EE3210 Lab 1: Introduction to MATLAB

Transcription

1 City University of Hong Kong Department of Electronic Engineering EE3210 Lab 1: Introduction to MATLAB Verification: The Warm-Up section must be completed during your assigned lab time. The steps marked Instructor Verification must also be signed off during the lab time. When you have completed a step that requires verification, simply demonstrate the step to the instructor. Lab Report: You are NOT required to turn in a report for this lab. However, you are recommed to complete the Experiment section in order to get familiar with the use of MATLAB. 1 Background MATLAB is a sophisticated language that serves as a powerful tool to better understand a myriad of topics, including control theory, filter design, and of course, signals and systems. MATLAB s flexible programming structure promotes rapid development and analysis. Outstanding visualization capabilities provide unique insight into system behavior and signal character. By exploring concepts with MATLAB, you will substantially increase your comfort with and understanding of course topics. 2 Warm-up 2.1 Getting Started MATLAB can be started by double clicking the MATLAB icon under Window XP environment. The following steps are useful for getting around under MATLAB. (a) View the MATLAB introduction by typing intro at the MATLAB prompt. This short introduction will demonstrate some basic MATLAB commands and their syntax. Explore the MATLAB help capability. Try the following (it is possible to force MATLAB to display only one screen full of information simultaneously by issuing the command more on): help help plot help colon help ops help zeros help ones lookfor filter %<--- keyword search

2 (c) Run the MATLAB demos. Type demo and explore some of the demos of MATLAB commands and MATLAB plotting facilities. (d) Use MATLAB as a calculator. pi*pi - 10 sin(pi/4) ans ^ 2 Try the following: %<--- "ans" holds the last result (e) Perform variable name assignment in MATLAB. Try the following: x = sin(pi/5); cos(pi/5) y = sqrt( 1 - x*x) ans %<--- assigned to what? (f) Complex numbers are natural in MATLAB. The basic complex operations are supported. Try the following: z = 3 + 4i conj(z) abs(z) angle(z) real(z) imag(z) J = sqrt(-1) exp(j*pi) exp(j*[pi/4 - pi/4]) (g) Plotting of real or complex function is easy in MATLAB. The basic plot command can plot a 2D graph defined by two vectors. Try the following: x = [ ]; y = x.*x - 3*x; plot(x, y) z = x + y*sqrt(-1) plot(z) %<--- complex values can be plotted Use help arith to learn how the operation x.*x is actually performed and compare this to matrix multiplication. 2.2 MATLAB Array Indexing (a) Make sure that the colon notation is fully understood. In particular, find out what the following MATLAB code will produce jkl = 2 : 4 : 17 jkl = 99 : -1 : 88 ttt = 2 : (1/9) : 4

3 tpi = pi * [2 : (-1/9) : 0] Extracting and/or inserting numbers in a vector is very easy to do. Consider the following definition: x = [ ones(1,4), [2:2:11], zeros(1,3) ] x(3:7) length(x) x(2:2:length(x)) (c) In the previous part the vector x contains 12 elements. Observe the result from the following assignment: x(3:7) = pi*(1:5) Now write a statement to replace the odd-indexed elements, x(1), x(3), and, etc, with the constant -77. Remember to use vector replacement. Instructor Verification (separate page) 2.3 MATLAB Script Files (a) Experimenting with vector processing in MATLAB. A vector can be considered as a set of numbers. Try the following: kset = -3:11; kset cos (pi*kset/4) %<--- comment: compute cosines Loops can be used in MATLAB. But this is NOT an efficient way to handle vector processing. It is better to avoid loops and use vector notation instead. Here a loop is used to compute a set of values from the sine function. Note that the index of x() begins at 1. Rewrite the following codes without using loop. x = [ ]; %<--- initialize the x vector to a null for k = 0:7 x(k+1) = sin(k*pi/4) x (c) Use the text editor in MATLAB to create a script file called funky.m. The file should contain the following lines:

