ECSE304_4_2010

# ECSE304_4_2010 - Solutions for Assignment#4 ECSE 304 Winter...

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Solutions for Assignment #4 ECSE 304 Winter 2010 By Vahid Raissi Dehkordi 1. Laplace Transform, LTI Systems and Feedback a)           1 0 1 10 1 10 1 10 1 10 1 10 1 10 1 10 10 1 10 1 1 sensor sensor t t t t yt x t ut t eut eut e u d e d e           No, because the output should be equal to the input, but it’s not. The extra term in the output ruins the temperature reading. b) 12 1 11 sensor s Hs ss  The sensor is causal. Therefore, the region of convergence is   Re 1 s  . This ROC includes the j -axis and as a result, the sensor is stable. c) We want , meaning that   comp x t     1 sensor comp G s . As a result: 1 1 2 comp sensor s Gs H s s  The common part of   Re 1 s (ROC of H) and the ROC of G is included in the ROC of GH, which is the whole s -plane. The only choice of ROC for G which makes it possible for both ROCs to have something in common is   Re 2 s , and that makes G causal. d) 1/s -2

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2. Speech Processing and Acoustics: Convolution and the Impulse Response a) 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 time (sec) magnitude The impulse response of the anechoic chamber is most likely a delta function or something very close to a delta. The delay can be found by noticing the number of zeros before the first delta function appears in the impulse response. The delay in the beginning of the graph (the silent part) determines the distance between the recorder and the speaker. Here the distance is 0.009s * 340m/s = 3.06m b) The code can be as follows: h = wavread('h.wav'); x = wavread('speech.wav'); plot([1 : length(h)] / 16000, h); y = conv(x, h); sound(x, 16000); sound(y, 16000); The anechoic chamber has no distortion to speech, because it suppresses most echoes. Convolution with the impulse response of an actual room, simulates the room’s acoustics, or, in
other words, applies a reverb effect. This is characterized by decaying, but persistent, echoes that create a feeling, or perceptual indication, of space. One can hear the echoes and low-frequency room murmur.

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ECSE304_4_2010 - Solutions for Assignment#4 ECSE 304 Winter...

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