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**Unformatted text preview: **Processing Fall 2007 Problem Set 8 Due: November 1, 2007 3. Consider the following sampling scenarios for audio applications: The first scenario is the conventional Nyquist sampling one while the second represents the "4x oversampling" scenario. In the latter, H e j is an ideal lowpass digital filter with cutoff 4 frequency at c = / 4 and denotes a "downsampling" operation (In the figure below, ( ) x 2 [n] = y o [4n] ). Answer the following questions about the two sampling systems: a) What is the cutoff frequency for each of the two antialiasing filters (assumed ideal)? b) For a sinusoidal input signal of frequency 5.5 kHz, what is the relative frequency of all the resulting digital sequences shown for both sampling systems? c) Repeat Part b) for an input frequency of 44 kHz. d) Comment on the role of the digital lowpass filter in the 4x system. e) (Bonus 25 points) Based on your answers above, discuss how the specifications of the antialiasing filter can be simplified for the 4x system. Consider only the edge frequencies for the passband and stopband in each case. x a (t ) H a1 ( j) A/D x1[n] (1/T1)= 44 kHz x a (t ) H a 2 ( j ) xo [n] A/D H (e j ) y o [n] 4 x2[ n] (1/T2)= 4X44...

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