CA1303148C - Non-recursive half-band filter - Google Patents
Non-recursive half-band filterInfo
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- CA1303148C CA1303148C CA000559077A CA559077A CA1303148C CA 1303148 C CA1303148 C CA 1303148C CA 000559077 A CA000559077 A CA 000559077A CA 559077 A CA559077 A CA 559077A CA 1303148 C CA1303148 C CA 1303148C
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
- H03H17/00—Networks using digital techniques
- H03H17/02—Frequency selective networks
- H03H17/0248—Filters characterised by a particular frequency response or filtering method
- H03H17/0264—Filter sets with mutual related characteristics
- H03H17/0273—Polyphase filters
- H03H17/0275—Polyphase filters comprising non-recursive filters
- H03H17/0276—Polyphase filters comprising non-recursive filters having two phases
-
- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
- H03H17/00—Networks using digital techniques
- H03H17/02—Frequency selective networks
- H03H17/06—Non-recursive filters
- H03H17/0621—Non-recursive filters with input-sampling frequency and output-delivery frequency which differ, e.g. extrapolation; Anti-aliasing
- H03H17/0635—Non-recursive filters with input-sampling frequency and output-delivery frequency which differ, e.g. extrapolation; Anti-aliasing characterized by the ratio between the input-sampling and output-delivery frequencies
- H03H17/065—Non-recursive filters with input-sampling frequency and output-delivery frequency which differ, e.g. extrapolation; Anti-aliasing characterized by the ratio between the input-sampling and output-delivery frequencies the ratio being integer
- H03H17/0657—Non-recursive filters with input-sampling frequency and output-delivery frequency which differ, e.g. extrapolation; Anti-aliasing characterized by the ratio between the input-sampling and output-delivery frequencies the ratio being integer where the output-delivery frequency is higher than the input sampling frequency, i.e. interpolation
-
- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
- H03H17/00—Networks using digital techniques
- H03H17/02—Frequency selective networks
- H03H17/06—Non-recursive filters
- H03H17/0621—Non-recursive filters with input-sampling frequency and output-delivery frequency which differ, e.g. extrapolation; Anti-aliasing
- H03H17/0635—Non-recursive filters with input-sampling frequency and output-delivery frequency which differ, e.g. extrapolation; Anti-aliasing characterized by the ratio between the input-sampling and output-delivery frequencies
- H03H17/065—Non-recursive filters with input-sampling frequency and output-delivery frequency which differ, e.g. extrapolation; Anti-aliasing characterized by the ratio between the input-sampling and output-delivery frequencies the ratio being integer
- H03H17/0664—Non-recursive filters with input-sampling frequency and output-delivery frequency which differ, e.g. extrapolation; Anti-aliasing characterized by the ratio between the input-sampling and output-delivery frequencies the ratio being integer where the output-delivery frequency is lower than the input sampling frequency, i.e. decimation
-
- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
- H03H2218/00—Indexing scheme relating to details of digital filters
- H03H2218/04—In-phase and quadrature [I/Q] signals
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- Physics & Mathematics (AREA)
- Engineering & Computer Science (AREA)
- Computer Hardware Design (AREA)
- Mathematical Physics (AREA)
- Digital Transmission Methods That Use Modulated Carrier Waves (AREA)
- Filters That Use Time-Delay Elements (AREA)
- Complex Calculations (AREA)
- Networks Using Active Elements (AREA)
Abstract
ABSTRACT
The invention relates to a non-recursive half-band filter and permits the conversion of a real input signal into a complex output signal in that its pulse response is modulated onto the complex carrier with a frequency of 1/4 or 3/4 the sampling frequency and whereby the zero phase of this frequency is an integral multiple of .pi./2. Furthermore, it permits the conversion of a complex input signal into a real output signal in that its pulse response is modulated onto the complex carrier with a frequency of the input sampling rate and whereby the zero phase of this frequency is an integral multiple of .pi./2 and whereby the sampling frequency is retained unchanged.
