Linear-phase filter implementation using orthonormal...

Details Linear-phase filter implementation using orthonormal... Linear-phase filter implementation using orthonormal...

1998-07-06

2001-07-31

Pham, Chi (Department: 2631)

Pulse or digital communications

Equalizers

C708S300000

Reexamination Certificate

active

06269115

ABSTRACT:

FIELD OF THE INVENTION
The present invention relates to digital communications, and more particularly relates to digital filtering of signals used in such communications, specifically, FIR linear-phase matched filters.
BACKGROUND OF THE INVENTION
Forward impulse response “FIR” digital filters are, in general, well known in the art of digital communications. FIR linear-phase matched filters are desirable in such art. FIR linear-phase matched filters can be designed to have both constant phase delay and constant group delay, which results in excellent distortion characteristics of such filters.
However, the design of FIR linear-phase matched filters to meet specific performance objectives is generally more difficult than the design of infinite impulse response filters for similar applications. In addition, such FIR filters implemented with recursive techniques can be subject to instability problems, such as limit-cycle oscillations.
Thus, it would be desirable to have a filter, and a design technique for such a filter, which is relatively simple, and which will approximate FIR linear-phase matched filters with little degradation in performance and freedom from distortion, while still providing significant savings in hardware.
SUMMARY OF THE INVENTION
According to the present invention, there is provided a forward impulse response, linear-phase matched filter, receiving as an input a sampled digital representation of an input signal, x(n), having n samples, and providing a filtered output, y
a
(n), having K stages, stage 0, stage 1, . . . stage k . . . stage K−2, stage K−1. The implementation of the filter includes a block in stage 0 for multiplying the values x(n) by the value
1
-
b
2
1
-
bz
-
1
to generate values v
0
(n). Blocks are provided in stages 1 through K−1 for generating the values v
k
(n) for k=1→K−1, where v
k
(n)=bv
k
(n−1)+v
k−1
(n−1)−bv
k
(n). Alternately, v
k
(n)=v
k−1
(n−1)(z
−1
−b)/(1−bz
−1
), expressed in terms of z-transform. Further blocks are provided in stages 0 through K−1 for multiplying v
k
(n) by a respective constant value, c
k
, for generating a series of intermediate values i
k
. A final block sums the intermediate values to produce said filtered output, y
a
(n). In the implementation the value b is a Laguerre parameter, and the value z is a z-transform of the filter behavior. A predetermined limiting function is applied in determining the value v
k
(n) to reduce the number of multiplications necessary to implement the filter function, while avoiding instabilities in the filter so implemented Discrete-time Laguerre sequences are effective for representing sequences in the form of orthogonal expansions. Taking advantage of the network realization of a Laguerre expansion, it is shown that approximating linear-phase matched filters by means of Laguerre expansion provides considerable savings in hardware implementations without adding significant distortion.
These and other features of the invention will be apparent to those skilled in the art from the following detailed description of the invention, taken together with the accompanying drawings.


REFERENCES:
patent: 4251886 (1981-02-01), Tomlinson et al.
patent: 4961206 (1990-10-01), Tomlinson et al.
patent: 5031194 (1991-07-01), Crespo et al.
patent: 5663983 (1997-09-01), Lin

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