lab7_digital_signal_processing - MASSACHUSETTS INSTITUTE OF...

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6.02 Spring 2008 1 of 9 Lab #7 M ASSACHUSETTS I NSTITUTE OF T ECHNOLOGY D EPARTMENT OF E LECTRICAL E NGINEERING AND C OMPUTER S CIENCE 6.02: Introduction to EECS II Spring 2008 Lab #7: Digital Signal Processing Goal: Design a digital circuit that implements a low-pass filter with a cut-off frequency of 1/8 of the sample rate. Verify the design using the JSim logic simulator and Matlab. Instructions: 1. Complete the pre-lab (see first section below). There are questions to be answered; please write your responses on a separate sheet of paper and turn them in at the beginning of lab on Wednesday. 2. Complete the activities for Wednesday’s lab (see second section below). 3. Prepare the requested material and think about the questions posed on the Check- off Sheet, then find a staff member to complete your post-lab interview. Pre-lab (due in lab, Wed., April 9, 2008) In this week’s lab we’ll be designing a digital low-pass filter with a cutoff frequency of 1/8 of the sample rate. In the pre-lab we’ll use Matlab to help develop the design parameters of the filter. Then in the lab we’ll design and test the logic itself using JSim, and then use Matlab at the very end to look at the FFT of the filter’s output on some test data. Step 1: Decide on filter architecture; calculate coefficients There are many choices for the architecture of a digital filter, varying in their logic complexity, throughput, rate of frequency roll-off, flatness of response in the passband and stopband, and stability when using integer arithmetic. Matlab provides many functions for designing filters as part of its Signal Processing Toolbox; we’ll make use some of these below. We’ll be using 2’s complement integer arithmetic in our filter design. While this keeps our logic simple and fast, it does introduce some quantization on the coefficient and data values, which appears as additional high frequency noise in the output data. This noise can cause stability problems for some filter architectures, but happily the FIR filters we’ve studied are good at handling this complication. With FIR filters there is a tradeoff we have to make between the number of taps and the steepness of the roll-off at the cut-
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6.02 Spring 2008 2 of 9 Lab #7 off frequency: more taps means steeper roll-off but also more logic. Each design makes this tradeoff differently; let’s use 11 taps for our design. To get started, fire up Matlab on an Athena workstation: athena% add 6.02 athena% It’s handy to have some test data on which to try our filter. We’ll use a 48kHz sample rate (this is a common sample rate in PC audio chips) and build a digital waveform containing sine waves at frequencies of 500Hz, 1.5kHz, 3kHz, 6kHz, 9kHz, 12kHz, 15kHz and 18kHz. In the Matlab command window enter the following commands: fs = 48000; % sample frequency n = 1024; % number of samples t = (1:n)/fs; % vector of n timepoints at 1/fs intervals % generate our test signal d = sin(2*pi*500*t) + sin(2*pi*1500*t) + sin(2*pi*3000*t);
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This note was uploaded on 08/23/2009 for the course EECS 6.02 taught by Professor Terman during the Spring '08 term at MIT.

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lab7_digital_signal_processing - MASSACHUSETTS INSTITUTE OF...

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