Linear Systems Probleml Consider the LTI CT system which has

Linear Systems

Probleml: Consider the LTI C-T system which has the following frequency response function: H(c) = { 0.5, 3.5

Ans)

a) The output response y(t) is obtained by multiplying corresponding gain H(w) for the given input frequency

The frequencies in the input signal given is w=0,2,4,5,6,out of which,4,5 is in between 3.5 <w< 5.5

so y(t)=0*3+0*2 sin(2t) -0.5*4 cos(4t+45^o)+0.5*5 sin(5t)- 0*8 cos(6t-75^o)

y(t)=-2 cos(4t+45^o)+2.5 sin(5t)

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b) Similary as in part-\'a\',only the frequencies in the range 3.5<w<5.5 has non-zero magnitude other wise zero

y(t)=2*0+0.5*4cos(4t-pi.4)+0.5*5cos(5t-pi/4)

y(t)=2 cos(4t-pi/4) +2.5 cos(5t-pi/4)

The other frequencies are in not in the range hence they have zero \'0\' magnitude,the output response is given below