ECE2111 Signals and Systems UMD, Spring 2013 Experiment 1: Representation and manipulation of basic signals in MATLAB

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1 ECE2111 Signals and Systems UMD, Spring 2013 Experiment 1: Representation and manipulation of basic signals in MATLAB MATLAB is a tool for doing numerical computations with matrices and vectors. It can also display information graphically. The best way to learn MATLAB is to start with matrices. Go to File->New->Script and start typing the code over there. 1)Vectors A)Creating vectors from given data: a)row Vector : To create a row vector type the elements with a space or a comma between the elements inside the square bracket. Create a vector with output: Yr= b)column Vector : To create the column vector, type the left square bracket [ and then enter the elements with a semicolon between them, or press the Enter key after each element. Type the right square bracket ] after the last element. Create a vector with output: Pop= B)Creating a vector with constant spacing by specifying the first term, the spacing and the last term Variable_name=m:q:n, Where m is first term q is spacing n is last term Create a vector A whose first term is 3, constant spacing is 2 and last term is 9. C)Creating a vector with constant spacing by specifying the first and last terms and the number of terms Page 1 of 11

2 Variable_name=linspace(xi,xf,n) Where xi is first term n is number of terms xf is last term Create a vector B whose first term is 3, number of terms is 3 and last term is 9. 2)Matrices A)Entering two 3x3 matrices and storing them in the variables A & B A = [ ; ; ]; B = [ ; ; ]; B)Compute the square of matrix A Asqr = A * A C)Compute the product A * B AB = A * B D)Compute the product B * A BA = B * A E)Add the two matrices A + B Sum = A + B F)Compute the square of matrix B G)The zeros, ones and eye Commands: a)use the zeros command to generate a matrix having 3 rows and 4 columns and all elements as 0. zr=zeros(3,4) b)use the ones command to generate a matrix having 5 rows and 6 columns and all elements as 1. Page 2 of 11

3 ne=ones(5,6) c)create an identity square matrix of order 5 using the eye command Idn=eye(5) H)Element-by-Element Operations: Element-by-element multiplication, division and exponentiation of two vectors or matrices is entered in MATLAB by typing aperiod in front of the arithmetic operator Symbol Description.* Multiplication.^ Exponentiation./ Right Division a)if A= And B= Give results for element-by-element multiplication and right division of matrices A and B. b)for the function y=(2x 2-5x+4) 3 /x 2, calculate the value of y for the following values of x:-2,-1,0,1,2,3,4,5 using element-by-element operations. 3)Generating Continuous Time Signals MATLAB only deals with discrete time signals, continuous time signals are represented in the form of discrete time signals. A)Plot y = sin(t) on the interval t = 0 to t = 10 then plot X = e (-2*t), Z = e (-0.2*t), Q = e (-0.02*t) The x-axis: in the time interval: 0 < t < 10 with increments of 0.3 t = [0:0.3:10]; y = sin(t); plot(t,y); x = exp(-2*t); z = exp(-0.2*t); q = exp(-0.02*t); figure,plot(t,x,t,z,t,q); B)Plot y = cos(t) on the interval t = 0 to t = 30 Page 3 of 11

4 The x-axis: in the time interval: 0 < t < 30 with increments of 0.2 C)For f=10hz, plot x=cos(2*pi*n*f*t) for n=1,2,3,4 on 4 different plots on the same figure using the subplot command t=[0:0.003:1]; x1=cos(2*pi*1*10*t); subplot(2,2,1),plot(t,x1) x2=cos(2*pi*2*10*t); subplot(2,2,2),plot(t,x2) x3=cos(2*pi*3*10*t); subplot(2,2,3),plot(t,x3) x4=cos(2*pi*4*10*t); subplot(2,2,4),plot(t,x4) j(π/8 t) D)Plot the complex exponential signal: y = e t = [0:0.3:20] y = exp(j*(pi/8)*t) plot(t,y) Question 1: What Warning do you get from Matlab after typing the code above? What you can do to improve? E)Repeat example D) using subplots and labeling the graphs t = [0:0.3:20]; y = exp(j*(pi/8)*t); subplot(2,2,1),plot(t,real(y)) title('real part of the signal exp(j*pi/8)*t ') xlabel('time (sec) ') ylabel('real part of y ') subplot(2,2,2),plot(t,imag(y)) title('imaginary part of the signal exp(j*pi/8)*t ') ylabel('imaginary part of y ') subplot(2,2,3), plot(t,abs(y)) title('magnitude of the signal exp(j*pi/8)*t ') ylabel('magnitude of y ') subplot(2,2,4), plot(t,angle(y)) title('phase of the signal exp(j*pi/8)*t ') ylabel('phase of y (radians) ') Page 4 of 11

