Appendix B
Attenuation, Phase Shift and Decibels
The transfer function of a linear time-invariant system, denoted by H(ω), is in general a complex function of ω. It is indicative of the manner in which time harmonic signals (sine and cosine) propagate through such a system. The modulus of H(ω) is the factor by which the amplitude of the incoming harmonic signal is scaled and the argument of H(ω) indicates the phase shift introduced by the system. We then can write
where
is the attenuation of the system in neper (abbreviated as Np) and b(ω) is the phase shift introduced by the system. The neper is an old unit that is not used in practice anymore. A more common measure of attenuation is the decibel (abbreviated as dB). The attenuation in dB is defined as
From the relation
we conclude that
From this it follows that 1 Np is equivalent to 8.686 dB. Because the neper is used infrequently, we will drop the subscript ‘d’ and henceforth speak about attenuation exclusively in terms of dB and ...
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