Question

How is the variance of the quantization error related to the size of the DFT?

(a) Equal

(b) Inversely proportional

(c) Square proportional

(d) Proportional

I got this question in homework.

My question is based upon Quantization Effects in the Computation of DFT topic in section DFT Efficient Computation – Fast Fourier Transform Algorithms of Digital Signal Processing

Answer 1

Correct option is (d) Proportional

The explanation: We know that each of the quantization has a variance of Δ^2/12=2^-2b/12.

The variance of the quantization errors from the 4N multiplications is 4N. 2^-2b/12=2^-2b(N/3).

Thus the variance of the quantization error is directly proportional to the size of the DFT.