You are to analyze the audio recording and playback system

Question

Q1: Sampling Theorem and Quantization

You are to analyze the audio recording and playback system shown below. The input audio frequency range is fÎ[0, 3.5] kHz. The listener's hearing range is fÎ[0, 8] kHz. The ADC operates at the programmable sample rate of f_s = n8kHz, n an integer.

a) What is the lowest sampling frequency f_s that will insure that the original audio signal x(t) can be (theoretically) reconstructed from its time-series samples x[k], without aliasing?

b) The room is presumed quiet and you begin recording at a sample rate of f_s=8k Sa/s.  When played back you hear a 2k Hz "buzzing sound" in the captured signal.  What is the expected minimum frequency of the extraneous tone that could have created this effect?

c) You decide to place an ideal analog lowpass anti-aliasing filter in front of the ADC. What should be the filter's passband cut-off frequency?

d) The signed ±10V ADC provides an 8-bit output with an input |x(t)|<10V.  What is the ADC's quantization step size?

e) The signed 8-bit ADC's output is sent to an accumulator that produces an output given by:

Attachment:- Practice_Exam_1_20011 (1).doc