## Signal to Noise Ratio

Signal to noise ratio (also referred to as S/N or SNR) is a measure commonly used in science and engineering which does a comparison between the level of desired signal to that of background noise. S/N ratio is defined as the ratio of signal power to the noise power, often expressed in decibels. Ratio above 1:1 (> 0 dB) means there’s more signal than noise. Although SNR is commonly mentioned in the context for electrical signals, it can also be applied to any signal. *Signal to noise* ratio, bandwidth and channel capacity of any communications channel are all connected by *Shannon Hartley theorem*.

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Lets say user has obtained the desired signal as well as the noise signal in the form of an array, then SNR calculation in MATLAB (before noise reduction) can be done as follows:

*snr (before) = mean( signal .^ 2 ) / mean( noise .^ 2 );*

*snr (before) db = 10 * log10 (snr_before) % in dB*

Post noise reduction, the residual noise is calculated as difference between the wanted signal & the actual signal. Calculation of SNR then becomes:

*residual_noise = signal – noise_reduced_signal; *

*snr_after = mean( signal .^ 2 ) / mean( residual_noise .^ 2 ); *

*snr_after_db = 10 * log10( snr_after )*

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Sample code:

*r = snr(x,y)*

*r = snr(x)*

*r = snr(x,fs,n)*

*r = snr(pxx,f,’psd’)*

*r = snr(pxx,f,n,’psd’)*

*r = snr(sxx,f,rbw,’power’)*

*r = snr(sxx,f,rbw,n,’power’)*

*r = snr(___,’aliased’)*

*[r,noisepow] = snr(___)*

*snr(___)** *

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