Solution to Q1 of Week 13 Quiz Pool


Suppose $ X(\omega)\,\! $ is the DTFT of a discrete-time signal $ x[n]\,\! $.

What is the DTFT of the time-reversal $ x[-n]\,\! $?

$ \begin{align} & \sum_{n=-\infty}^{\infty} x[-n]e^{-j\omega n} \\ & \quad (\text{change of variable} \;\; m=-n) \\ = & \sum_{m=-\infty}^{\infty} x[m]e^{j\omega m} = X(-\omega) \\ \end{align} $


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Alumni Liaison

Ph.D. 2007, working on developing cool imaging technologies for digital cameras, camera phones, and video surveillance cameras.

Buyue Zhang