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:
Now, if we carry out a limited development of , we get:
In order to avoid a frequency distortion, it is necessary that be cancelled. ...