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

• US 5,511,014 A
• Filed: 09/23/1993
• Issued: 04/23/1996
• Est. Priority Date: 09/25/1992
• Status: Expired due to Fees

• Current Assignee: Alcatel NV (Nokia Corporation)
• Original Assignee: Alcatel NV (Nokia Corporation)
• Inventors: Dany, Jean-Claude, Wautier, Armelle, Mourot, Christophe
• Primary Examiner(s): Ramirez, Ellis B.
• Assistant Examiner(s): PIPALA, EDWARD J
• Application Number:
  US08/125,663
• Time in Patent Office: 943 Days
• Field of Search: 364/572, 364/724.01, 364/724.03, 364/725, 324/76.28, 324/76.29, 324/76.31, 324/76.44, 333/167
• US Class Current: 708/300
• CPC Class Codes: H03H 17/0216 Quefrency domain filters

Abstract

A method for determining the transmittance of a filter circuit adapted to transform the impulse response of a filter into a minimal phase response entails computing the theoretical frequency response of the filter circuit and the minimal phase frequency impulse response with a causality condition applied to the cepstrum of the minimal phase response, determining the theoretical transmittance as the inverse fast Fourier transform of the theoretical frequency response, estimating the transmittance of the filter circuit by truncation of the theoretical transmittance of which only a predetermined number of coefficients are retained and determining the minimal phase global response from a limited expansion of the cepstrum.

Claims

1. 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 impulse response G(z), serially connected to a detector for generating second symbols responsive to the first symbols and circuitry receiving an output of the filter medium and operatively connected to the filter circuit for generating coefficients corresponding to said transmittance P(z), a method for controlling said circuitry comprising the steps of:

(a) 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;

(b) 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);

(c) 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;

(d) determining said global frequency response G(f) from said cepstrum G(f);

(e) 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;

(f) 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;

(g) determining an estimated transmittance P(z) of the filter circuit by truncating said transmittance C(z) thereby retaining only a predetermined number of coefficients thereof; and

(h) providing said coefficients corresponding to said estimated transmittance P(z) so as to operate the filter circuit.

2. The method according to claim 1, wherein said step (d) further comprises determining said global frequency response G(f) from a limited expansion of said cepstrum G(z).

3. The method according to claim 2, wherein a count of operations performed and a respective computation time associated with steps (a) through (g) are fixed and independent of an associated length of the filter medium and wherein said limited expansion and respective transforms each have a corresponding predetermined size.

4. The method according to claim 1, further comprising the step of:

(i) obtaining an estimated G_o (z) of said minimal phase impulse response G(z) by;

(1) computing coefficients of said minimal phase impulse response G(z) as an inverse discrete Fourier transform of said minimal phase frequency response G(f); and

(2) retaining a predetermined number of significant coefficients to obtain said estimated G_o (z).

5. The method according to claim 1, further comprising the step of:

(j) obtaining an estimated G₁ (z) forming a casual part of a product of the filter impulse response H(z) and said estimated transmittance P(z) of the filter transmittance P(z).

6. The method according to claim 1, wherein said step (b) comprises substeps comprising:

(1) determining said real part a(f) of said 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) said even part p(f) and said odd part q(f) when the impulse response H(z) does not have respective zeros on said unity circle; and

(2) heuristic processing to determine said real part a(f) of the frequency response H(f) of the filter medium to thereby extract from said real part of a(f) said even part p(f) and said odd part q(f), when the impulse response H(z) of the filter medium has said zeros on said unity circle, using a(f)=-1/21n(H(f)H*(f)+ε

)

where ε

represents an adjustment parameter.

7. 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.

8. The method according to claim 7, wherein said step (c) further comprises determining said global frequency response G(f) from a limited expansion of said cepstrum G(z).

9. The method according to claim 8, wherein a count of operations performed and a respective computation time associated with steps (a) through (f) are fixed and independent of an associated length of the filter medium and wherein said limited expansion and respective transforms each have a corresponding predetermined size.

10. The method according to claim 7, further comprising the step of:

(h) obtaining an estimated G_o (z) of said minimal phase response G(z) by;

(1) computing coefficients of said minimal phase impulse response G(z) as an inverse discrete Fourier transform of said minimal phase frequency response G(f); and

(2) retaining a predetermined number of significant coefficients to obtain said estimated G_o (z).

11. The method according to claim 7, further comprising the step of:

(i) obtaining an estimated G₁ (z) forming a casual part of a product of the filter impulse response H(z) and said estimated transmittance P(z) of the filter transmittance P(z).

12. The method according to claim 7, wherein said step (a) comprises substeps comprising:

(1) determining said real part a(f) of said 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) said even part p(f) and said odd part q(f) when the impulse response H(z) does not have respective zeros on said unity circle; and

(2) heuristic processing to determine said real part a(f) of the frequency response H(f) of the filter medium to thereby extract from said real part of a(f) said even part p(f) and said odd part q(f), when the impulse response H(z) of the filter medium has said zeros on said unity circle, using a(f)=-1/21n(H(f)H*(f)+ε

)

where ε

represents an adjustment parameter.

13. 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.

14. The filter circuit as recited in claim 13, wherein said transversal filter means comprises a finite impulse response digital transversal filter.

15. The filter circuit as recited in claim 13, wherein said algorithm-based computation means comprises means for determining said real part a(f) of said 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) said even part p(f) and said odd part q(f) when the impulse response H(z) does not have respective zeros on said unity circle, for heuristic processing to determine said real part a(f) of the frequency response H(f) of the filter to thereby extract from said real part of a(f) said even part p(f) and said odd part q(f), when the impulse response H(z) of the filter has said zeros on said unity circle, using a(f)=-1/21n(H(f)H*(f)+ε

), where ε

represents an adjustment parameter, for determining said cepstrum G(f)=-1n(G(f)) of said 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 said 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, for calculating said theoretical transmittance C(z) of the transversal filter means as said inverse Fourier transform of said theoretical frequency response C(f) of the transversal filter means, for determining coefficients representing said estimated transmittance P(z) of the transversal filter means by truncating said theoretical transmittance C(z) thereby retaining only said predetermined number of respective transmittance coefficients, and for providing said number of said coefficients to said transversal filter means.

16. 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).

17. The receiver as recited in claim 16, wherein said algorithm-based computation means comprises means for determining said real part a(f) of said 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) said even part p(f) and said odd part q(f) when the impulse response H(z) does not have respective zeros on said unity circle, for heuristic processing to determine said real part a(f) of the frequency response H(f) of the filter medium to thereby extract from said real part of a(f) said even part p(f) and said odd part q(f), when the impulse response H(z) of the filter medium has said zeros on said unity circle, using a(f)=-1/21n(H(f)H*(f)+ε

).wherein ε

represents an adjustment parameter, for determining said global frequency response G(f) from said cepstrum G(f), for determining said 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 said theoretical transmittance C(z) of said transversal filter means as said inverse Fourier transform of said theoretical frequency response C(f) of said transversal filter means for determining coefficients representing said estimated transmittance P(z) of the transversal filter means by truncating said theoretical transmittance C(z) thereby retaining only said number of respective transmittance coefficients, for providing said number of said coefficients to said transversal filter means, and for generating said estimated minimal phase impulse response G(z) corresponding to said output of said transversal filter means.