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solns6_600 - ECE-600 Homework#6 Introduction to Digital...

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ECE-600 Introduction to Digital Signal Processing Winter 2010 Homework #6 Nov. 12, 2010 HOMEWORK SOLUTIONS #6 1. In all plots, I used N = 2048 DFT points, because this gave a very smooth plot (i.e., Matlab’s plot command, which linearly interpoloates the DFT magnitudes, gave a very close approximation to the true DTFT magnitude). I chose a power-of-two value for N because this allowed Matlab to calculate the DFT using a radix-2 FFT, which is very fast. I used the following to plot the DFT using a dB magnitude scale and a Hz frequency scale: Ydft = 20*log10(abs(fft(yn,N))); plot([0:N/2-1]/N/T,Ydft(1:N/2)); I also plotted the true frequencies of the 4 sinusoids using dotted lines, but you could not have done this since you were not given this information. (a) i. Rectangular window : 0 10 20 30 40 50 60 -20 -10 0 10 20 30 40 rectangular window, N=2048 DFT magnitude Hz The two strongest sinusoids are visible at approximately 17 and 20 Hz. It is not possible to distinguish the weaker sinusoids from the sidelobes of the two strong sinusoids. P. Schniter, 2010 1
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ii. Triangular window : 0 10 20 30 40 50 60 -40 -30 -20 -10 0 10 20 30 triangular window, N=2048 DFT magnitude Hz
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