Signal-to-Noise Ratio (audio/image)

How noisy is a signal with $40$, $30$, $20$, $10$, $0$, $-10$ or $-20$ dB SNR? Try it by yourself.

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40
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SNR is defined as the ratio of the power of a signal to that of the additional noise:

$$ \mathrm{SNR} = \frac{\sigma_x^2}{\sigma_n^2} $$

or, in decibels:

$$ \mathrm{SNR\ [dB]} = 10\log_{10}\left(\frac{\sigma_x^2}{\sigma_n^2}\right) $$

The imposed SNR is obtained by measuring the power of the input signal and adding noise with unit variance, scaled to achieve the chosen SNR.

$$ \sigma_n = \sqrt{\frac{\sigma_x^2}{\mathrm{SNR}}} $$

Noise becomes quickly visible and audible as the SNR decreases.