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

If the difference d(n) = x(n)–ax(n-1), then what is the optimum choi

1.	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» 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 \({γ_{xx} (1)}{γ_{xx} (0)} = {γ_{xx} (1)}{σ_x^2}\).

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