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ps8_fall06

# ps8_fall06 - Department of Electrical and Computer...

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Department of Electrical and Computer Engineering Digital Speech Processing Homework No. 8 Problem 1 – The uniform probability density function is defined as p ( x ) = 1 Δ | x | < Δ / 2 0 otherwise Find the mean and variance of the uniform distribution. Problem 2 – Consider the Laplacian probability density function p ( x ) = 1 2 σ x e - 2 | x | x Find the probability that | x | > 4 σ x . Problem 3 – A speech signal is bandlimited by an ideal lowpass filter, sampled at the Nyquist rate, quantized by a uniform B -bit quantizer, and converted back to an analog signal by an ideal D/A converter, as shown in the figure above. Define y [ n ] = x [ n ] + e 1 [ n ] where e 1 [ n ] is the quantization error. Assume that the quantization step is Δ = 8 σ x / 2 B and that B is large enough so that we can assume: 1. e 1 [ n ] is stationary 2. e 1 [ n ] is uncorrelated with x [ n ] 3. e 1 [ n ] is a uniformly distributed white noise sequence We have seen that, under these conditions, the signal-to-quantizing noise ratio is: 1

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SNR 1 = σ 2 x σ 2 e
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ps8_fall06 - Department of Electrical and Computer...

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