The invention relates to a non-recursive half-band filter and permits the conversion of a real input signal into a complex output signal in that its pulse response is modulated onto the complex carrier with a frequency of 1/4 or 3/4 the sampling frequency and whereby the zero phase of this frequency is an integral multiple of .pi./2. Furthermore, it permits the conversion of a complex input signal into a real output signal in that its pulse response is modulated onto the complex carrier with a frequency of the input sampling rate and whereby the zero phase of this frequency is an integral multiple of .pi./2 and whereby the sampling frequency is retained unchanged.
Description
~;~03148 l 27371-176 The inven~ion relates to a non-recursive half-band filter. Such filters are known from the paper entitled "Interpolation, Extrapolation, and Reduction of Computation Speed in Digital Filters" by Bellanger et al in IEEE Transactions on Acoustics, Speech and Signal Processing, Vol. ASSP-22, No. 4, August 1974, page 231 seqq.
The known half-band filters process real input signals into real output signals.
The present invention is based on the object of providing a non-recursive half-band filter which permits the conversion of a complex real-value input signal into a complex-value output signal or vice-versa in a less costly manner.
In accordance with a broad aspect of the invention there is provided a non-recursive half-band filter for converting, at a sampling frequency fA = l/T, a real input signal s(kT) into a complex output signa~ s(kT), where k is a running index, comprising means for modulating its pulse response h(l), where l =
-l~N-l)/2 to (N-l)/2 and the filter length N is an odd integer, onto a complex carrier with a frequency + 1~4 of the sampling frequency fA = l/T to produce h(l) = h(l)v ei(~ 2n/fA/4fA + ~0) j+l~ ei~ h(l) the zero phase ~0 of this frequency being an integral multiple m of ~/2 (~0 = m ~n/2 where m = 0, 1, 2, 3 ...).
In accordance with another broad aspect of the invention there is provided a non-recursive half-band filter for converting, at a sampling frequency fA = l/T, a complex input signal s(kT) into a real output signal s(kT), where k is a running index, ~' 2 27371~176 comprising means for modulating its pulse response h(l) with respect to the sampling frequency fA, where l = -(N-l)/2 to (N-1)~2 and the filter length N is an odd integer, onto a complex carrier with a frequency of +fA/4 to produce h(l) h(l)u ej(+2n/fA~4fA + ~0) = j+l ei~ h(l), the zero phase ~0 of this frequency being an integral multiple m of ~/2 (~0 - m ~/2 where m = O, 1, 2, 3 ...).
The non-recursive half-band filter according to the invention permits the conversion of real digital input signals into complex digital output signals while retaining the sampling frequency and the conversion of complex digital input signals into real digital output signals also while retaininq the sampling frequency. This relatively inexpensive half-band filter is thus suitable as a digital pre-filter or post-filter for digital systems processing complex signals and as a digital partial filter in an arrangement of antialiasing filters for band limiting according to the sampling theorem. The advantage of the half-band filter is its linear phase and simultaneous low cost.
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The known half-band filters process real input signals into real output signals.
The present invention is based on the object of providing a non-recursive half-band filter which permits the conversion of a complex real-value input signal into a complex-value output signal or vice-versa in a less costly manner.
In accordance with a broad aspect of the invention there is provided a non-recursive half-band filter for converting, at a sampling frequency fA = l/T, a real input signal s(kT) into a complex output signa~ s(kT), where k is a running index, comprising means for modulating its pulse response h(l), where l =
-l~N-l)/2 to (N-l)/2 and the filter length N is an odd integer, onto a complex carrier with a frequency + 1~4 of the sampling frequency fA = l/T to produce h(l) = h(l)v ei(~ 2n/fA/4fA + ~0) j+l~ ei~ h(l) the zero phase ~0 of this frequency being an integral multiple m of ~/2 (~0 = m ~n/2 where m = 0, 1, 2, 3 ...).
In accordance with another broad aspect of the invention there is provided a non-recursive half-band filter for converting, at a sampling frequency fA = l/T, a complex input signal s(kT) into a real output signal s(kT), where k is a running index, ~' 2 27371~176 comprising means for modulating its pulse response h(l) with respect to the sampling frequency fA, where l = -(N-l)/2 to (N-1)~2 and the filter length N is an odd integer, onto a complex carrier with a frequency of +fA/4 to produce h(l) h(l)u ej(+2n/fA~4fA + ~0) = j+l ei~ h(l), the zero phase ~0 of this frequency being an integral multiple m of ~/2 (~0 - m ~/2 where m = O, 1, 2, 3 ...).
