# HW2 - x ( t ) = sinc 2 (50 t ) + cos(120 πt ) . 5. Project...

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ECE 402: Communications Engineering Homework 2 (Fall 2009) Due: Tuesday 9/15 1. Find the energy spectral density and autocorrelation of the signal x ( t ) = e - 2 t u ( t ) What signal energy is located in the frequency band | f | < 1 Hz? Hint: The following integral might be useful: Z dx x 2 + a 2 = 1 a tan - 1 x a . 2. Find the power spectral density of the periodic wave x ( t ) = X n = -∞ sinc 2 ([2 t - 4 n ]) . What fraction of the signal power is located at frequencies between | f | < 0 . 9 Hz? 3. Suppose the signal x ( t ) = 2 + sin(2 πt ) + 3cos(6 πt ) is the input to an ideal lowpass ﬁlter with frequency response H ( f ) = ( 1 , | f | < 2 0 , otherwise Find the output of the ﬁlter, and its DC, AC, and total power. 4. Find the maximum time between samples in order to recover the following signal exactly:
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Unformatted text preview: x ( t ) = sinc 2 (50 t ) + cos(120 πt ) . 5. Project 1, Chapter 2: Download sound7.wav from the course webpage and import it into MATLAB (a) What is the sampling rate? What is the duration of the audio clip? (b) Use MATLAB to plot the PSD of the signal (dBW/Hz vs. Hz). (c) What is the average power in this signal? (d) What fraction of the signal power lies in frequencies | f | ≤ 4 kHz? Hint: Remember that the DFT is periodic, so that X [-n ] = X [ N-n ]. Turn in your codes, plots and the analysis. 1...
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## This note was uploaded on 01/28/2012 for the course ECE 402 taught by Professor Townsend during the Fall '08 term at N.C. State.

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