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SYSC 3501 Assignment 2 Solutions, Assignments of Signals and Systems Theory

Solutions is assignment 2 for SYSC 3501

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SYSC 3501 Winter 2013
Solutions to Assignment 2
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  • SYSC 3501 Winter
  • Solutions to Assignment

= 0.5 X 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 4 [10 Marks]

The signal, x ( t )  1 cos(2  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 )?