Non-recursive half-band filter with complex valued coefficients

Details Non-recursive half-band filter with complex valued coefficients Non-recursive half-band filter with complex valued coefficients

1989-08-18

1991-11-26

Shaw, Dale M.

Boots, shoes, and leggings

G06F 1531

Patent

active

050688170

DESCRIPTION:

BRIEF SUMMARY
BACKGROUND OF THE INVENTION

The invention relates to a non-recursive half-band filter. Such filters have become known from the paper by Bellanger et al, entitled, "Interpolation, Extrapolation, and Reduction of Computation Speed in Digital Filters," published in IEEE Transactions on Acoustics, Speech and Signal Processing, Vol. ASSP-22, No. 4, August, 1974, pages 231-235.
The known half-band filters process real input signals into real output signals.
The German application P 3,621,737.9-35 discloses a non-recursive half-band filter which permits the conversion of a real input signal into a complex output signal or vice versa. In that process, the sampling rate was changed.


SUMMARY OF THE INVENTION

It is an object of the present invention to provide a non-recursive half-band filter that makes it possible to convert a complex input signal into complex output signal in an inexpensive manner.
This is accomplished by a non-recursive half-band filter having a filter length N, and including: at least one input and an output, the input for receiving a complex input signal s.sub.l (kT) having a real component s.sub.rl and an imaginary component s.sub.il at a sampling frequency fA, where fA =l/T; and means for processing and converting the received complex input signal s.sub.l (kT) =js.sub.il into a complex output signal s(kT), where k is a running index, without changing the sampling frequency, the processing and converting means operating according to a function of h(l) and the equation: ##EQU2## and including means for modulating a pulse response h(l), where l =-(N-1)/2 to (N-1)/2 and N is an odd filter length, onto a complex carrier at a frequency of .+-.1/2 of the sampling frequency to yield: .multidot.e.sup.j.phi.0 .multidot.h(l) .pi./2.
Another aspect of the invention is provided by a non-recursive half-band filter having a processing and converting means with first partial filter means for generating a real component s.sub.rl (kT) of a complex output signal and second partial filter means for generating an imaginary component s.sub.il (kT) of the complex output signal. In this inventive filter, each partial filter means includes means for weighting the real and imaginary components of a complex input signal with values equal to a function of h(l); a chain of (N-31 1)/2 delay members having a delay time of 2T and a center delay member divided into two members where each divided member has a delay time of T; and means for forming a plurality of difference signals wherein the forming means of the first partial filter means and the forming means of the second partial filter means respectively feed a weighted real component and a weighted imaginary component to the first delay member of its respective chain of delay members and substract the respective weighted component from the output signal of the last delay member of the respective chain to respectively form a difference signal furnishing the real component s.sub.rl (kT) of the complex output signal and the imaginary component s.sub.il (kT) of the complex output signal. In addition, the weighting means weights additional momentary values of the filter input signal with a value equal to other functions of h(l) of the pulse response and the forming means adds the additional weighted values to a transversal signal of the chain of delay members at further points. The weighting means of the first partial filter means and the weighting means of the second partial filter means further weight the imaginary component and the real component, respectively of the complex input signal with a value equal to the function h(O) and feed the respective weighted component into the center delay member of the respective chain.
The non-recursive half-band filter according to the invention permits the conversion of complex digital input signals into complex digital output signals without a change in sampling frequency. This relatively inexpensive half-band filter is thus suitable as a digital pre-filter or post-filter for digital systems employed to process complex signals and

REFERENCES:
patent: 4020333 (1977-04-01), Nussbaumer
patent: 4606045 (1986-08-01), Miller
patent: 4736392 (1988-04-01), Kammeyer et al.
IEEE Trans. on Acoustics, Speech, and Signal Processing, Band ASSSP-22, nr. 4, Aug, 1974, Bellanger et al., "Interpolation Extrapolation and Reduction of Computation Speed in Digital Filters".

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