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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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Lab_07__Sampling__Convolution__and_FIR_Filtering_joshdean_ECE3220_Lab7_Joshua_Dean

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