The non-recursive half-band filter according to the invention permits the conversion of real digital input signals into complex digital output signals while retaining the sampling frequency and the conversion of complex digital input signals into real digital output signals also while retaininq the sampling frequency. This relatively inexpensive half-band filter is thus suitable as a digital pre-filter or post-filter for digital systems processing complex signals and as a digital partial filter in an arrangement of antialiasing filters for band limiting according to the sampling theorem. The advantage of the half-band filter is its linear phase and simultaneous low cost.
-- !
-3- 27371-:L76 ~303148 The lnvention will now be described in more detail on the basis of the accompanying drawings, in which:
Figure 1 is a block circuit diagram of a digital filter according to the invention, Figures 2a to 2c show a few amplitude responses of half-band filters plotted versus frequency, Figures 3 and 4 show particularly favourable circuit variations for a half-band filter, Figure 5 is a block circuit diagram of a transposed, reverse operated half-band filter for processing a complex input signal into a real output signal, Figure 6 is a detailed circuit arrangement for the filter according to Figure 5, whereby this circuit arrangement was developed from that of Figure 3 through transposition, i.e. by reversing all the arrow directions and replacing a branching member by an add-er and vice-versa, The circuit arrangement according to Figure 7 resulted in corresponding manner from that of Figure 4.
In Figure 1 the real input signal s(kT) is fed to the digital half-band filter DF which generates from it the complex output signal s(kT).
Figure 2A shows the amplitude frequency response of a prototypehalf-band filter, its pass band extending from fA/4 +~ f to +fA/4 - ~ f (half value) and its stop band likewi.se having a -~ 2 7 371-176 i31~3148 w~ r~ Ar. Ii~lrtllerlllor~, it is c~laK~teristi~ rOr Illr~
f- -bal~tl ri I I e~ that l:lle tl alls.i.tloll rrom the stop b~ll(l to tlle pass hall~l ;.s ~: 0ll~3tc~nt and occurs at a wicltll oll 2~ . 'rhis trans-; t..iO~ alld ;.s al-rallged syl~ letr.ically to fl~/4. 1\ ~urther charact-erist.ic Or the h~lr-balld filter is that its ripple is identical .i.n the pass ball(l and tlle stop band, namely ôl = ô2 = ~. In such a ri] ter a plllse response h(] ) results where 1 = O to N-l and the ri.Lter lengt:ll N is an odd integer. It furtller results that every second value equals zero, except for the mean main value talso see in this connection Figure 2 on page 233 of the above-noted paper by Bellanger et al) .
I;`i.gure 2b shows the requency response lll J . It can be seen that thi s :llrequency response is shi~ted to tlle right by the rrequency fA/4 compared to the frequency response oE the prototype hal r-balld ~ilter . Figure 2b also illustrates the spectrulll ¦ s¦ Or ~ real input signal s(kT) sampled at the sampling rrequellcy r~, 9a;.d spectrum, on account o~ the samplillg at f~, beil-g repeated periodically in the frequency ranges [m.fl~, (m I -li) . fl~ ] in the normal pOSitiOIl and in the ~requency ranges [(m~ ). rZ~, (m-l-l).~l~] in the reversed pOSitiOIl witll m = .. -1, 0 -~]..... The reversed position between fA/2 and fA, and naturally all repetitions, is suppressed by the real-value input s.ignal s (kl'), applied to the hali~-band filter according to the invelltioll without a change in the sampling rate and at the same ~ I 3 ~
1303~48 time a comple~ signal s(kT) is generated, see Figure 2c.
~ t this point it is no~ed that a complex signal is obtailled in the reversed position at the output of the half-band filter if the frequency response of the prototype half-band filter according to Figure 2a is shifted by -fA/4 or, what is equivalent, by +3f~/4.
