Consider th insider the sinusoidal signal x ( ) = cos ( 27 for ) . Suppose that x ( 1 ) is ideally sampled , i . e * ( 1 ) = * ( 4 ) [ 8 ( 6 - NTS ) at a rate of f Is samples per second . The sampled waveform y ( t ) is then passed through an ideal lowpass filter H ( jc ) with cut off frequency fo = Is 2 Hz and amplitude gain H ( jo Is. Denote the output of the lowpass filter by 2 ( t ) ( a ) Draw a block diagram of this system ( 6 ) Sketch Y ( 10 ) and H ( 10 ) VS the quantity f fs ( horizontal axis ) on the same plot for the case where Is = 3 fo / 2 and @ = 2 If ( C ) Find z ( ) when Is = 3 fo / 2 . Does 2 ( 1 ) = * ( 1 ) ? Is the Nyquist condition satisfied ? ( d ) For the system in part ( a ) above , find a value of fs and a value of fo so that the output is given by 2 ( 1 ) = cos ( for ) + cos ( 2 To for ) when the input is ( 1 ) = COS ( 2It for ) Notes : ( 1 ) To make things more concrete , it might be useful to do this problem first by choosing particular values for fo , Is and foes , to = 10 , Is = 15 and fo = 7.5 ( 2 ) The answer for part ( d ) is not be unique . i . e . , there is more than one pair of Is and fo values that works