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Ideally, yes. But the ideal noncausal and infinite duration waveform can be truncated in time with a slight distortion in frequency domain.
Take the noncausal pulse. Shift it in time (delay) and truncate it for negative time (i.e. p(t)=0 for t<0). This causal pulse can be approximated.
It can be also truncated in time if digital FIR techniques are used (i.e. p(t)=0 for t>T, where T is the duration of the approximation).
SQRC is used in practice, for example Wideband CDMA systems. With SQRC, we actually split the RC into two idential function at transmitter and receiver, respectively. Therefore, the receiver SQRC performs matched filtering.
I dont know It wud be helpful or not but JUST GO THROUGH THIS AND SEE!!
I have been doing research on raised cosine pulses and the answers to ur questions are
(1) the raised cosine pulse that we use is causal as only haalf of the pulse is used for pulse shaping. Moreover,it is common engineering practice to split the pulse in half, i.e., to deploy a root (of the frequency response) pulse at the transmitter side, and the same root pulse at the receiver side that acts as a matched filter . Further, the filters are digitally implemented with a truncated oversampled causal version. For complexity reasons it is desirable that the tails decay rapidly
in order to allow quick truncation, and minimize the resulting intersymbol interference (ISI) at the receiver. This is because the auto-convolution of the truncated root pulse is not Nyquist anymore.
(2) The complete assembly o fwat u call a raised cosine filter is given by the eqn,