(t1,y1,'r',t2,y2,'b'),grid;

Use hold function % Sinusoidal 1 T=6; t1=0:0.01:20; y1=sin(2pi/T.t1); plot(t1,y1,'r‘); hold on %Sinusoidal 2 t2=0:0.01:20; y2=sin(4pi/T.t2); plot(t2,y2,'b'); grid on;

Square wave with period T. Example: t=0:0.01:20; T=5; %period y=sign(sin(2pi/T.t)); % or y=mod(t.*1/T,1)>1/2; plot(t,y),grid; axis([0 20 -1.5 1.5]);

Sine signal with period N: Example: n=0:20; m=1; N=7; %period y=sin(2pim/N.*n); stem(n,y),grid; .

Combination of Two Continuous-Time Signals t=0:0.01:20; T1=2; T2=4; y1=cos(2pi/T1t); y2=sin(2pi/T2t); y3=y1+y2; plot(t,y3),grid;

Code n=0:60; N1=2; m1=3; N2=4; m2=2; y1=cos(m1/N12pi.n); y2=sin(m2/N22pi.n); y3=y1+y2; stem(n,y3),grid;

Homework 1.26 d) x[n]=cos[pin/2]cos[pin/4] Code n=-15:15; x= cos(pi.n/2)cos(pi.*n/4) Stem(n,x),grid Result: period N=8 (It verifies our analysis in the tutorial class.)

y = ej (2 pi / T)t with period T. (Euler’s formula: ejx = cos(x) + j sin(x)) Code T=6; t=0:0.01:10; y=exp(j2pi/T.*t); figure(1); plot3(t,real(y),imag(y)); grid on; axis square;