matched filter srrc
Hello tohji,
Suppose that the noise at the input of the receiving SRRC filter is AWGN (additive, white and gaussian noise). The noise Power Spectral Density (PSD) at the output has a shape proportional to |H(f)|^2, this is a raised cosine shape.
The autocorrelation function of the noise is the Fourier transform of the PSD, and this is the shape of the pulse (after SRRC Rx filtering), that has zero-crossings at the times nT (n = any nonzero integer, T = symbol time) because it is designed in order to avoid intersymbol interference (ISI). So, noise samples nT seconds apart are not correlated at the output of this filter. As the noise at the filter output is still gaussian, they are independent.
Conclusion: noise samples corresponding to the times at which the signal is sampled for symbol decisions are not correlated (and independent).
This property is valid for any shape that gives no ISI and that is evenly split between Tx and Rx in order to have a matched filter.
Regards
Z