Digital filter bank

In a frequency multiplex circuit including a digital filter bank for effecting conversion between a frequency multiplexed signal and a plurality of weighted filter signals, and discrete Fourier transformation means connected to said filter bank for effecting a discrete Fourier transformation between the weighted filter signal and L individual complex signals appearing on separate lines, wherein:

• the frequency multiplexed signal contains component signals each associated with a respective individual complex signal and having a bandwidth B;
• the weighted filter signals are complex signals having the form ##EQU17## where n<m,
• n=0, 1, 2, . . . ,
• m=1, 2, . . . ,
• i=p.multidot.L+q
• q=0, 1, 2, . . . L-1, and
• i, p, q=(0, 1, 2, 3, . . . )
• the frequency multiplexed signal is s(k) and has a sampling rate of f.sub.A ;
• h(i) is a coefficient representing a pulse response of a finite length for i=0, 1, 2, . . . N-1, which pulse response has a complex rotation factor;
• the discrete Fourier transformation has the form ##EQU18## where s.sub.l (kM) represents the individual complex signals and DFT { } is the discrete Fourier transformation, M is a sampling rate reduction factor, M.ltoreq.L, and the discrete Fourier transformation involves sampling with respect to every Mth value of the weighted filter signals;
• each component signal of the frequency multiplexed signal is associated with a respective channel having a channel number, l, and a center channel frequency f.sub.l =l.multidot.B+B.multidot.n/m and l=0, 1, 2, . . . L-1, the improvement wherein:
• the frequency multiplexed signal is a complex signal, s(kT)=s.sub.r (kT)+js.sub.i (kT) with a real portion Re=s.sub.r (kT) and an imaginary portion Im=s.sub.i (kT), and k is a time factor= . . . , -1, 0, +1 . . . ;
• and
• said filter bank comprises:
• two chains of N-1 delay members each having a delay of T and each processing a respective portion of the complex signal, where N is the number of frequency multiplexed signal values associated with each set of weighted filter signal values and T=1/f.sub.A ;
• sampling means for sampling the signals associated with each delay member at a rate corresponding to the sampling rate of the frequency multiplexed signal reduced by M;
• first processing means for effecting conversion between each sample signal associated with a given delay member and an associated weighted sample signal, wherein each weighted sample signal corresponds to a sample signal multiplied by a complex coefficient h(i)=h.sub.r (i)+jh.sub.i (i), where h.sub.r (i)=h(i).multidot.cos (2.pi..multidot.in/Lm) and h.sub.i (i)=h(i).multidot.sin (2.pi.i.n/Lm);
• and second processing means for effecting conversion between selected weighted complex filter signals v(kM,q) and respective ith weighted sample signals.

In a frequency multiplex circuit including a digital filter bank for effecting conversion between a frequency multiplexed signal and a plurality of weighted filter signals, and discrete Fourier transformation means connected to said filter bank for effecting a discrete Fourier transformation between the weighted filter signal and L individual complex signals appearing on separate lines, wherein:

• the frequency multiplexed signal contains component signals each associated with a respective individual complex signal and having a bandwidth B;
• the weighted filter signals are complex signals having the form ##EQU19## where
• i=p.multidot.L+q
• q=0, 1, 2, . . . L-1, and
• i, p, q=(0, 1, 2, 3, . . . )
• the frequency multiplexed signal is s(k) and has a sampling rate of f.sub.A ;
• h(i) is a coefficient representing a pulse response of a finite length for i=0, 1, 2 . . . N-1, which pulse response has a complex rotation factor;
• the discrete Fourier transformation has the form ##EQU20## where s.sub.p (kM) represents the individual complex signals and DFT { } is the discrete Fourier transformation, M is a sampling rate reduction factor, M.ltoreq.L, and the discrete Fourier transformation involves sampling with respect to every Mth value of the weighted filter signals;
• each component signal of the frequency multiplexed signal is associated with a respective channel having a channel number, l, and a center channel frequency f.sub.l =l.multidot.B+B/2 and l=0, 1, 2, . . . L-1, the improvement wherein:
• the frequency multiplexed signal is a complex signal, s(kT)=s.sub.r (kT)+js.sub.i (kT) with a real portion Re=s.sub.r (kT) and an imaginary portion Im=s.sub.i (kT), and k is a time factor= . . . , -1, 0, +1 . . . ;
• and
• said filter bank comprises:
• two chains of N-1 delay members each having a delay of T and each processing a respective portion of the complex signal, where N is the number of frequency multiplexed signal values associated with each set of weighted filter signal values and T=1/f.sub.A ;
• sampling means for sampling the signals associated with each delay member at a rate corresponding to the sampling rate of the frequency multiplexed signal reduced by M;
• first processing means for effecting conversion between each sample signal associated with a given delay member and an associated weighted sample signal;
• second processing means for effecting conversion between selected weighted filter signals and selected weighted sample signals;
• and third processing means for effecting conversion between complex selected weighted filter signals and those signals multiplied by e.sup.j2.pi.q/L.

