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Consider we have QPSK signal with carrier frequency 10kHz. Generally, we demodulate or use matched filter on the the QPSK signal and recover the transmitted bit or the symbols. If the QPSk signal is noisy can we use band pass filter before demodulation, where the pass band is around 10 kHz? The QPSK signal has discontinuity when the bit/symbol changes, so are we going to loose valuable information if we band pass the signal before matched filter? Is there an appropriate band width of the band pass filter which can be applied so that matched filter still works after the band pass filter?

EDIT: More importantly can a band pass filter prior to matched filter show better results? If so under what conditions?

This question is also asked in: https://electronics.stackexchange.com/posts/444921/edit

Creator
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Yes, you can bandpass the QPSK signal before matched filtering and demodulation if you wish to do so, but what you need to devote some thought to is whether such an action is a wise decision. The answer might depend on various parameters that you have left unspecified.

  • Bandwidth of bandpass filter $<$ QPSK signal bandwidth
    In this case, the filtered QPSK signal now has intersymbol interference (ISI) in it whereas the incoming signal did not, which makes the subsequent matched filtering and demodulation more problematical. Equalization might be needed to ameliorate the ISI which will add to the cost/weight/power consumption of the receiver, and error probability will likely suffer.
    I didn't bring up the issue of the center frequency of the bandpass filter in the previous paragraph, but if the center frequency is different from the carrier frequency, then there is a whole 'other can of worms that you will have opened up.
  • Bandwidth of bandpass filter $>$ QPSK signal bandwidth
    This is a much better notion that the previous one. The issue of mismatch between center frequency of the filter and the carrier frequency is still there, though. But, is this a good idea? Maybe, maybe not. Remember that the matched filter is also a bandpass filter. Indeed, as pointed out here, the matched filter has transfer function $S^*(f)$ where $S(f)$ is the Fourier transform of the QPSK signal, and so the matched filter has large gain at frequencies where the signal is strong and low gain at frequencies where the signal is weak -- a resume'-writer, no less, since it is emphasizing the strong points and playing down the weak ones. Thus, additional bandpass filtering ahead of the matched filter is not really necessary from a purely DSP perspective. However, your circuit designer colleagues might well insist on the extra bandpass filtering on the grounds that it helps with dynamic range issues in low SNR situations.

So, explore all the ramifications before jumping into bandpass filtering. Do you really need to use a bandpass filter, or can you get by without it?

Dilip Sarwate
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