Consider a discrete-time ideal highpass filter whose frequency response is specified as
Chapter 6, Problem 6.6(choose chapter or problem)
Consider a discrete-time ideal highpass filter whose frequency response is specified as
\(H\left(e^{j \omega}\right)=\left\{\begin{array}{ll}
1, & \pi-\omega_{c} \leq|\omega| \leq \pi \\
0, & |\omega|<\pi-\omega_{c}
\end{array}\right.\)
(a) If h[n] is the impulse response of this filter, determine a function g[n] such that
\(h[n]=\left(\frac{\sin \omega_{c} n}{\pi n}\right) g[n]\)
(b) As \(\omega_{c}\) is increased, does the impulse response of the filter get more concentrated or less concentrated about the origin?
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