October 2006
Intermediate to advanced
369 pages
8h 11m
English
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4.7. Linear phase filters (maximally flat delay or MFD): Bessel and Thomson filters
4.7.1. Reminders on continuous linear phase filters
In some applications, we need a filter with a transfer function whose phase varies linearly with the frequency in a specific range.
Let us assume a continuous-time filter represented by its transfer function H(j2πf) = |H(j2πf)| exp(j
(f)). If we have been looking at |H(j2πf)|, we must also take the characteristics of (f) into account.
To do that, we look at an input signal that is made of two sinusoidal components:
The filtered signal then is written as:
or
Now, if we carry out a limited development of 
, we get:
Taking equation (4.68) into account, equation (4.67) is written as:
In order to avoid a frequency distortion, it is necessary that be cancelled. ...
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