5 Now replace the highlighted lines with the following lines subplot(2,2,4), plot(t,angle(y)*(180/pi)) title('phase of the signal exp(j*pi/8)*t ') ylabel('phase of y (degrees) ') Question 2: What s the difference after changing the code? 4)Operation with signals MATLAB allows you to add, subtract, multiply, divide, scale, and exponentiate signals. Be careful! The vector representation of the signals should have the same time origins and the same number of elements. A)Given the signals x 1 and x 2 perform the following operations: y 1 = x 1 + x 2 ; y 2 = x 1 - x 2 ; y 3 = x 1 * x 2 ; y 4 = x 1 / x 2 ; y 5 = 2 x 1 ; y 6 = (x 1 ) (The above line is NOT codes.) Matlab codes are given as follows: % - A symbol used to make comments for coding; codes starting with % are not executed % Defining the signals x1 = 5*sin((pi/4)*[0:0.1:15]); x2 = 3*cos((pi/7)*[0:0.1:15]); % Plotting the signals subplot(2,4,1), plot(x1) title('x1 = 5 sin(pi/4)t ') ylabel('x1 (volts) ') subplot(2,4,2), plot(x2) title('x2 = 3 cos(pi/7)t ') ylabel('x2 (volts) ') % Addition y1 = x1 + x2; % addition y2 = x1 - x2; % subtraction y3 = x1.* x2; % multiplication y4 = x1./ x2; % division y5 = 2*x1; % scaling y6 = x1.^3; % exponentiation % Plotting the signals subplot(2,4,3), plot(y1) title('y1 = x1 + x2 ') 3 Page 5 of 11

6 ylabel('y1 (volts) ') subplot(2,4,4), plot(y2) title('y2 = x1 x2 ') ylabel('y2 (volts) ') subplot(2,4,5), plot(y3) title('y3 = x1 * x2 ') ylabel('y3 (volts)^2 ') subplot(2,4,6), plot(y4) title('y4 = x1 / x2 ') ylabel('x1/x2 ') subplot(2,4,7), plot(y5) title('y5 = 2*x1 ') ylabel('y5 (volts) ') subplot(2,4,8), plot(y6) title('y6 = x1 ^ 3 ') ylabel('y6 (volts)^3 ') 5)Generating Discrete Time Signals A)Plot the discrete time signal defined as: x[n] = 2n -3 < n < 3, 0 otherwise a) Plotting only the interval [ ] n = [-3: 3] x = 2 * n b).- Plotting the time interval [ ] n = [-3: 3] x = 2 * n n = [-5: 5] x = [ 0 0 x 0 0] c).- Plotting the time interval [ ] n = [-3: 3] x = 2 * n n = [-5: 5] x = [ 0 0 x 0 0] Page 6 of 11

7 n = [-50:50] x = [zeros(1,45) x zeros(1,45)]; B)Generate and plot the sequence g[n] = A (a ) n with A = 10 and a = -0.9, -10 < n < 10, 0 otherwise n = [-10:1:10] ; % defining the samples g = 10*(-0.9).^n; % defining the sequence figure % open a new window for the graphic stem(n,g) axis([-10, 10, -30, 30]); xlabel('sample number, n '); ylabel('g[n] '); title('exponential sequence '); grid text(0.6, 15, 'g[n] = 10(-0.9).^n '); 6)Control flow MATLAB has the following flow control constructs: if statements switch statements for loops while loops break statements The if, for, switch and while statements need to terminate with an end statement. A)if statement: x=-3; if x>0 str='positive'; elseif x<0 str='negative'; elseif x==0 str='zero'; else str='error'; end What is the value of str after execution of the above code? (type str) Shortcut to convert between codes and comments: Select the codes->ctrl R: to convert the codes to comments Select the codes->ctrl T: to convert the comments back to codes B)while statement: Page 7 of 11

8 x=-10; while x<0 x=x+1; end What is the value of x after execution of the above loop? C)for loop: x=0; for i=1:10 x=x+1; end What is the value of x after execution of the for loop? D)break statement: The break statement lets you exit early from a for or a while loop: x=-10; while x<0 x=x+2; if x==-2 break; end end What is the value of X? E)Repeat example 3C using while loop where n goes from 1 to 4. 7)Exercise: Write the code to get output exactly same as shown in the figure below Page 8 of 11

9 Demo: 1)Show b part of 2I 2)Show 3B 3)Show 6E 4)Show 7 Report Requirements: Individual lab report Attached with the cover page (available on website) This lab report should contain the following: 1. Statement of the Problem: Define the problem and goals of the experiment. 2. Results: a. Present all the results for 1 and 2 b. Print out all the plots of 3, 4 and 5 and provide explanation c. Answer the questions in 3 d. Provide the results from Control Flow 3. Exercises: Attached 4. Conclusions: Give comments to your results. Exercises: 1. Which of the following is a discrete time signal: a) y(t) = 5 sin (ω t) b) y[n] = 5 sin(20 π f n) c) y(t) = e (-2*t) Refer to the Matlab script below to answer questions 2 & 3: n = [-3: 3] x = 2 * n n = [-5: 5] x = [ 0 0 x 0 0] n = [-50:50] x = [zeros(1,45) x zeros(1,45)]; Page 9 of 11

10 2. What does the command stem do? a) to plot a continuous time signal b) to plot a discrete time signal 3. What does the command zeros do? x = [zeros(1,45) x zeros(1,45)]; (Two correct answers) a) to make the vectors n and x of same length b) to plot a discrete time signal c) to pad the vector x with 45 zeros on the left and 45 zeros on the right 4. For a signal y(t) = e (-2*t), what matlab command will be used to plot the magnitude of the signal: a) plot(t,mag(y)) b) plot(t,abs(y)) c) plot(t,real(y)) d) plot(t,imag(y)) Page 10 of 11

11 5. For a complex exponential signal: y = e j(π/8 t)), which of the following is the correct magnitude plot: Page 11 of 11