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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://dsp.stackexchange.com/questions/59079/can-we-band-pass-filter-qpsk-signal

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The matched filter is precisely that - it will filter out as much noise as is possible.

The reason you might want to use a band-pass filter (or ideally, a root-raised cosine) is to use less bandwidth. If you look at the spectrum of unfiltered QPSK, it will have a lot of out-of-band power. You don't want this in practice (because people transmitting on those other bands will be disturbed by this) and so you filter it.

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  • \$\begingroup\$ My question is for the receiver side only. I understand why matched filter is used. But can we use a band pass filter before matched filter? Will it reduce the performance of matched filter? More importantly can a band pass filter prior to matched filter show better results? If so under what conditions? \$\endgroup\$ – Creator Jun 23 at 9:48
  • \$\begingroup\$ The Bandpass must be square root Raised Cosine in both Tx and Rx in order to get the ideal zero ISI which depends on tolerances. \$\endgroup\$ – Sunnyskyguy EE75 Jun 24 at 0:49
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I've guided people who designed GSM receivers. You can view GSM as a minimum-shift-keying orthogonal-symbol 4-symbol communication system. The GSM symbols has a moderate amount of crosstalk, because of raised-cosine filtering in both the TX and the RX. Given all this filtering, the GSM channels can be tightly packed, with only ONE unused channel between active channels. (that is from memory). We DID FIND THE NEED to restrict the IF bandwidth right out of the down-conversion mixer, to avoid overloading on highly-amplified random-noise. The bandwidth was about 1MHz, about 4X the GSM single-side-band spectral occupancy.

You have to decide what Bit Error Rate penalties are acceptable, in your communication system. Filtering (aka ISI) is one penalty, but if needed to avoid CLIPPING on random noise, then you do what is needed to preserve the signal.

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