Frequency domain automatic equalizer utilizing the discrete Fourier transform

• US 4,100,604 A
• Filed: 07/19/1976
• Issued: 07/11/1978
• Est. Priority Date: 07/19/1976
• Status: Expired due to Term

• Current Assignee: Xerox Corporation (Xerox Holdings Corp.)
• Original Assignee: Xerox Corporation (Xerox Holdings Corp.)
• Inventors: Perreault, Donald A.
• Primary Examiner(s): Gensler, Paul L.
• Application Number:
  US05/706,703
• Time in Patent Office: 722 Days
• Field of Search: 333/18, 333/70 T, 328/155, 328/167, 235/152, 235/156, 235/193, 325/42
• US Class Current: 708/821
• CPC Class Codes: H04B 3/141 using multiequalisers, e.g. bump, cosine, Bode

Abstract

An automatic equalizer for calculating the equalization transfer function and applying same to equalize received signals. The initial calculation as well as the equalization proper are conducted entirely within the frequency domain. Overlapping moving window samplings are employed together with the discrete Fourier transformation and a sparse inverse discrete Fourier transformation to provide the equalized time domain output signals.

Claims

1. A frequency domain equalizer for automatically equalizing the discrete Fourier components X_n of a received electrical signal x(t) transmitted through a transmission channel comprising:

(a) means for sampling a test pulse transmitted through said transmission channel for providing a discrete set of test sample values f_k, where k = 0, 1 . . . N-1, and N is an integer,

(b) means for calculating the discrete Fourier transform of said test sample values f_k to provide the discrete Fourier components F_n, n = 0, 1 . . . N-1,

(c) means for providing reference values H_n representing the discrete Fourier components corresponding to an ideal, undistorted test pulse,

(d) means for calculating a correction factor C_n for each value F_n such that

space="preserve" listing-type="equation">C.sub.n ·

F.sub.n = H.sub.n,

(e) means for storing said calculated correction factors C_n,

(f) means for subsequently sampling said received electrical signal x(t) to provide a discrete set of signal sample values x_k, k = 0, 1 . . . N-1,

(g) means for calculating the discrete Fourier transform of said signal sample values x_k to provide the discrete Fourier components X_n,

(h) means for multiplying X_n by the stored correction factors C_n to produce frequency equalized components Y_n for n = 0, 1 . . . N-1 where

space="preserve" listing-type="equation">Y.sub.n = C.sub.n ·

X.sub.n, and

(i) means for calculating the inverse discrete Fourier transform of the components Y_n to provide an output signal in the time domain corresponding to said received electrical signal.

2. A frequency domain equalizer as recited in claim 1 wherein said received electrical signal x(t) is real, N is an even integer, n = 0, 1 . . . N/2, and said means for calculating the inverse discrete Fourier transform comprises means for calculating a sparse inverse discrete Fourier transform having only real parts of said components Y_n as inputs thereto.

3. A frequency domain equalizer as recited in claim 2 wherein said output signal from said means for calculating said sparse inverse discrete Fourier transform comprises a single output value for said discrete signal sample values x_k, k = 0, 1 . . . N-1.

4. A frequency domain equalizer as recited in claim 3 wherein said means for sampling said signal x(t) comprises means for providing N samples x_k of said signal x(t), each sample spaced a time interval T/N apart, where T is the sample set time frame.

5. A frequency domain equalizer as recited in claim 4 further comprising an input analog delay line for receiving said signal x(t), said delay line having taps spaced apart at time intervals T/N.

6. A frequency domain equalizer as recited in claim 4 further comprising means for time shifting said signal x(t) to provide different discrete sets of signal sample values x_k, each set time displaced by an amount t₀, where 0<

t₀ ≦

T/N, whereby a sliding window sampling of said received signal x(t) is provided.

7. A frequency domain equalizer are recited in claim 2 wherein said means for calculating C_n comprises means for calculating the real, R, and imaginary, I, parts of C_n, in terms of the real and imaginary parts of H_n and F_n as follows:

##EQU10##

8. A frequency domain equalizer as recited in claim 7 wherein said means for calculating said correction factors C_n comprises solely analog circuit means.

