Question

The real vlaued continuous time function x(t) has Fourier transform $X\left(\omega \right)$ are

A signal y(t) has Fourier transform $Y\left(\omega \right)$ , the magnitude response of $Y\left(\omega \right)$ is same as that of magnitude response of $X\left(\omega \right)$ , but phase response of
$Y\left(\omega \right)$ is

Then relationship between y(t) and x(t ) is

• A. y(t) = x(-t+a)
• B. y(t) = x(t-a)
• C. y(t) = x(t+a)
• D. y(t) = x(t-a)

Answer 1

The correct option is B y(t) = x(t-a)

We can see that magnitude plot of $Y\left(\omega \right)$ is same as that of magnitude plot of $X\left(\omega \right)$.
But phase plot of $Y\left(\omega \right)$ is equal to mirror image phase of $X\left(\omega \right)+a\omega =Y\left(\omega \right)=X(-\omega )+a\omega$
Thus
$y\left(t\right)=x(-t-a)$