A#13 - shown, where . Find the center frequency, ( ) ( ) (...

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Assignment #13 ECSE-2410 Signals & Systems - Spring 2009 Due Tue 03/17/09 1(20). Consider the signal x ( t )=3cos( π t )+2cos(3 t )+cos(4 t ). (a) Find the Nyquist sampling frequency, ω s , which guarantees that x ( t ) can be recovered from its samples. (b) Suppose the signal x ( t ) is amplitude modulated by a carrier signal c ( t )=cos(2000 t ), so that the resulting signal is y ( t )= x ( t ) c ( t ). What is the highest frequency present in the modulated signal, y ( t )? 2(25). Find the largest sampling frequency, s , so that the signal x ( t )=cos(10 t ), when sampled and appropriately filtered, has an alias frequency of =5 rad/sec. 3(30). The following system, called a regenerative frequency divider, cuts the input frequency by half, as
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Unformatted text preview: shown, where . Find the center frequency, ( ) ( ) ( ) t y t x t a = c , of the bandpass filter in terms of . Also, find , the limit of the size of the passband, max B max B B < , in terms of . ( ) = t t y 2 1 cos B 2 H ( ) c ) ( t a ) cos( ) ( t t x = c 4(25). Suppose we wish to transmit the signal, ( ) ( ) t t x 1000 cos 100 = using a modulator that creates the signal, ( ) ( ) ( ) ( t A t x t w 000 , 10 cos ) + = . Find the value of A so that would allow asynchronous demodulation to have a modulation index, m , of 95%....
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