there. I currently get stuck on a question. I was asking to find an inverse discrete-time Fourier transform for the ideal high pass filter. Here is the question It is getting more confused after I read the second solution of this post How to produce a high-pass filter from a low-pass one?
It tends out I can either calculate it by time-shifting property Or I can calculate it through the definition But they lead to a different result. My textbook solution said the second one is correct. But I cannot find any problem with the first one.
If we assume $\ 0 \le n < N-1$ for $h[n]$, using N = 61, $\alpha =30$, cutoff analog frequency $=1500Hz$. (Assume the sampling rate $=44100 Hz$ )
I got these two graphs:
(for the second)
I really don't know why they lead to different results.