Figure 3 shows a detailed exemplary embodiment of a half-band filter according to the invention~
Both Figure 3 and Figure 4 depict examples of a realization for a filter length of N = 11 with a chain of six delay members of which four delay members have a time delay of 2T and two members, symmetrically inserted between the four delay members, have a time delay of T. Figure 3 depicts two realizat-ions, namely for a modulation phase angle ~O = O and pO = ~ corre-sponding to m = 0 and m = 2. The output signal of the delay members of the left chain half is weighted (multiplied) with h(O) = ~ and thus produces the real component Sr(kT) of the output signal. For m = 2, the weighting is -~. Further processing in the delay chain is in such a way that (N+1)/4 = 3 differential signals are formed:
first differential signal = input signal of the first delay member minus the output signal of the last delay member, second differential signal = input signal of the second delay member minus the output signal of the second-last delay member, and third differential signal = input signal of the third delay member minus the o~tput signal of the third-last, i.e. the right, middle delay member.
These differential signals are subsequently weighted (multiplied), summed and thus produce the imaginary component of the output signal s(kT). The weighting is effected according to the following tables.
Examples for N = 1 and h(-l~ = h(l) for 1 = O, 1, ...5, corresponding to the prototype half-band filter according to the frequency response of Figure 2a:
Table 1:
m = O (m - 2 with in each case a different sign for the complex coefficients _ = Re(h) + jJm(h)) Re(_) O O O h(O) O O
Jm(_) -h(5) h(3) -h(l) O h(l) -h(3) h(5) Table 2:
m = 1 (m a 3 with in each case a different sign for the complex coefficients) Re(h) h(5) -h(3) h(l) O -h(l) h(3) -h(5) Jm(_) O O O h(O) O O O
~ 2~371-176 1303~48 The realization according to F'igure 4 is effected in the same manner as that according to Figure 3, with the only difference being in the other zero phase value ~0 = m ~/2 where m = 1. and 3, which merely results in a different weighting.
Figure 5 shows the block circuit diagram for the reversed use of the half-band filter according to Figure l, namely for generating a real output signal from a complex input signal. For this purpose the previously represented circuits are transposed, resulting in a reversal of all arrow directions and replacement of a branching member by an adder and vice-versa.
In corresponding manner the exemplary embodiment for the circuit arrangement of Figure 6 evolves from Figure 3 and the circuit arrangement according to Figure 7 evolves from Figure 4.
Figure 1 is a block circuit diagram of a digital filter according to the invention, Figures 2a to 2c show a few amplitude responses of half-band filters plotted versus frequency, Figures 3 and 4 show particularly favourable circuit variations for a half-band filter, Figure 5 is a block circuit diagram of a transposed, reverse operated half-band filter for processing a complex input signal into a real output signal, Figure 6 is a detailed circuit arrangement for the filter according to Figure 5, whereby this circuit arrangement was developed from that of Figure 3 through transposition, i.e. by reversing all the arrow directions and replacing a branching member by an add-er and vice-versa, The circuit arrangement according to Figure 7 resulted in corresponding manner from that of Figure 4.
In Figure 1 the real input signal s(kT) is fed to the digital half-band filter DF which generates from it the complex output signal s(kT).
Figure 2A shows the amplitude frequency response of a prototypehalf-band filter, its pass band extending from fA/4 +~ f to +fA/4 - ~ f (half value) and its stop band likewi.se having a -~ 2 7 371-176 i31~3148 w~ r~ Ar. Ii~lrtllerlllor~, it is c~laK~teristi~ rOr Illr~
f- -bal~tl ri I I e~ that l:lle tl alls.i.tloll rrom the stop b~ll(l to tlle pass hall~l ;.s ~: 0ll~3tc~nt and occurs at a wicltll oll 2~ . 'rhis trans-; t..iO~ alld ;.s al-rallged syl~ letr.ically to fl~/4. 1\ ~urther charact-erist.ic Or the h~lr-balld filter is that its ripple is identical .i.n the pass ball(l and tlle stop band, namely ôl = ô2 = ~. In such a ri] ter a plllse response h(] ) results where 1 = O to N-l and the ri.Lter lengt:ll N is an odd integer. It furtller results that every second value equals zero, except for the mean main value talso see in this connection Figure 2 on page 233 of the above-noted paper by Bellanger et al) .
