solnsmid2_600(2)

solnsmid2_600(2) - ECE-600 Introduction to Digital Signal...

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Unformatted text preview: ECE-600 Introduction to Digital Signal Processing Au10 Midterm #2 Nov. 22, 2010 MIDTERM #2 SOLUTIONS 1. (a) Since the signal is bandlimited to less than half of the sampling frequency, there will be no aliasing. Thus, we know that X ( e j T ) = 1 T X c ( j ) for | | < T . This imples that a frequency component at f Hz in x ( t ) will map to = 2 fT rad/sample, with its amplitude multiplied by 1 T . This explains the location of the right triangle. Because the signal is real-valued, there must be a symmetry around the frequency 0, which explains the left triangle. X ( e j ) 4 2 4 4 2 (b) The DFT samples the DTFT on the grid of points = 2 N k for k = 0 ,...,N 1. X [ k ] k 4 1 2 3 4 5 6 7 (c) Downsampling-by-two yields the DTFT Y ( e j ) = 1 2 1 p =0 X ( e j +2 p 2 ). Y ( e j ) 2 3 2 2 2 3 2 2 2 (d) Upsampling-by-two yields the DTFT Z ( e j ) = X ( e j 2 ). Note additional spectral copies! Z ( e j ) 4 8 4 3 4 7 8 8 4 3 4 7 8 2 2 P. Schniter, 2010 1 2. (a) Linear convolution of length- M sequence { x [ n ] } and length- L filter...
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This note was uploaded on 03/05/2011 for the course ECE 600 taught by Professor Clymer,b during the Fall '08 term at Ohio State.

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solnsmid2_600(2) - ECE-600 Introduction to Digital Signal...

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