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In this problem, we derive an empirical formula for the average

In this problem, we derive an empirical formula for the average

In this problem, we derive an empirical formula for the average signal-to-(quantization) noise ratio of a DM system with a sinusoidal signal of amplitude A and frequency fm as the test signal. Assume that the power spectral density of the granular noise generated by the system is governed by the formula SN (A?) = ?2/6A?s where A?s is the sampling rate and ? is the step size. The DM system is designed to handle analog message signals limited to bandwidth W.
(a) Show that the average quantization noise power produced by the system is N = 4p2A2A?2mW/3A?3s where it is assumed that the step size ? has been chosen in accordance with die formula used in Problem 3.27 so as to avoid slope overload.
(b) Hence determine the signal-to-(quantization) noise ratio of the DM system for a sinusoidal input.

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