I;`i.gure 2b shows the requency response lll J . It can be seen that thi s :llrequency response is shi~ted to tlle right by the rrequency fA/4 compared to the frequency response oE the prototype hal r-balld ~ilter . Figure 2b also illustrates the spectrulll ¦ s¦ Or ~ real input signal s(kT) sampled at the sampling rrequellcy r~, 9a;.d spectrum, on account o~ the samplillg at f~, beil-g repeated periodically in the frequency ranges [m.fl~, (m I -li) . fl~ ] in the normal pOSitiOIl and in the ~requency ranges [(m~ ). rZ~, (m-l-l).~l~] in the reversed pOSitiOIl witll m = .. -1, 0 -~]..... The reversed position between fA/2 and fA, and naturally all repetitions, is suppressed by the real-value input s.ignal s (kl'), applied to the hali~-band filter according to the invelltioll without a change in the sampling rate and at the same ~ I 3 ~
1303~48 time a comple~ signal s(kT) is generated, see Figure 2c.
~ t this point it is no~ed that a complex signal is obtailled in the reversed position at the output of the half-band filter if the frequency response of the prototype half-band filter according to Figure 2a is shifted by -fA/4 or, what is equivalent, by +3f~/4.
Figure 3 shows a detailed exemplary embodiment of a half-band filter according to the invention~
Both Figure 3 and Figure 4 depict examples of a realization for a filter length of N = 11 with a chain of six delay members of which four delay members have a time delay of 2T and two members, symmetrically inserted between the four delay members, have a time delay of T. Figure 3 depicts two realizat-ions, namely for a modulation phase angle ~O = O and pO = ~ corre-sponding to m = 0 and m = 2. The output signal of the delay members of the left chain half is weighted (multiplied) with h(O) = ~ and thus produces the real component Sr(kT) of the output signal. For m = 2, the weighting is -~. Further processing in the delay chain is in such a way that (N+1)/4 = 3 differential signals are formed:
first differential signal = input signal of the first delay member minus the output signal of the last delay member, second differential signal = input signal of the second delay member minus the output signal of the second-last delay member, and third differential signal = input signal of the third delay member minus the o~tput signal of the third-last, i.e. the right, middle delay member.
These differential signals are subsequently weighted (multiplied), summed and thus produce the imaginary component of the output signal s(kT). The weighting is effected according to the following tables.
Examples for N = 1 and h(-l~ = h(l) for 1 = O, 1, ...5, corresponding to the prototype half-band filter according to the frequency response of Figure 2a:
Table 1:
m = O (m - 2 with in each case a different sign for the complex coefficients _ = Re(h) + jJm(h)) Re(_) O O O h(O) O O
Jm(_) -h(5) h(3) -h(l) O h(l) -h(3) h(5) Table 2:
m = 1 (m a 3 with in each case a different sign for the complex coefficients) Re(h) h(5) -h(3) h(l) O -h(l) h(3) -h(5) Jm(_) O O O h(O) O O O
~ 2~371-176 1303~48 The realization according to F'igure 4 is effected in the same manner as that according to Figure 3, with the only difference being in the other zero phase value ~0 = m ~/2 where m = 1. and 3, which merely results in a different weighting.
Figure 5 shows the block circuit diagram for the reversed use of the half-band filter according to Figure l, namely for generating a real output signal from a complex input signal. For this purpose the previously represented circuits are transposed, resulting in a reversal of all arrow directions and replacement of a branching member by an adder and vice-versa.
In corresponding manner the exemplary embodiment for the circuit arrangement of Figure 6 evolves from Figure 3 and the circuit arrangement according to Figure 7 evolves from Figure 4.
Claims (9)
1. A non-recursive half-band filter for converting, at a sampling frequency fA = 1/T, a real input signal s(kT) into a complex output signal s(kT), where k is a running index, comprising means for modulating its pulse response h(1), where 1 =
-1(N-1)/2 to (N-1)/2 and the filter length N is an odd integer, onto a complex carrier with a frequency ? 1/4 of the sampling frequency fA = 1/T to produce h(1) = h(1) ? ej(? 2.pi./fA/4fA + ?O) = h(1), the zero phase ?O of this frequency being an integral multiple m of .pi./2 (?O
= m ? .pi./2 where m = 0, l, 2, 3 ...).
