EE4209/EE5809 Digital Audio --decibels dB
1. The origin of this particular choice of units and the terms decibels can be traced tothe definition of power ratios in systems.
2. Specifically, since the square of the magnitude of the Fourier transform of a signal can be interpreted asthe energy per unit frequency, or power, in a signal.
3. The square of the magnitude , |H(jw) | ^2 of the frequency response of a ssytem can be thought of as the POWER RATIO between the input and the output of an LTI system.
4. In honor of Alexander GRaham Bell, the inventor ofthe telephone, the term " bel" was introduced to indicate a factor of 10 in a power ration, and " decibel" was used to denote one-tenth of this factor on a logarithmic scale (so that the cascade of 10 systems with 1-dB power rations each would result in 1 bel of power amplification.)
5. Thus, 10 log| H(jw)|^2 is the number of decibels of power amplification for the frequency response H(jw), and this in turn 20log |H(jw) | in magnitude amplification.