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I facing a problem in GSM simulation. I am having a perfect GMSK modulated (I can assume that GMSK filter is 200kHz or 270 kHz band limited) signal in Tx path adding AWGN of 6dB SNR (Noise 6dB below Signal). I am passing this through a baseband filter at receiver of 160 kHz. I am ok with the signal distortion due to stricter LP filter then signal bw but I want to estimate SNR at output of the filter.

Shouldn't I get an improvement of 10*log10(270000) - 10*log10(160000) in dB. Even if yes, what are the steps to reproduce and check the estimate the same feeding some known GMSK signal

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No, it isn't that simple. Your low-pass filter is also throwing away some of the signal energy, which reduces the SNR improvement you can expect. Since the signal energy isn't distributed uniformly across frequency (like the noise is), it will require a more complicated formula (integration?) to predict the theoretical SNR improvement.

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