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# hw9 - 6[30 Consider the CT signal x t = rect t A where t is...

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BME 311 PROBLEM SET #9 April 5, 2006 DUE DATE: April 12, 2006 Show work on separate sheets of paper. Include all hand plots, Matlab plots, and Matlab code. 1. [20] O&W 7.21. 2. [20] O&W 7.22. 3. [30] O&W 7.29. 4. [20] O&W 7.35. 5. [25] Consider the CT signal x ( t ) = 1 A sinc( t A ), where t is in units of seconds and A = 4. (a) What is the Nyquist sampling period, T N ? (b) Consider the DT signal x [ n ] generated from the samples of x ( t ). Using Matlab’s fft function, calculate the Fourier transform of x [ n ] for - N 2 n N 2 - 1, where N = 64. Plot the magnitude and phase of the DTFT X (e ) from - π to π . Do this for two values of T , one where x ( t ) is adequately sampled, and one where it is not.
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Unformatted text preview: 6. [30] Consider the CT signal x ( t ) = rect( t A ), where t is in units of seconds and A = 7. (a) Analytically determine the FT of this signal and plot in Matlab. (b) Sample x ( t ) with a sampling period T = 1. Determine, analytically or numerically, the DTFT of the sampled signal and plot in Matlab. (c) Compare the continuous and DT FTs over the frequency range -π to π . (d) Take the result of part (a) and create the spectrum Y (e jω ) = X (e jω )+ X [e j ( ω +2 π ) ]+ X [e j ( ω-2 π ) ]. Plot this spectrum from -π to π and compare with parts (a) and (b). 1...
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