4 - Professor BJ Trivedi EEL 3135 Fall 2011 Ch 13...

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Unformatted text preview: Professor BJ Trivedi EEL 3135 Fall 2011 Ch 13 Additional Problems Answers 1. :: 1 add 1 mult :: 2 add 1 mult :: 2 add 1 mult This leads to a Total of 5 adds 3 multiplies 2. The Figure below shows the butterfly representation of a decimation-in-time FFT algorithm for N=8. The bold line shows a path from sample x[7] to DFT sample X[2]. a. The gain is b. There is one path. In general, there is only one path from any input to any output sample. c. By tracing paths, we see that 3. Referring to the figure. The first stage of butterflies produces {2,2,2,2,0,0,0,0}. The phase factor multiplications do not change this sequence. The next stage produces {4, 4, 0, 0, 0, 0, 0, 0,} which again remains unchanged by the phase factors. The last state produces {8, 0,0, 0, 0, 0, 0, 0}. The bit reversal to permute the sequence into proper order unscrambles only zeros so the result remains unchanged. ...
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