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Unformatted text preview: y [ n ]. 3. Consider a continuous-time LTI system S whose frequency response is ⎩ ⎨ ⎧ ≥ = otherwise , 250 , 1 ) ( ω j H . When the input to this system is a signal x ( t ) with fundamental period T = π /7 and Fourier series coefficients a k , it is found that the output y ( t ) is identical to x ( t ). For what values of k is it guaranteed that a k = 0? 4. Consider the following system, with t t c t c c ω cos ) ( ) ( 2 1 = = . The ideal low pass filter has cutoff frequency m , where c m << . Sketch | Y ( j )| and | Z ( j )|. Identify all amplitudes and frequencies of importance. 1 ) ( j M m 1 −ω m × × x ( t ) y ( t ) z ( t ) Ideal Low Pass Filter m t ( ) c 1 t c 2 t ( ) ( )...
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- Spring '09