ECE405CA1Su2010 - ECE 405 COMPUTER ASSIGNMENT #1 SU 2010...

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ECE 405 COMPUTER ASSIGNMENT #1 SU 2010 ©DR. JAMES S. KANG 1. A rectangular pulse train with amplitude h = 1V, period T o = 1ms, and pulse width τ = 0.25ms, shown in Figure 1, is applied to 4 th -order Butterworth lowpass filter with cutoff frequency 2 π / τ . Plot the waveforms in the time domain and the spectrums in the frequency domain for the input and output of the filter. Also plot the magnitude and phase spectrum of the filter. Figure 1 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 x 10 -3 0 0.5 1 t f(t) Fourier Series Approximation Notice that the normalized transfer function of the 4 th -order Butterworth lowpass filter is given by 432 1 () 2.6131259 3.4142136 2.6131259 1 Hs SSSS = ++++ To transform this normalized lowpass filter to a lowpass filter with cutoff frequency 2 π / τ , use the following procedure: T01=10^-3; tau1=T01/4; N=20; n1=-N:N; %Butterworth Filter %n=4 syms S woa w1 w2 w3 w4 s format long e NLPF1=1/(S^4+2.6131259*S^3+3.4142136*S^2+2.6131259*S+1) %Normalized LPF to Frequency Transformed LPF FTLPF=simple(subs(NLPF1,S,s/woa)) LPF=subs(FTLPF,woa,2*pi/tau1) [numLp,denLp]=numden(LPF) numL=sym2poly(numLp) denL=sym2poly(denLp) numL1=numL/denL(1) denL1=denL/denL(1) num=numL1 den=denL1 format short ; wo=2*pi/T01 H=num./(den(1)*(j*n1*wo).^4+den(2)*(j*n1*wo).^3+den(2)*(j*n1*wo).^2 ...
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ECE405CA1Su2010 - ECE 405 COMPUTER ASSIGNMENT #1 SU 2010...

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