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Joshua Dean Lab 7: Sampling, Convolution, and FIR Filtering April 11, 2011 The George Washington University School of Engineering and Applied Science ECE 3220 Digital Signal Processing Lab Section 30 GTA: Damon Conover Total Grade = 95/100 [10] Section 3.1: Plot x[n] and w[n] [10 points] [10] Section 3.1.1: Plot y[n] and w[n] [10 points] [15] Section 3.1.1-2: Plot difference between x[n] and y[n], calculate worst-case error, and explain significance [15 points] [5] Section 3.1.3: Determine values for r and P [5 points] [10] Section 3.1.3: Implement echo filter [10 points] [5] Section 3.2.1: Plot impulse response of overall cascaded system [5 points] [5] Section 3.2.1: Work out impulse response of overall cascaded system and state what it would need to be to achieve perfect deconvolution [10 points] [10] Section 3.2.2: Filter echart in two dimensions and plot result [10 points] [10] Section 3.2.2: Deconvolve filtered echart, plot result, and explain significance [10 points] [15] Section 3.2.3: Deconvolve filtered echart with filters of different sizes, compute worst-case error, and explain the differences [15 points] [] Plot original and filtered signals using inout and describe the differences [15 points extra credit]
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Introduction : The objective of this laboratory experiment was to learn how to implement FIR filters in MATLAB, and study the response of FIR filters to various signals. The FIR filters were used to analyze the properties of convolution (linearity and time-invariance). These properties were used to perform deconvolution. Deconvolution undoes the effects of the FIR filter. This lab blurs images and creates echoes of sound files. Experiment : 3.1 Deconvolution Experiment for 1-D Filters Using the firfilt() function to implement the FIR filter, w[n] = x[n] − 0.9x[n − 1], on x[n], the input signal(xx = 256*(rem(0:100,50)<10);). The input and output waveforms were plotted using subplot. The discrete-time signals were plotted using the stem function while restricting the horizontal axis to the range 0 ≤ n ≤ 75. The length of the filtered signal was found by using the sum of the length of the input signal and the length of the filter signal divided by 2. The
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This note was uploaded on 11/14/2011 for the course ECE 3220 taught by Professor Conover during the Fall '11 term at GWU.

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