9. A frequency domain equalizer as recited in claim 7 wherein the numerators of RC_n and IC_n are calculated upon sampling said test pulse, and the reciprocal of the denominators of RC_n and IC_n are calculated upon sampling of an additional test pulse, and said equalizer comprises means for storing said numerators and reciprocal of said denominators for n = 1 . . . (N/2)-1.

10. A frequency domain equalizer as recited in claim 7 wherein said means for calculating C_n comprises a single time shared circuit for calculating C_n for n = 1 . . . (N/2)-1.

11. A frequency domain equalizer as recited in claim 10 wherein said single time shared circuit only calculates the value RH_n ·

RF_n + IH_n ·

IF_n.

12. A frequency domain equalizer as recited in claim 1 wherein said means for calculating the discrete Fourier transform of f_k and x_k, said correction factors C_n, and said inverse discrete Fourier transform of Y_n comprises solely analog circuit means.

13. A frequency domain equalizer as recited in claim 1 wherein said means for calculating C_n comprises means for calculating the real, R, and imaginary, I, parts of C_n, n = 0 . . . N/2, for N an even integer in terms of the real and imaginary parts of H_n and F_n as follows:

##EQU11##

14. A frequency domain equalizer as recited in claim 13 wherein said means for calculating C_n further comprises holding circuit means for storing values corresponding to (RH_n RF_n + IH_n IF_n), (RF_n IH_n - RH_n IF_n) and 1/((RF_n)² + (IF_n)²).

15. A frequency domain equalizer for automatically equalizing the discrete Fourier transform components X_n of a received electrical signal x(t) comprising:

(a) means for storing equalizer transfer components C_n,

(b) means for samplaing said received electrical signal x(t) to provide a set of signal sample values x_k, k being a sample time index having values 0, 1 . . . N-1, and N being an integer,

(c) means for calculating the discrete Fourier transform of said sample values x_k to provide said discrete Fourier components X_n, n = 0, 1 . . . N-1,

(d) means for calculating equalized components Y_n where

space="preserve" listing-type="equation">Y.sub.n = C.sub.n ·

X.sub.n n = 0, 1 . . . N-1,

(e) means for calculating the inverse discrete Fourier transform of the set of components Y_n to provide an output signal corresponding to one sample time index of said received electrical signal.

16. A frequency domain equalizer as recited in claim 15 further comprising:

(a) means for replacing the sample set x_k, k = 0, 1 . . . N-1 by a sample set shifted in time an amount t₀, 0<

t₀ ≦

T/N where T is the sample set time frame,

(b) means for calculating the discrete Fourier transform components X_n of the shifted sample set,

(c) means for calculating equalized components Y_n for said shifted sample set,

(d) means for calculating the inverse discrete Fourier transform of the set of components Y_n for said shifted set to provide another output signal corresponding to said one sample time index of said received electrical signal.

17. A frequency domain equalizer as recited in claim 16 wherein said sample values have only real values, N is an even integer and said discrete Fourier transform, said inverse discrete Fourier transform and said equalized components are calculated for n ranging in one of the groups n = 0, 1 . . . N/2 and n = 0, N/2, (N/2) + 1, (N/2) + 2 . . . N-1.

18. A frequency domain equalizer as recited in claim 17 wherein said means for calculating said inverse discrete Fourier transform comprises means for calculating only one output signal per sample set.

19. A frequency domain equalizer as recited in claim 18 wherein said one output signal of the inverse discrete Fourier transform corresponds to either the 0^th or the N/2^th time sample index.

20. A frequency domain equalizer as recited in claim 18 wherein said means for calculating said inverse discrete Fourier transform comprises a sparse inverse discrete Fourier transform circuit having only real parts of said components Y_n as inputs thereto.

21. A frequency domain equalizer as recited in claim 16 where N/T is selected to be greater than or equal to 1/2w_max where w_max is the maximum frequency component of the signal x(t).

