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Unformatted text preview: 1 (f) + 0.25 [ X 1 (f 2 f c ) + X 1 (f + 2 f c )] + 0.25 j [X 2 (f 2 f c ) + X 2 (f + 2 f c ) ]] Applying the LPF to y 4 ( t ): Z(f) = 0.5 X 1 (f) all the higher frequency components will be cut off z(t) = 0.5 x 1 (t) Problem 3 [10 Marks] The signal, x ( t ) = 1 + cos(2 π t ) + 2sin( 4 t ) Volt, is passed through an LTI filter, h ( t ) , whose transfer function is shown in the figure below. The output signal of the filter is y ( t ) . a) Find the Fourier transform of x ( t ) and sketch its magnitude spectrum,  X ( f ) . The magnitude spectrum is sketched by plotting weights of the delta functions. b) What is the fundamental frequency f 0 of x ( t ) ? c) Find the input PSD, P x ( f ) and sketch it. d) Find the output PSD, P y ( f ) and sketch it. P y (f) = H(f) 2 P x (f) 1 1 16...
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This note was uploaded on 02/15/2011 for the course SYSC 3501 taught by Professor Fewrf during the Spring '11 term at Carleton.
 Spring '11
 fewrf

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