Home › Previous year questions › GATE 2016 EC (EC3) › Question 45GATE 2016 EC (EC3) – Question 45 Networks, Signals and Systems · Discrete-time Signals · 2 marks · Numerical answer
A continuous speech signal sampled at 8 kHz is grouped into N-sample blocks. Each DFT must be computed in real time by radix-2 decimation-in-frequency FFT. A sequential processor takes 20 μs per complex multiplication, including multiplication by ±1; addition/subtraction time is negligible. The maximum N is ________.
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Show answer and explanation Correct answer: 4096 to 4096
Explanation A radix-2 N-point FFT requires $(N/2)\log_2N$ complex multiplications. Processing time is therefore $10N\log_2N$ μs.
A new N-sample block arrives every N/8000 seconds, or 125N μs. Real-time operation requires $10N\log_2N\le125N$, hence $\log_2N\le12.5$.
N must be a power of two, so the largest allowed exponent is 12: **N=4096**.
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