22. A frequency domain equalizer for automatically equalizing the discrete Fourier components X_n of a received electrical signal x(t) transmitted through a transmission channel comprising:

(a) means for storing distortion equalization correction factors, C_n, associated with said signal x(t),

(b) means for sampling said signal x(t) to provide a plurality of sets, i, of sample values x_k, k = 0, 1 . . . N-1, said values x_k corresponding to samples of the signal x(t) time displaced by an amount T/N from one another where T is a sample time frame and N is an integer,

(c) said sampling means providing the i^th sample set time delayed from the i-1^th sample set by an amount t₀ where, 0<

t₀ ≦

T/N, thereby providing an overlapping sliding window sampling of said signal x(t),

d) means for generating the discrete Fourier transformer components corresponding to each sample set of values x_k of said plurality of sample sets,

(e) means for multiplying said generated components X_n by said factors C_n for each of said sets i, such that

space="preserve" listing-type="equation">Y.sub.n = X.sub.n ·

C.sub.n

and

(f) means for generating the inverse discrete Fourier transform of the set of components Y_n to provide an output signal corresponding to one value of k for each set, i, of values x_k, said value of k being the same value for each set i.

23. Apparatus as recited in claim 22 wherein said correction factors C_n are the discrete Fourier transform components of the impulse response function of the equalizer.

24. Apparatus as recited in claim 23 wherein said means for generating the inverse discrete Fourier transform comprises means for providing only real parts of said components Y_n as inputs thereto.

25. Apparatus as recited in claim 23 wherein the sampling rate of said sampling means is given by N/T, and said sampling rate is at least equal to the Nyquist sampling rate for said received signal x(t).

26. A method of equalizing the discrete Fourier transform components X_n of a received electrical signal x(t) comprising the steps of:

(a) storing equalizer transfer components C_n,

(b) sampling the received electrical signal x(t) to provide a set of signal sample values x_k, k being a sample time index having values 0, 1 . . . N-1, N being an integer,

(c) calculating the discrete Fourier transform of said sample values x_k, k = 0, . . . N-1 to provide the discrete Fourier components X_n, n = 0, . . . N-1,

(d) multiplying each component X_n by the corresponding component C_n thereby producing equalized components

space="preserve" listing-type="equation">Y.sub.n = C.sub.n ·

X.sub.n n - 0, . . . N-1,

(e) calculating the inverse discrete Fourier transform of the set of components Y_n to provide an output signal corresponding to one sample time index of the received electrical signal.

27. A method as recited in claim 26 further comprising the steps of:

(a) replacing the sample set x_k, k = 0 . . . N-1 by a sample set shifted in time an amount t₀, 0<

t₀ ≦

T/N, where T is the sample set time frame,

(b) calculating the discrete Fourier transform components X_n of the shifted sample set,

(c) providing equalized components Y_n for the shifted sample set,

(d) calculating the inverse discrete Fourier transform of the set of components Y_n for said shifted sample set to provide an output signal corresponding to said one sample time index of said received electrical signal.

28. A method as recited in claim 27 wherein said sample values have only real values, N is an even integer and said discrete Fourier transform, said inverse discrete Fourier tansform and said equalized components are calculated for n ranging in one of the groups, n = 0, 1 . . . N/2 and n = 0, N/2, (N/2) + 1, (N/2) +2 . . . N-1.

29. A method as reccited in claim 28 wherein said one time sample index of said inverse discrete Fourier transform is either the 0^th or the N/2^th time sample index.

30. A method of equalizing the discrete Fourier transform components X_n of a received electrical signal x(t) comprising the steps of:

(a) storing distortion equalization correction factors, C_n, associated with said signal x(t),

(b) sampling said signal x(t) to provide a plurality of sets, , of real sample values x_k, k = 0, 1 . . . N-1, said values x_k corresponding to samples of x(t) time displaced by an amount T/N from one another where T is a sample time frame and N is an integer,

(c) delaying the i^th sample set with respect to the i-1^th sample set by an amount t₀ where 0<

t₀ ≦

T/N, thereby providing overlapping sliding window sampling of said signal x(t),

(d) generating the discrete Fourier transform of said sample values x_k, k = 0 . . . N-1 to provide the discrete Fourier components X_n, n = 0 . . . N-1,

(e) multiplying said generated components X_n by said factors C_n for each of said sets i, such that

space="preserve" listing-type="equation">Y.sub.n = X.sub.n ·

C.sub.n

and

(f) generating the inverse discrete Fourier transform of the set of components Y_n to provide an output signal corresponding to one value k for each set of values x_k, said value of k being the same value for each set i.

31. A method as recited in claim 30 wherein said correction factors C_n are the discrete Fourier transform components of the impulse response function of the equalizer.

32. A method as recited in claim 31 further comprising the step of generating the inverse discrete Fourier transform by providing only real parts of said components Y_n as inputs thereto.