Boots – shoes – and leggings
Patent
1991-12-24
1993-01-05
Malzahn, David H.
Boots, shoes, and leggings
36472413, 36472416, G06F 1531
Patent
active
051777002
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.
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 real input signal into a complex output signal, or vice versa, in an inexpensive manner.
The above object is achieved according to a first aspect of the invention by a non-recursive half-band filter with complex coefficients for processing a real input signal s(kT) by having the sampling frequency fA=1/T and for converting this real input signal s(kT) into a complex output signal s(2kT), wherein the filter complex coefficients h(l), where l=-(N-1)/2 to (N-1)/2 and the filter length N is odd, have alternating purely real and purely imaginary values, and therefore no complex values in the fullest sense, and wherein the pulse response of a half-band filter h(l) having exclusively real values and the characteristics h(l)=h(-l) for all .vertline.l.vertline..ltoreq.(N-1)/2 and h(l)=0 for 1=.+-.2, .+-.4, . . . , is modulated onto the complex carrier of a frequency of .+-.1/4 of the input sampling frequency fA=1/T to yield .multidot.e.sup.j.phi.0 .multidot.h(l) of .pi./2 (.phi.0=m.multidot..pi.2 where m=0, 1, 2, 3, . . . ).
The above object is achieved according to another aspect of the invention by a non-recursive half-band filter with complex coefficients for processing a complex input signal s(2kT) and for doubling the sampling frequency fA'=1/2T to fA=2fA' and for converting this complex input signal s(2kT) into a real output signal s(kT), and wherein the filter complex coefficients h(l), where l=-(N-1)/2 to (N-1)/2 and the filter length N is odd, alternatingly have purely real and purely imaginary values, and therefore no complex values in the fullest sense, and the pulse response of a half-band filter h(l) having exclusively real values and the characteristics h(l)=h(l) for all .vertline.l.vertline..ltoreq.(N-1)/2 and h(l)=0 for l=.+-.2, .+-.4, . . . , is modulated onto the complex carrier of a frequency of .+-.1/4 of the output sampling frequency fA=1/T to yield .multidot.e.sup.j.phi.0 .multidot.h(l) of .pi./2 (.phi.0=m.multidot..pi./2 where m=0, 1, 2, 3, . . . ).
The above object is achieved according to still a further object of the invention by a non-recursive half-band filter, which converts a real input signal s(kT) into a complex output signal s(kT) where k is a running index, while maintaining the sampling frequency fA=1/T, in that the filter pulse response h(l), where l=-(N-1)/2 to (N-1)/2 and N is an odd filter length, is modulated onto a complex carrier at a frequency of .+-.1/4 of the sampling frequency fA=1/T, to yield .multidot.e.sup.j.phi.0 .multidot.h(l) .pi./2 (.phi.0=m.multidot..pi./2 where m=0, 1, 2, 3, . . . ).
The above object is achieved according to still a further aspect of the invention by a non-recursive half-band filter, which converts a complex input signal s(kT) where k is a running index into a real output signal s(kT), while maintaining the sampling frequency fA=1/T, in that the filter pulse response h(l) with reference to the sampling frequency fA, where l=-(N-1)/2 to (N-1)/2 and the filter length N is odd, is modulated onto the complex carrier at a frequency of .+-.fA/4 to yield .multidot.e.sup.j.phi.0 .multidot.h(l) (.phi.0=m.multidot..pi./2 where m=0, 1, 2, 3, . . . ).
The novel non-recursive half-band filter according to each of the first two aspects of the invention permits the conversion of real digital input signals into complex digital output signals with a simultaneous reduction of the sampling frequency by a factor of two, and the conversion of complex digital input signal
REFERENCES:
patent: 4344149 (1982-08-01), Meeberg et al.
patent: 4612625 (1986-09-01), Bertrand
patent: 4766562 (1988-08-01), Vary
patent: 4825396 (1989-04-01), Gazsi
patent: 4852035 (1989-07-01), Michener
patent: 4893264 (1990-01-01), Noll et al.
patent: 4896320 (1990-01-01), Gockler
Bellanger et al, "Interpolation, Extrapolation, and Reduction of Computation Speed in Digital Filters" IEEE Trans. on Acoustics, Speech & Signal Processing vol. ASSP-22, No. 4 Aug. 1974 pp. 231-235.
Ansari, "Elliptic Filter Design for a Class of Generalized Halfband Filters", IEEE Trans. on Acoustics, Speech & Signal Processing vol. ASSP-33 No. 4 Oct. 1985 pp. 1146-1150.
ANT Nachrichtentechnik GmbH
Malzahn David H.
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