-1(N-1)/2 to (N-1)/2 and the filter length N is an odd integer, onto a complex carrier with a frequency ? 1/4 of the sampling frequency fA = 1/T to produce h(1) = h(1) ? ej(? 2.pi./fA/4fA + ?O) = h(1), the zero phase ?O of this frequency being an integral multiple m of .pi./2 (?O
= m ? .pi./2 where m = 0, l, 2, 3 ...).
2. A non-recursive half-band filter for converting, at a sampling frequency fA = 1/T, a complex input signal s(kT) into a real output signal s(kT), where k is a running index, comprising means for modulating its pulse response h(1) with respect to the sampling frequency fA, where 1 = -(N-1)/2 to (N-1)/2 and the filter length N is an odd integer, onto a complex carrier with a frequency of ?fA/4 to produce h(1) = h(1) ? ej(?2.pi./fA/4fA + ?O) = h(1), the zero phase ?O of this frequency being an integral multiple m of .pi./2 (?O - m ?
.pi./2 where m = 0, 1, 2, 3 ...).
.pi./2 where m = 0, 1, 2, 3 ...).
3. A non-recursive half-band filter according to claim 1, wherein each sampling value of the input signal s(kT) is guided to a chain of (N-1)/2 delay members having a time delay of 2T, whereby the middle delay member is divided into two members having a time delay of T, wherein in each case differential signals are formed from the output signal of the last delay member minus the input signal of the first delay member = first differential signal, output signal of the second-last delay member minus the input signal of the second delay member = second differential signal, output signal of the third-last delay member minus the input signal of the third delay member = third differential signal, etc., wherein these differential signals are subjected to a weighting (multiplication) with a value h(1) of the pulse response, are subsequently summed and then produce either the real or imaginary component of the filter output signal s(kT), and wherein from the chain middle the input signal delayed with the time delay T = (N-1)/2 is weighted with the value h(O) which produces the imaginary or real component of the filter output signal s(kT).
4. A non-recursive half-band filter according to claim 3, wherein N = 11 and m = 1, the first differential signal is weighted with -h(5), the second differential signal is weighted with h(3) and the third differential signal is weighted with -h(1), and h(O) = 1/2, and wherein the sum of the differential signals produces the real component sr(kT) and the signal weighted with h(O) produces the imaginary component si(kT).
5. A non-recursive half-band filter according to claim 3, wherein N = 11 and m - 3, the first differential signal is weighted with h(5), the second differential signal is weighted with -h(3) and the third differential signal is weighted with h(1) and that h(O) = -1/2, and wherein the sum of the differential signals produces the real component sr(kT) and the signal weighted with h(O) produces the imaginary component si(kT).
6. A non-recursive half-band filter according to claim 3, wherein N = 11 and m = 0, the first differential signal is weighted with h(5), the second differential signal is weighed with -h(3) and the third differential signal is weighted with h(1), and wherein the sum of the differential signals produces the imaginary component si(kT) and the signal weighted with h(O) = 1/2 produces the real component sr(kT).
7. A non-recursive half-band filter according to claim 3, wherein N = 11 and m = 2, the first differential signal is weighted with -h(5), the second differential signal is weighted with h(3), the third differential signal is weighted with -h(1), and wherein the sum of the differential signals produces the imaginary component si(kT) and the signal weighted with h(O) = -1/2 produces the real component sr(kT).
8. A non-recursive half-band filter according to claim 2, wherein a chain of (N-1)/2 delay members having a time delay of 2T
are provided, whereby the middle delay member is divided into two members having a time delay of T, wherein the imaginary component si(kT) weighted with a value h(1) of the pulse response is fed to the first delay member of this chain and is subtracted from the output signal of the last delay member of this chain, said differential signal supplying the real filter output signal s(kT), wherein additional instantaneous values weighted with a value h(1) of the pulse response of the imaginary component si(kT) of the filter input signal are added to the transverse signal of this delay member chain at the further points, and wherein in the middle of the delay chain there is an additive feed of the real component sr(kT) of the complex filter input signal to the transverse signal of the chain weighted with h(O).