4 tt = -2 : 0.05 : 3; xx = sin(2*pi*0.789*tt); plot(tt, xx), grid on %<--- plot a sinusoid title('test PLOT of SINUSOID') xlabel('time(sec)') (d) Run the script from MATLAB by typing funky %<--- will run the commands in the file type funky %<--- will type out the contents of funky.m to the screen (e) Add three lines of code to the script so as to plot a cosine on top of the sine. Use the hold function to add commands to plot the result from the following statement 0.5*cos(2*pi*0.789*tt) See help hold in MATLAB for the usage. Instructor Verification (separate page) 2.4 MATLAB Sound (a) Run the Matlab sound demo by typing xpsound at the Matlab prompt. If you are unable to hear the sound in the Matlab demo then ask the lab instructor for help. Now generate a tone (i.e., a sinusoid) in Matlab and listen to it with the sound command. The frequency of the tone should be set at 2 khz and the duration should be set at 1 second. Use a sampling rate of 8000 samples/second. The sampling frequency affects the time-vector in the following way: tt=0:(1/fs):dur; where fs is the desired sampling rate and dur is the desired duration in second. Read the online help for sound to get more information on using this command. Instructor Verification (separate page)

5 3. Experiment: Using Matlab 3.1 Functions The following exercises were designed to help you writing functions in Matlab. (a) Find the mistake(s) in the following function: function x=cosgen(f,dur) %COSGEN Function to generate a cosine wave % usage: % x=cosgen(f,dur) % f=desired frequency % dur=duration of the waveform in seconds % t=[0:1/(20*f):dur]; % gives 20 samples per period y=cos(2*pi*f*t); Find the mistake(s) in the following function: function [sum,prod]=sumprod(x1,x2) %SUMPROD Function to add and multiply two complex numbers % usage: % [sum,prod]=sumprod(x1,x2) % x1=a complex number % x2=another complex number % sum=sum of x1 and x2 % prod=product of x1 and x2 % sum=z1+z2; prod=z1*z2; (c) Explain the following lines of Matlab code: yy=ones(7,1) * rand(1,4); xx=randn(1,3); yy=xx(ones(6,1),:); (d) Write a function which will perform the same task as the following codes but without using FOR loop. function Z=expand(x,ncol) %EXPAND Function to generate a matrix Z with identical columns equal % to an input vector x % usage: % Z=expand(x,ncol)

6 % x=the input vector containing one column for Z % ncol=the number of desired columns % x=x(:); %this turns the input vector x into a column vector Z=zeros(length(x),ncol); for i=1:ncol Z(:,i)=x; 3.2 Vectorization (a) Explain the following lines of Matlab code: A=randn(6,3); A=A.* (A>0); Write a function which will perform the same task as the following codes but without using FOR loops. function Z=replacez(A) % REPLACEZ Function that replaces the negative elements % of a matrix with the number 77 % usage: % Z=replacez(A) % A=input matrix whose negative elements are to % be replaced with 77 % [M,N]=size(A); for i=1:m for j=1:n if A(i,j) < 0 Z(i,j)=77; else Z(i,j)=A(i,j); Hint: Matlab logical operators may be helpful in completing this exercise. Use help to get more information about these commands. 3.3 Manipulating Sinusoids with Matlab Generate two 3 khz sinusoids with arbitrary amplitudes and phases. x ( t) = A cos( 2π (3000 t + φ ) x ( t) = A cos( 2π (3000 t + φ ) 1 1 ) ) 2

7 (a) Select the values of amplitudes and phases at random. Let A 1 = 13 and use your age for A 2. For the phases, use the last two digits of your Student ID for φ 1 (in degrees), and take φ 2 = -30. Note that, when performing computations, make sure to convert the units from degree to radian! Make a plot of both signals over time duration of approximately 3 cycles. Make sure that the plot will include sample at t = 0, and also make sure that you have at least 20 samples per period for plotting. (c) Verify that the phases of the two signals x 1 (t) and x 2 (t) are correct at t = 0, and also verify that each one has the correct maximum amplitude. (d) Use subplot(3,1,1) and subplot(3,1,2) to make a three-panel subplot that will put both of the plots on the same page. See help subplot for the usage. (e) Create a third signal as the sum of the two sinusoids, i.e., x 3 (t) = x 1 (t) + x 2 (t). In Matlab, this accounts to summing the vectors that hold the samples of each sinusoid. Make a plot of x3(t) over the same time duration as used in the last plots. Include this as the third panel in the plot by using subplot(3,1,3). (f) Measure the magnitude and phase of x 3 (t) directly from the plot. sufficient annotation to show how the magnitude and phase were measured. Hand in the plot with

8 Lab 1 Instructor Verification Sheet Submit this page to the instructor at the of the lab session. Name: _ Date: Part 2.2 Vector replacement using the colon operator. Verified: Part 2.3 Run the modified function funky from a file. Verified: Part 2.4 Use the sound command to play a 2 khz tone. Verified: