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I am trying to figure out what seems very trivial thing about down sampling and up sampling. The problem that I am facing is how to find the effects of up sample on a signal followed by a filter and/or a filter followed by down sampling. Here is a problem related to this from the Oppenhiem and Schafer book.

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I am trying to see what happens to x[n] after it pass the hlp[n], considering that hlp[n] has wc = pi/4. Will there be a gain on this or just the frequency is affected?

Please help, Thanks in advance

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do you go to concordia by any chance? this question looks waaaayyy to famaliar. :)

I asked a similar question a while back, the answers provided there should help.

up sample and down sample

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I think, this will act like low pass filter with $\pi/2$ instead of $\pi/4$ cutoff frequency

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