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We are used to deal with pulse shaped signals, for example signals that go through root raised cosine filters at the transmit, and then matched with root raised cosine filters at the receive

In addition to these functions there are carrier phase and frequency synchronization, symbol timing synchronization at the output of the matched filter , equalization, etc..

Very briefly please, how would things be different at the receiver, if any, when receiving a signal that has not been pulse shaped by any conventional pulse shaping filter at the transmit(for whatever reason)?

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closed as unclear what you're asking by lennon310, MBaz, Peter K. Feb 5 at 14:07

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  • $\begingroup$ Any symbol has a duration, and this duration is the duration of the pulse. How could you transmit symbols without pulse shaping? $\endgroup$ – BlackMath Jan 21 at 0:21
  • $\begingroup$ yes any symbol has a duration, a rectangular pulse will have a spectrum like a sinc function going theoretically from -inf to + inf, that is why you pulse shape it in order to limit its frequency content but you could very well if you are not bound by any frequency restrictions send it without pulse shaping. a Morse signal for example is sent without pulse shaping. $\endgroup$ – Hatem Tawfik Jan 21 at 1:21
  • $\begingroup$ I am not sure even Morse signals don't have a pulse shape. It's a combination of pulses of different duration, but is your question on Morse signals, or on modern digital communication systems? I think any signal other than the delta dirac function must be represented by a pulse. $\endgroup$ – BlackMath Jan 21 at 1:51
  • $\begingroup$ yes I am talking about rectangular pulses that have not gone through a pulse shaping filter $\endgroup$ – Hatem Tawfik Jan 21 at 2:40
  • $\begingroup$ I am talking about sending a bpsk signal without pulse shaping it $\endgroup$ – Hatem Tawfik Jan 21 at 2:43
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Since you are talking about digital communication you are going to have a symbols. When u send a symbol $s(t)$ you are going to send it with a symbol time $T_{sym}$ so we can say that any symbol that is sent equals to $s(t)\Pi(\dfrac{t}{2T_{sym}})$ where $\Pi$ is the rectangular function. So basically any discrete time signal has a rectangular shaping pulse.

E.g.

In BPSK you will be sending one of the following symbols: $$ S_1(t)=1 $$ $$ S_0(t)=-1 $$ Since I am sending the symbols for a known time $T$

I am practically multiplying them with a rectangular window with the length of $T$

so for the data series $a$ the signal $S(t)$ will be : $$ S(t) = \sum_{k=0}^\infty S_{a_k}(t)\Pi(\dfrac{t-kT_{sym}}{ 2T_{sym} }) $$

And the matched filter in the receiver will be the average over $T_{sym}$ (or integration over $T_{sym}$) which is otherwise known as a rect.

Which is the same way you would do with other shaping pulses

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  • $\begingroup$ Thank you to all that answered this question. My confusion has been cleared now $\endgroup$ – Hatem Tawfik Jan 21 at 17:45

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