ELEMENTARY FIR FILTER QUESTION

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kingmakerbull

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1)For an FIR bandpass filter, there is a peak at zero in the frequency domain which is retained from the multiplication of the sinc function by a sine wave. But in time domain there is a valley corresponding to the peak.How is it possible?

2)The actual magnitude of |Hbp(m)| is half that of the original |Hlp(m)| because half the values in hbp(k) are zero when sshift(k) corresponds exactly to fs/4. Can somebody explain me in detail?
 

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