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What happens if you filter a discrete bandpass signal of length $N$ with a bandpass filter(Hann truncated sinc) of length $L$ and apply a window of length $N$ to the filtered signal of length $N+L-1$ to get back the signal to its original length $N$?

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  • $\begingroup$ Your question has beeen answered. Do not hesitate to vote for the useful ones and accept the most suitable $\endgroup$ – Laurent Duval Feb 9 '17 at 17:26
  • $\begingroup$ Answer upvotes and better answer validation are required for this question $\endgroup$ – Laurent Duval Jul 28 at 14:27
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If you want the output signal to have the same length as the input signal you would usually disregard the last $L-1$ samples of the result of the convolution. In Matlab/Octave, you could just use the function filter instead of conv. This will compute one output sample for each input sample, and, consequently, the output signal will have the same length as the input signal.

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You cannot "really" apply a window whose length is different from the size of the signal, since it resorts to a sample-wise product. However, you can for instance apply a composite window, made of a standard window $w$ for the first $N$ samples, and filled with zeros for the remaining samples (to the right). If $w$ is a rectangular window, you get with conv.m what you would have with filter.m, plus the flat tail, as explained by @MattL; the red lines (filter.m) and blue crosses (conv.m) are matching perfectly:

filters and windows

Of course, you could use a non-rectangular window (here the Hann), and you get a nicer apodization at the edges (the signal is flattened to $0$), but you could as well window the output of filter.m

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  • $\begingroup$ Thanks for the reply. But the underlying problem for asking this question is, in filtered OFDM at the transmitter each OFDM symbol is filtered by a band pass filter and transmitted. So, if you are applying filter for each OFDM symbol, the filtering operation creates tails and interfere with the previous and the next OFDM symbols. To reduce this interference you can window the filtered OFDM symbol and remove the tails. I wnat to understand the effect of this windowing with respect to interference caused by it to the frequency bands adjacent to the frequency band of the band pass filter applied $\endgroup$ – pardhu jyothi Dec 31 '18 at 7:36

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