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

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

Outline 1. Periodic Signals 2. Signal Combination 3. Matlab Graphing http://www.mathworks.com MATLab Manual ELG3125 Signal and System Analysis Fall 2010 School of Information Technology and Engineering

Continuous-Time Sinusoidal Signals � Sine signal with period T: 1 π 2 0.8 = y sin( t ) 0.6 T 0.4 � Example: 0.2 0 T=6; %Period -0.2 t=0:0.01:60; -0.4 -0.6 y=sin(2*pi/T.*t); -0.8 plot(t,y),grid; -1 0 10 20 30 40 50 60 ELG3125 Signal and System Analysis Fall 2010 School of Information Technology and Engineering

Exponential Function Signal 150 � Exponential function ω t = 0 x e 100 � Example: t=0:0.01:20; omega=1; ; 50 y=exp(omega .*t); plot(t,y),grid; 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 ELG3125 Signal and System Analysis Fall 2010 School of Information Technology and Engineering

Plot Two Continuous-time Signals in One Graph (Method1) 1 0.8 � Use plot function 0.6 %Sinusoidal 1 0.4 T=6; t1=0:0.01:20; 0.2 0 y1=sin(2*pi/T.*t1); -0.2 %Sinusoidal 2 -0.4 t2=0:0.01:20; -0.6 y2=sin(4*pi/T.*t2); -0.8 -1 plot(t1,y1,'r',t2,y2,'b'),grid; 0 2 4 6 8 10 12 14 16 18 20 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 1 % Sinusoidal 1 0.8 T=6; t1=0:0.01:20; 0.6 y1=sin(2*pi/T.*t1); 0.4 plot(t1,y1,'r‘); 0.2 hold on 0 %Sinusoidal 2 -0.2 t2=0:0.01:20; -0.4 -0.6 y2=sin(4*pi/T.*t2); -0.8 plot(t2,y2,'b'); -1 grid on; 0 2 4 6 8 10 12 14 16 18 20 ELG3125 Signal and System Analysis Fall 2010 School of Information Technology and Engineering

Square Wave 1.5 � Square wave with period T. � Example: 1 t=0:0.01:20; 0.5 T=5; %period 0 y=sign(sin(2*pi/T.*t)); -0.5 % or y=mod(t.*1/T,1)>1/2; plot(t,y),grid; -1 axis([0 20 -1.5 1.5]); -1.5 0 2 4 6 8 10 12 14 16 18 20 ELG3125 Signal and System Analysis Fall 2010 School of Information Technology and Engineering

Discrete-Time Sinusoidal Signals 1 0.8 � Sine signal with period N: 0.6 0.4 0.2 � Example: 0 n=0:20; -0.2 m=1; -0.4 N=7; %period -0.6 y=sin(2*pi*m/N.*n); -0.8 stem(n,y),grid; -1 0 5 10 15 20 25 30 . 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. ELG3125 Signal and System Analysis Fall 2010 School of Information Technology and Engineering

X[ n] = cos(n/ 8-pi) Result: NOT periodic 1 0.8 0.6 0.4 X= 114 0.2 X= 164 X= 13 Y= 0.11259 Y= 0.079564 X= 63 Y= 0.054177 Y= 0.021017 0 -0.2 -0.4 -0.6 -0.8 ELG3125 Signal and System Analysis Fall 2010 -1 0 20 40 60 80 100 120 140 160 180 200 School of Information Technology and Engineering

Discrete-Time Sinusoidal Signals Homework 1-26 c) 1 � x[n]=cos((pi/8)n 2 ) 0.8 � Code 0.6 0.4 n=0:100; 0.2 x=cos(power(n,2)*pi/8); 0 stem(n,x,’r’),grid; -0.2 -0.4 � Result: period N=8; -0.6 -0.8 -1 0 5 10 15 20 25 ELG3125 Signal and System Analysis Fall 2010 School of Information Technology and Engineering

Discrete-Time Exponential Signals � Exponential signal 150 y[n]=e -n � Example 100 n=0:10; y=exp(0.5*n); 50 stem(n,y),grid; 0 0 1 2 3 4 5 6 7 8 9 10 ELG3125 Signal and System Analysis Fall 2010 School of Information Technology and Engineering

Combination of Two Continuous-Time Signals 1.5 t=0:0.01:20; 1 T1=2; T2=4; 0.5 y1=cos(2*pi/T1*t); 0 y2=sin(2*pi/T2*t); -0.5 y3=y1+y2; -1 plot(t,y3),grid; -1.5 -2 0 2 4 6 8 10 12 14 16 18 20 ELG3125 Signal and System Analysis Fall 2010 School of Information Technology and Engineering

Combination of Two Discrete-Time Signals1 ------Addition � Code 1.5 n=0:60; 1 N1=2; m1=3; 0.5 N2=4; 0 m2=2; y1=cos(m1/N1*2*pi.*n); -0.5 y2=sin(m2/N2*2*pi.*n); -1 y3=y1+y2; -1.5 stem(n,y3),grid; 0 10 20 30 40 50 60 ELG3125 Signal and System Analysis Fall 2010 School of Information Technology and Engineering

Combination of Two Discrete-Time Signals2 ------Multiplication � Homework 1.26 d) 1 � x[n]=cos[pi*n/2]cos[pi*n/4] 0.8 0.6 0.4 � Code 0.2 n=-15:15; 0 x= cos(pi.*n/2)*cos(pi.*n/4) -0.2 Stem(n,x),grid -0.4 -0.6 -0.8 Result: period N=8 -1 (It verifies our analysis in the -15 -10 -5 0 5 10 15 tutorial class.) 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. 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. 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. ELG3125 Signal and System Analysis Fall 2010 School of Information Technology and Engineering

3D Plotting Example � y = e j (2 pi / T)t with period T. (Euler’s formula: 1 e jx = cos(x) + j sin(x)) � Code 0.5 T=6; 0 t=0:0.01:10; y=exp(j*2*pi/T.*t); -0.5 figure(1); plot3(t,real(y),imag(y)); -1 1 grid on; 0.5 30 0 20 axis square; -0.5 10 -1 0 ELG3125 Signal and System Analysis Fall 2010 School of Information Technology and Engineering

Enjoy signal…… ELG3125 Signal and System Analysis Fall 2010 School of Information Technology and Engineering