This blog is about digital signal processing (DSP), about digital communications, and about discrete-time and continuous-time signals and systems. Some of the posts are inspired by questions on dsp.stackexchange.com. If I think that one of my answers on dsp.stackexchange could be interesting and relevant for a wider audience I might also share it here.
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Hello Matt, thanks for your good explanation on the connection of the replicated discrete signal x[n] (x with tilda) DTFT to its DFT, as a Dirac comb on http://dsp.stackexchange.com/questions/17814/why-does-the-dft-assume-the-transformed-signal-is-periodic
ReplyDeleteI must admit that I struggle with the proof.
I got up to the following:
X^{tilda}(ω) = ∑_{k=-∞}^{∞}e^{-jωkN}X₀(ω),
where your notation is followed, and X₀(ω) is the DTFT of the signal x₀[n], known in only N points and zero outside.
Can you please, point to the step by step proof of this connection?
Thanks in advance,
Robert
You can answer directly to robertlexton@gmail.com or Robert.logozar@gmail.com.
Robert, I've added a proof to my answer. BTW, on DSP.SE you can leave a comment under an answer and the author will be notified.
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