In a frequency multiplex circuit including a digital filter bank for effecting conversion between a frequency multiplexed signal and a plurality of weighted filter signals, and discrete Fourier transformation means connected to said filter bank for effecting a discrete Fourier transformation between the weighted filter signals and L individual complex signals appearing on separate lines, wherein:

• the frequency multiplexed signal contains component signals each associated with a respective individual complex signal and having a bandwidth B;
• the weighted filter signals have the form ##EQU21## where n=0, or n=1 and m=2,
• i=p.multidot.L+q,
• q=0, 1, 2, . . . L-1, and
• i, p, q=(0, 1, 2, 3, . . . )
• the frequency multiplexed signal is s(k) and has a sampling rate of f.sub.A ;
• h(i) is a coefficient representing a pulse response of a finite length for i=0, 1, 2, . . . N-1, which pulse response has a complex rotation factor;
• the discrete Fourier transformation has the form ##EQU22## where s.sub.l (kM) represents the individual complex signals and DFT { } is the discrete Fourier transformation, M is a sampling rate reduction factor, M.ltoreq.L, and the discrete Fourier transformation involves sampling with respect to every Mth value of the weighted filter signals;
• each component signal of the frequency multiplexed signal is associated with a respective channel having a channel number, l, and a center channel frequency f.sub.l =l.multidot.B+B.multidot.n/m and l=0, 1, 2, . . . L-1, the improvement wherein:
• the frequency multiplexed signal is a complex signal, s(kT)=s.sub.r (kT)+js.sub.i (kT) with a real portion Re=s.sub.r (kT) and an imaginary portion Im=s.sub.i (kT), and k is a time factor= . . . , -1, 0, +1 . . . ;
• and
• said filter bank comprises two identical signal processing systems, each associated with a respective complex signal portion and each comprising:
• multiposition switch means having a contact switchable between M terminals and M chains of delay members, each chain being connected to a respective terminal of said switch means and containing a number of delay members equal to the largest integer which is not greater than N/M, and each delay member producing a delay of MT, with the associated portion of the frequency multiplexed signal being present at said switch means contact, said switch means being operative to connect said contact cylically to each terminal in turn at the sampling rate of f.sub.A from terminal to terminal so that said contact is cyclically connected to each terminal at a rate of f.sub.A /M;
• and
• first processing means connected to said delay members for affecting conversion between each sample signal associated with a given delay member and an associated weighted product signal according to the relation
• P(.mu., .upsilon.)=s.sub..mu. (kM-.upsilon.M).multidot.h(.mu.+.upsilon.M),
• where
• P is the weighted product signal,
• .mu. is the associated chain=0, 1 . . . M-1,
• s.sub..mu. is the sample signal at the associated terminal,
• .upsilon. is the associated delay member=0, 1, 2 . . . , and
• h is the weighting coefficient;
• and
• said filter bank further comprises:
• second processing means connected to said first processing means of each said signal processing system for effecting conversion between the weighted product signals and L intermediate complex signals v(kM, q), each portion of each intermediate complex signal being the sum of selected weighted product signals for which .mu.=pM+p.lambda.+q-.alpha.M, where .alpha.=(pM+p.lambda.+q)/M and .lambda.=L-M;
• and
• third processing means connected to said second processing means for effecting conversion between each intermediate complex signal and an associated weighted filter signal, such that each weighted filter signal is
• v(kM, q).multidot.e.sup.j.pi.nq/L (=1 for n=0).

