GATE 2024 IN – Question 25
The number of complex multiplications required for a 16-point DFT using the decimation-in-time radix-2 FFT is ______ (integer).
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Correct answer: 32 to 32
Explanation
A radix-2 FFT has $\log_2N$ stages with $N/2$ butterflies each. Counting one complex twiddle multiplication per butterfly gives $(16/2)\log_2 16=8(4)=\boxed{32}$. This conventional operation count includes trivial twiddle factors.