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The noise power you should know a priori, or it will be not possible to compute the SNR. About the bandwidth, one approach is to perform the Fourier Transform (if you are workign with samples use the FFT algorithm) ans measure points 3dB (or 6dB or another threshold that you can define) below the maximum point. Probably, the bandwidth of the sampled signal is the same of your band-pass filter in the front-end of your receiver.
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