We can see the behaviour of the transversal filter in the time domain from its answer
given to the Dirac-impulse (weight function). If the delaying chain is ideal, namely the
members of the chain are free from loss, and they are individually with T-delay
independently from the frequency, the output signal of the T-filter consists of impulse
echoes of number N and Cn size at both sides of the main signal, from T
durations of each other (Figure T.3.).
Weight function of the T-filter:
(where the delta means the Dirac-function).
If an x(t) signal gets to the input of a T-filter, then the y(t) signal
occurring on the output is:
(where * means the convolution). Switching over the frequency domain, we can describe the
transmission characteristics of the T-filter:
If there is necessary to generate small echoes on both sides of the main signal, i.e. We
can assume, that:
then the amplitude- and running time characteristics of the ideal T-filter can be
described approximately:
As it occurs from the coherences mentioned above, in the case of small echoes, signals of
the individual symmetrical branches realize cosinusoid characteristics independently from
each other. For setting of the size of the nth cosinusoid component of amplitude and
running time characteristic we have a pair of coefficients, thus we can provide the
independence of the two characteristic components, so the circuit has usually not a
minimal phase. It is obvious, that the characteristic of a T-filter with an ideal
artificial delaying line is periodical according to 1/T:
However, only the band of the characteristic of the T-filter spreading to 1/2T frequency
can be chosen independently because of the restriction (sampling theorem).
T-filter can be applied excellently in the 0...1/2T frequency band, as a
corrector of group delay and attenuation. The correction means
here, that we can realize with the help of the T-filter a four-pole, which is connected to
a cascade with the network to be equalized, thus the transmission characteristic of the
original network realizes the criterion of the distortionless transmission.