GATE EC 2016 Set 3 — Question 45
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Signals & Systems → Discrete-Time Signals → DFT & FFT
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Question
A continuous-time speech signal is sampled at a rate of 8 kHz and the samples are subsequently grouped in blocks, each of size . The DFT of each block is to be computed in real time using the radix-2 decimation-in-frequency FFT algorithm. If the processor performs all operations sequentially, and takes 20 s for computing each complex multiplication (including multiplications by 1 and ) and the time required for addition/subtraction is negligible, then the maximum value of is __________
Correct answer
4096 to 4096
Solution
Given:
Sampling frequency Hz.
Time to collect samples = seconds.For a radix-2 FFT algorithm, the number of complex multiplications required for an -point DFT is .
Time for one complex multiplication = s.
Total computation time for one block = s.For real-time processing, the computation time must be less than or equal to the time taken to collect the samples for the next block:
Since must be a power of 2 for the radix-2 FFT algorithm, the maximum possible value for is .
Sampling frequency Hz.
Time to collect samples = seconds.For a radix-2 FFT algorithm, the number of complex multiplications required for an -point DFT is .
Time for one complex multiplication = s.
Total computation time for one block = s.For real-time processing, the computation time must be less than or equal to the time taken to collect the samples for the next block:
Since must be a power of 2 for the radix-2 FFT algorithm, the maximum possible value for is .
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