090119HomeWork2

090119HomeWork2 - ECE 700 Digital Signal Processing Home...

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1 ECE 700 Digital Signal Processing Home Work 2 Due 1/26/09 Part I 1. Show that the two systems shown below are equivalent, where H 0 ( z ) is the zero th component in the M -way polyphase decomposition of H ( z ). 2. (Mitra, problem 13.42) Consider the system shown below. Show that the system is time-invariant and derive the transfer function from each input to each output. 3. (It’s a matrix world) Let [2 ] [1 ] [0] [1] [2] x x x x x x ⎛⎞ ⎜⎟ = ⎝⎠ # # represent the signal {[] , } . xn n −∞< <∞ For each of the following operations, find the matrix H that implements the given operation as . y Hx =
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2 a. 0 [] [][ ] k yn hkxn k = =− b. c. d. H ( z ) causal e. H ( z ) causal
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3 Part II (MATLAB Exercises) In this problem, you will design and implement a linear phase, FIR low pass filter , H ( z ) using three different methods. The overall filter should meet the following specifications: Sampling frequency 10000Hz Passband edge frequency 50 Hz Stopband edge frequency 55 Hz Maximum passband ripple 0.01 Maximum stopband ripple 0.003 1)
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090119HomeWork2 - ECE 700 Digital Signal Processing Home...

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