1.

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»

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



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