Question

How many quantization errors are present in one complex valued multiplication?

(a) One

(b) Two

(c) Three

(d) Four

The question was posed to me in a national level competition.

This interesting question is from Quantization Effects in the Computation of DFT in chapter DFT Efficient Computation – Fast Fourier Transform Algorithms of Digital Signal Processing

Answer 1

The correct choice is (d) Four

The best I can explain: We assume that the real and imaginary components of {x(n)} and {WN^kn} are represented by ‘b’ bits. Consequently, the computation of product x(n). WN^kn requires four real multiplications. Each real multiplication is rounded from 2b bits to b bits and hence there are four quantization errors for each complex valued multiplication.