An LTID system frequency response over |omega| < or equal to pie is H(Omega) = r

Question

An LTID system frequency response over |omega| < or equal to pie is H(Omega) = rect (Omega / pie) * e^ -j*2*Omega, Omega being the symbol for big omega , absolute value of Omega < or equal to pie. Find the output y[n] of this system, if the input x[n] is given by: A. sinc (pie*n / 2) B. sinc (pie *n) This question is from the second edition of linear systems and signals by B.P. Lathi. Chapter 9, question 9.4-5 Thanks so much for any help regarding this question

Explanation / Answer

u have h(w) given.. get the forrier trransform of the given input signal Asinc has fourier transform as 2* pi* A *rect(w)... ......... so sinc(n *pi/2) ----> 4rect(w) and sinc(pi*n)----> 2rect(w).... we know that convolution in time domain is equivalent to multiplication in frequency domain. so multiply the frequency domain input and output... you will get fourer transform of output as a) 4rect(w) *e^ -j*2*w and b) 2rect(w)*e^ -j*2*w ........now take inverse transform of these function... inv ta=ransform of rect function is sinc... but it is also multiplied by e^ -j*2*w so delay the sinc

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