In a frequency multiplex circuit including a digital filter bank for effecting conversion between a frequency multiplexed signal and a plurality of weighted filter signals, and discrete Fourier transformation means connected to said filter bank for effecting a discrete Fourier transformation between the weighted filter signals and 4 individual complex signals appearing on separate lines, wherein:

• the frequency multiplexed signal contains component signals each associated with a respective individual complex signal and having a bandwidth B;
• the weighted filter signals are complex signals having the form ##EQU23##
• i=4p+q
• q=0, 1, 2, 3, and
• i, p, q=(0, 1, 2, 3, . . . )
• the frequency multiplexed signal is s(k) and has a sampling rate of f.sub.A ;
• h(i) is a coefficient representing a pulse response of a finite length for i=0, 1, 2 . . . N-1, which pulse response has a complex rotation factor, where N=8.mu.-1 and .mu.=1, 2, 3 . . . )
• the discrete Fourier transformation has the form ##EQU24## where s.sub.l (kM) represents the individual complex signals and DFT { } is the discrete Fourier transformation, M=2 and the discrete Fourier transformation involves sampling with respect to every 2nd value of the weighted filter signals;
• each component signal of the frequency multiplexed signal is associated with a respective channel having a channel number, l, and a center channel frequency f.sub.l =l.multidot.B+B/2 and l=0, 1, 2, 3, the improvement wherein:
• the frequency multiplexed signal is a complex signal, s(kT)=s.sub.r (kT)+js.sub.i (kT) with a real portion Re=s.sub.r (kT) and an imaginary portion Im=s.sub.i (kT), and k is a time factor= . . . , -1, 0, +1 . . . ;
• and
• said filter bank comprises, for each portion of the frequency multiplex signal;
• first delay means consisting of a chain of (N-1)/2 delay members each having a delay of 2T=2f.sub.A, second delay means consisting of one delay member having a delay of T(N-3)/2;
• and switch means for deriving samples of the associated complex signal portion at the sampling rate of f.sub.A and supplying successive samples to alternate ones of said delay means;
• said first delay means having (N+1)/2 successively numbered output points, the first output point being at the input of the first delay member in said chain, connected to said switch means, and each succeeding output point being at the output of each succeeding delay member of said chain, starting with the first delay member;
• first multiplying means connected for multiplying the signals at the odd numbered output points by the .sqroot.2 scaled coefficients h(4a), where a=0, 1, 2 . . . , and combining the multiplied signals to form a product sum v.sub.r (0) for the real portion or v.sub.i (0) for the imaginary portion;
• second multiplying means connected for multiplying the signals at the even numbered output points by the .sqroot.2 scaled coefficients h(4a+2), and combining the multiplied signals to form a product sum -v.sub.r (2) for the real portion or v.sub.i (2) for the imaginary portion;
• wherein said first and second multiplying means are operative for causing the multiplied signals associated with each alternate pair of successive output points, starting with the first output point, to be evaluated as positive and for causing the multiplied signals associated with the intervening pairs of successive output points to be evaluated as negative;
• and
• third multiplying means connected for multiplying the output of one delay member of said second delay means by 1/2;
• and
• said filter bank further comprises arithmetic means connected to said third multiplying means for each portion of the frequency multiplexed signal for forming a signal v.sub.i (3) representing the sum of the signals produced by the two said third multiplying means and a signal v.sub.r (3) representing the signals produced said third multiplying means associated with the real portion less the signal produced by said third multiplying means associated with the imaginary portion;
• and
• said discrete Fourier transformation means are connected to receive the signals v.sub.r (0), v.sub.1 (0), -v.sub.r (2), v.sub.i (2), v.sub.r (3) and v.sub.1 (3) as complex signals and to form four complex signals s.sub.o (2k) . . . s.sub.3 (2k) having the following relationships:
• s.sub.0r (2k)=v.sub.r (0)+v.sub.r (2)+v.sub.r (3),
• s.sub.0i (2k)=v.sub.i (0)+v.sub.i (2)+v.sub.i (3),
• s.sub.1r (2k)=v.sub.r (0)-v.sub.r (2)+v.sub.i (3),
• s.sub.1i (2k)=v.sub.i (0)-v.sub.i (2)-v.sub.r (3),
• s.sub.2r (2k)=v.sub.r (0)+v.sub.r (2)-v.sub.r (3),
• s.sub.2i (2k)=v.sub.i (0)+v.sub.i (2)-v.sub.i (3),
• s.sub.3r (2k)=v.sub.r (0)-v.sub.r (2)-v.sub.i (3), and
• s.sub.3i (2k)=v.sub.i (0)-v.sub.i (2)+v.sub.r (3).

