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may be expressed in decibels (dB) as

:

and

:

In a similar manner, SNR may be expressed in decibels as

:

Using the definition of SNR

:

Using the quotient rule for logarithms

:

Substituting the definitions of SNR, signal, and noise in decibels into the above equation results in an important formula for calculating the signal-to-noise ratio in decibels, when the signal and noise are also in decibels:
:

In the above formula, P is measured in units of

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