Non-recursive half-band filter with complex valued coefficients for complex input and output signals

DETAILED DESCRIPTION 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: h(l) =h(l) .
multidot.
e.
sup.
j(.
+-.
2.
sup.
[lfA/4fA +.
phi.
0) =j.
sup.
.
+-.
1 .
multidot.
e.
sup.
j.
phi.
0 .
multidot.
h(l) wherein the null phase .
phi.
0 of this frequency is an integer multiple m of .
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