Question

To reduce the dynamic range of the difference signal d(n) = x(n) – \(\hat{x}(n)\), thus a predictor of order p has the form?

(a) \(\hat{x}(n)=\sum_{k=1}^pa_k x(n+k)\)

(b) \(\hat{x}(n)=\sum_{k=1}^pa_k x(n-k)\)

(c) \(\hat{x}(n)=\sum_{k=0}^pa_k x(n+k)\)

(d) \(\hat{x}(n)=\sum_{k=0}^pa_k x(n-k)\)

This question was addressed to me in an international level competition.

My enquiry is from Oversampling A/D Converters in section Sampling and Reconstruction of Signals of Digital Signal Processing

Answer 1

The correct answer is (b) \(\hat{x}(n)=\sum_{k=1}^pa_k x(n-k)\)

Best explanation: The goal of the predictor is to provide an estimate \(\hat{x}(n)\) of x(n) from a linear combination of past values of x(n), so as to reduce the dynamic range of the difference signal d(n) = x(n)-\(\hat{x}(n)\). Thus a predictor of order p has the form  \(\hat{x}(n)=\sum_{k=1}^pa_k x(n-k)\).