# lab4 - EE 341 Spring 2011 Lab 4: Properties of...

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1 EE 341 Spring 2011 Lab 4: Properties of Discrete-Time Fourier Transform (DTFT) Report due in your discussion section June 1, 2, or 3 Objective In this lab, we will learn properties of the discrete-time Fourier transform (DTFT), such as conjugate symmetry and discrete-time convolution via DTFT multiplication. At the end, you will experiment with examples of real-world data: stock prices, music, and animal sounds. Credit for the concepts, code, and data samples for this lab goes to Prof. Somsak Sukittanon at Univ. of Tennessee, who got his Ph.D. from UW Electrical Engineering, and won our EE dept’s Best Teacher Award. MATLAB commands for TAs to go over (Do not turn this part in) [H,w] = freqz( b, a, N ); Brief description: Example of how to use it: [H,w] = freqz( b, a, N, ‘whole’ ); Brief description: Example of how to use it: [H,w] = freqz( b, a, N, fs ); Brief description: Example of how to use it:

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2 Part 1: The Frequency Domain This lab makes use of the DTFT  [] j jn n X ex n e  but will estimate it with relatively long yet finite sequences of data. 1. Case 1: You have a data sequence (not a difference equation), say x [ n ]. Examples are speech, music, and stock data. To estimate the Fourier transform, use freqz with b equal to the data and a = 1. I normally use N = 512 or 1024 to zero pad the data and make the DTFT estimate smooth. If x [ n ] is longer than 1024, you need to use N equal or greater than the length of x [ n ]. Usage: [H, W] = freqz( B, A, N ); [H, W] = freqz( x, 1, 512 ); The Matlab program below shows how to plot and label the magnitude and phase response obtained from freqz . 2. Case 2: You have a difference equation such as 20 1 2 [ ] [2 ] [ ] [1 ] ] yn ayn bxn   For this case, create a and b vectors in MATLAB to use with freqz. Be careful, because in the above example, 0 1 a and 1 0 a implicitly. Refer to the code below for a numeric example.
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lab4 - EE 341 Spring 2011 Lab 4: Properties of...

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