are provided, whereby the middle delay member is divided into two members having a time delay of T, wherein the imaginary component si(kT) weighted with a value h(1) of the pulse response is fed to the first delay member of this chain and is subtracted from the output signal of the last delay member of this chain, said differential signal supplying the real filter output signal s(kT), wherein additional instantaneous values weighted with a value h(1) of the pulse response of the imaginary component si(kT) of the filter input signal are added to the transverse signal of this delay member chain at the further points, and wherein in the middle of the delay chain there is an additive feed of the real component sr(kT) of the complex filter input signal to the transverse signal of the chain weighted with h(O).
9. A non-recursive half-band filter according to claim 8, wherein m = 0 or 2 and N = 11, and wherein the instantaneous values that are fed in of the real component sr(kT) or of the imaginary component si(kT) of the filter input signal are weighted as follows:
at the input of the first delay member with ?h(5), at the input of the second delay member with ?h(3), at the input of the third delay member with ?h(1), at the input of the second-last delay member with ?h(1), at the input of the last delay member with ?h(3), and at the output of the last delay member with ?h(5), and wherein h(O) = ?1/2.
at the input of the first delay member with ?h(5), at the input of the second delay member with ?h(3), at the input of the third delay member with ?h(1), at the input of the second-last delay member with ?h(1), at the input of the last delay member with ?h(3), and at the output of the last delay member with ?h(5), and wherein h(O) = ?1/2.
Applications Claiming Priority (2)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| DEP3705207.1 | 1987-02-19 | ||
| DE19873705207 DE3705207A1 (en) | 1987-02-19 | 1987-02-19 | NON-RECURRENT HALF-BAND FILTER |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CA1303148C true CA1303148C (en) | 1992-06-09 |
Family
ID=6321282
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CA000559077A Expired - Fee Related CA1303148C (en) | 1987-02-19 | 1988-02-17 | Non-recursive half-band filter |
Country Status (5)
| Country | Link |
|---|---|
| EP (1) | EP0339037B1 (en) |
| JP (1) | JPH01503346A (en) |
| CA (1) | CA1303148C (en) |
| DE (1) | DE3705207A1 (en) |
| WO (1) | WO1988006380A1 (en) |
Families Citing this family (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| DE3621737A1 (en) * | 1986-06-28 | 1988-01-21 | Ant Nachrichtentech | NON-RECURRENT HALF-BAND FILTER |
| DE4026477A1 (en) * | 1990-08-22 | 1992-03-05 | Ant Nachrichtentech | METHOD FOR PROCESSING A DIGITAL FREQUENCY MULTIPLEX SIGNAL AND ITS DISASSEMBLY |
| DE4337135C1 (en) * | 1993-10-30 | 1994-09-01 | Ant Nachrichtentech | Drop-and-add multiplexer for converting and conditioning a frequency-division multiplex signal |
| DE4444870C1 (en) * | 1994-12-16 | 1995-10-26 | Ant Nachrichtentech | Demodulator for complex-valued vestigial sideband signal |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| DE3621737A1 (en) * | 1986-06-28 | 1988-01-21 | Ant Nachrichtentech | NON-RECURRENT HALF-BAND FILTER |
-
1987
- 1987-02-19 DE DE19873705207 patent/DE3705207A1/en active Granted
- 1987-12-24 EP EP19880900452 patent/EP0339037B1/en not_active Expired - Lifetime
- 1987-12-24 JP JP50086787A patent/JPH01503346A/en active Pending
- 1987-12-24 WO PCT/DE1987/000607 patent/WO1988006380A1/en active IP Right Grant
-
1988
- 1988-02-17 CA CA000559077A patent/CA1303148C/en not_active Expired - Fee Related
Also Published As
| Publication number | Publication date |
|---|---|
| WO1988006380A1 (en) | 1988-08-25 |
| EP0339037A1 (en) | 1989-11-02 |
| EP0339037B1 (en) | 1993-02-17 |
| DE3705207C2 (en) | 1989-04-06 |
| JPH01503346A (en) | 1989-11-09 |
| DE3705207A1 (en) | 1988-09-01 |
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