Question

If the difference d(n) = x(n)–ax(n-1), then what is the optimum choice for a = ?

(a) \({γ_{xx} (1)}{σ_x^2}\)

(b) \({γ_{xx} (0)}{σ_x^2}\)

(c) \({γ_{xx} (0)}{σ_d^2}\)

(d) \({γ_{xx} (1)}{σ_d^2}\)

I have been asked this question in a job interview.

Query is from Oversampling A/D Converters in division Sampling and Reconstruction of Signals of Digital Signal Processing

Answer 1

The correct option is (a) \({γ_{xx} (1)}{σ_x^2}\)

Easiest explanation: An even better approach is to quantize the difference, d(n) = x(n)–ax(n-1), w here a is a parameter selected to minimize the variance in d(n). This leads to the result that the optimum choice of a is \({γ_{xx} (1)}{γ_{xx} (0)} = {γ_{xx} (1)}{σ_x^2}\).