Topic: Digital Signal Processing
Difference in number of complex multiplier required for 16 point DFT and 16-point radix-2 FFT is
- A. 30
- B. 63
- C. 224
- D. 256
Answer: C. 224
Explanation: An N-point DFT requires $N^2$ complex multiplications, which for N=16 is $16^2 = 256$. An N-point radix-2 FFT requires $\frac{N}{2} \log_2(N)$ complex multiplications, which for N=16 is $\frac{16}{2} \log_2(16) = 8 \times 4 = 32$. The difference is $256 - 32 = 224$.