2.Filtering Long Sequences: (20 Pts)The length of a sampled speech signal is 61359samples and the sampling rate is 8000 samples per second. We wish to use the overlap-save filtering procedure with an FIR digital filter with 150 coefficients.(a) Determine the total number of complex multiplications required to filter the in-put sequence using an FFT algorithm directly without using the overlap-saveprocedure. The FFT size must be a power of 2 and it should be large enough to
(b) Determine the total number of complex multiplications required to filter the se-quence using the overlap-save procedure and a block size of 1024 samples.
Solution:

ECE 513 Test #1
Instructor: Dr. Cranos Williams
5
2. (cont’d)

ECE 513 Test #1
Instructor: Dr. Cranos Williams
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3.ROC and Stabilization: (20 Pts)Given the following transfer functionH(z) =z-1(z+3-4j)(z+3+4j)(z+0.8)=z-1z3+6.8z2+29.8z+20(a) Draw the pole-zero plot and specify all possible Regions of Convergence (ROC).Which one of these ROC’s (if any) would yield a stable system?(b) Draw the estimated magnitude response of the stable system from (a). NOTE:An approximation is fine. What type of filter is this?(c) Derive a transfer function for a stable AND causal system that has the samemagnitude response as the stable system from (b).

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