Method for determining the transmittance of a filter circuit adapted to transform the impulse response of a filter into a minimal phase response and filter implementing this method

In a receiver, connected to a filter medium transmitting first symbols and having an impulse response H(z), having a filter circuit providing a transmittance P(z), such that the filter circuit and the filter medium collectively possess a global impulse response characterized as a minimal phase response, serially connected to a detector for generating second symbols responsive to the first symbols, and a computer, connected to an estimator generating an estimate of a frequency response H(f) of the filter medium as a Fourier transform H(z) of the impulse response H(z) of the filter medium, the computer being connected to the filter circuit for generating coefficients corresponding to an estimated transmittance H(z), a method of operating said computer comprising the steps of:

• (a) determining a real part a(f) of a cepstrum H(f)=-1n(H(f) of the frequency response H(f) of the filter medium to thereby extract from said real part of a(f) an even part p(f) and an odd part q(f);
• (b) determining a cepstrum G(f)=-1n(G(f)) of a global frequency response G(f) from said even part p(f) and said odd part q(f) of said cepstrum H(f) of the impulse response H(z) of said filter medium;
• (c) determining said global frequency response G(f) from said cepstrum G(f);
• (d) determining a theoretical frequency response C(f) of the filter circuit responsive to said global frequency response G(f) and the frequency response H(f) of said filter medium;
• (e) calculating a theoretical transmittance C(z) of the filter circuit as an inverse Fourier transform of said theoretical frequency response C(f) of the filter circuit;
• (f) determining the estimated transmittance P(z) of the filter circuit by truncating said theoretical transmittance C(z) thereby retaining only a predetermined number of coefficients thereof;
• and
• (g) providing said coefficients corresponding to said estimated transmittance P(z) so as to operate the filter circuit.

A filter circuit located in a receiver providing received symbols to a detector via said filter circuit and associated with a filter such that a global impulse response of said filter and said filter circuit represents a minimal phase response, said filter circuit comprising:

• transversal filter means having a transmittance P(z) for filtering said symbols;
• estimating means for estimating a frequency response H(f) of the filter as a Fourier transform H(z) of the impulse response H(z) of the filter;
• and
• algorithm-based computation means, operatively connected between said estimator means and said transversal filter means, for determining a real part a(f) of a cepstrum H(f)=-1n(H(f) of the frequency response H(f) of the filter to thereby extract from said real part of a(f) an even part p(f) and an odd part q(f), for determining a cepstrum G(f)=-1n(G(f) of a global frequency response G(f) from said even part p(f) and said odd part q(f) of said cepstrum H(f) of the impulse response H(z) of said filter, for determining said global frequency response G(f) from said cepstrum G(f), for determining a theoretical frequency response C(f) of the transversal filter means responsive to said global frequency response G(f) and the frequency response H(f) of said filter, for calculating a theoretical transmittance C(z) of the transversal filter means as an inverse Fourier transform of said theoretical frequency response C(f) of the transversal filter means, for determining coefficients representing and estimated transmittance P(z) of the transversal filter means by truncating said theoretical transmittance C(z) thereby retaining only a predetermined number of respective transmittance coefficients, and for providing said number of said coefficients so as to operate said transversal filter means.

A receiver to which transmitted symbols are applied via a filter medium having an impulse response H(z) and producing detected symbols, said receiver comprising:

• transversal filter means receiving coefficients representing a transmittance P(z) for filtering said symbols, wherein said transversal filter means and the filter medium collectively provide a global impulse response G(z) representing a minimal phase response;
• estimating means for estimating a frequency response H(f) of the filter medium as a Fourier transform H(z) of the impulse response H(z) of the filter medium;
• algorithm-based computation means, operatively connected between said estimating means and said transversal filter means, for determining a real part a(f) of a cepstrum H(f)=-1n(H(f)) of the frequency response H(f) of the filter medium to thereby extract from said real part of a(f) an even part p(f) and an odd part q(f), for determining a cepstrum G(f)=-1n(G(f)) of a global frequency response G(f) from said even part p(f) and said odd part q(f) of said cepstrum H(f) of the impulse response H(z) of said filter medium, for determining said global frequency response G(f) from said cepstrum G(f), for determining a theoretical frequency response C(f) of said transversal filter means responsive to said global frequency response G(f) and the frequency response H(f) of said filter medium, for calculating a theoretical transmittance C(z) of said transversal filter means as an inverse Fourier transform of said theoretical frequency response C(f) of said transversal filter means for determining coefficients representing an estimated transmittance P(z) of the transversal filter means by truncating said theoretical transmittance C(z) thereby retaining only a predetermined number of respective transmittance coefficients, for providing said number of said coefficients so as to operate said transversal filter means, and for estimating an estimated minimal phase impulse response G(z) corresponding to an output of said transversal filter means;
• and
• detector means receiving filtered symbols for generating said detected symbols responsive to said estimated minimal phase impulse response G(z).