hw2_501_Au11

# hw2_501_Au11 - ECE-501 Introduction to Analog and Digital...

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Unformatted text preview: ECE-501 Introduction to Analog and Digital Communications Autumn 2011 Homework #2 Sep. 30, 2011 HOMEWORK ASSIGNMENT #2 Due Mon. Oct. 10, 2011 (in class) Reading: 1. Ch. 2.10-2.12 (the sections on Fast Fourier Transform Algorithms and Computation of the IDFT are optional). 2. Ch. 3.1–3.5. Problems: 1. In this problem you will use MATLAB to study causal linear-phase LPFs. (a) One way to design a causal linear-phase LPF is to truncate the t o-shifted sinc impulse response h ( t ) = 2 B sinc(2 B ( t − t o )) so that h ( t ) = 0 for t < 0 and t > 2 t o . For a single-sided bandwidth of B = 20 Hz and an impulse response length of 2 t o = 0 . 5 seconds, generate a T s = 0 . 001-sampled version of this impulse response in MATLAB and use plottf.m to plot the impulse and frequency magnitude responses. Comment on the non-ideality of the magnitude response of this filter. (b) Another way to generate a causal linear-phase LPF is to use MATLAB’s built-in filter design routines. Here you will use firls.m to repeat the filter design task in part (a). As described in the lecture, firls is used as follows: h = firls(Lf, [0,fp,fs,1], [G,G,0,0])/Ts; fp fs 1 G f 1 / (2 T s ) Lf +1 = impulse response length { 0, fp } , { fs , 1 } = normalized freq pairs { G , G } , { 0, 0 } = corresp. magnitude pairs For a fair comparison with the truncated-sinc design of part (a), use the same values of t o , T s , and passband gain, and set the passband and stopband cutoffs to be 0 . 9 B and 1 . 1 B Hz, respectively, for the same B . ( Hint: This implies Lf = 2 t o /T s and G = 1. Also, don’t forget to normalize the cutoff frequencies by 1 2 T s when setting fp and fs !) 2. In this problem you will experiment with the effects of filtering in MATLAB. Use a sampling rate of 1 T s = 1000 Hz throughout....
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hw2_501_Au11 - ECE-501 Introduction to Analog and Digital...

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