In a frequency multiplex circuit including a digital filter bank for effecting conversion between a frequency multiplexed signal and a plurality of weighted filter signals, and discrete Fourier transformation means connected to said filter bank for effecting a discrete Fourier transformation between the weighted filter signals and 4 individual complex signals appearing on separate lines, wherein:

• the frequency multiplexed signal contains component signals each associated with a respective individual complex signal and having a bandwidth B;
• the weighted filter signals are complex signals having the form ##EQU25##
• i=4p+q
• q=0, 1, 2, 3, and
• i, p, q=(0, 1, 2, 3, . . . )
• the frequency multiplexed signal is s(k) and has a sampling rate of f.sub.A ;
• h(i) is a coefficient representing a pulse response of a finite length for i=0, 1, 2 . . . N-1, which pulse response has a complex rotation factor, where N=8.mu.+3 and .mu.=1, 2, 3 . . . )
• the discrete Fourier transformation has the form ##EQU26## where s.sub.l (kM) represents the individual complex signals and DFT { } is the discrete Fourier transformation, M=2 and the discrete Fourier transformation involves sampling with respect to every 2nd value of the weighted filter signals;
• each component signal of the frequency multiplexed signal is associated with a respective channel having a channel number, l, and a center channel frequency f.sub.l =l.multidot.B+B/2 and l=0, 1, 2, 3, the improvement wherein:
• the frequency multiplexed signal is a complex signal, s(kT)=s.sub.r (kT)+js.sub.i (kT) with a real portion Re=s.sub.r (kT) and an imaginary portion Im=s.sub.i (kT), and k is a time factor= . . . , -1, 0, +1 . . . ;
• and
• said filter bank comprises, for each portion of the frequency multiplex signal:
• first delay means consisting of a chain of (N-1)/2 delay members each having a delay of 2T=2f.sub.A, second delay means consisting of one delay member having a delay of T(N-3)/2;
• and switch means for deriving samples of the associated complex signal portion at the sampling rate of f.sub.A and supplying successive samples to alternate ones of said delay means;
• said first delay means having (N+1)/2 successively numbered output points, the first output point being at the input of the first delay member in said chain, connected to said switch means, and each succeeding output point being at the output of each succeeding delay member of said chain, starting with the first delay member;
• first multiplying means connected for multiplying the signals at the odd numbered output points by the .sqroot.2 scaled coefficients h(4a), where a=0, 1, 2 . . . , and combining the multiplied signals to form a product sum v.sub.r (0) for the real portion or v.sub.i (0) for the imaginary portion;
• second multiplying means connected for multiplying the signals at the even numbered output points by the .sqroot.2 scaled coefficients h(4a+2), and combining the multiplied signals to form a product sum -v.sub.r (2) for the real portion or v.sub.i (2) for the imaginary portion;
• wherein said first and second multiplying means are operative for causing the multiplied signals associated with each alternate pair of successive output points, starting with the first output point, to be evaluated as positive and for causing the multiplied signals associated with the intervening pairs of successive output points to be evaluated as negative;
• and
• third multiplying means connected for multiplying the output of one delay member of said second delay means by 1/2;
• and
• said filter bank further comprises arithmetic means connected to said third multiplying means for each portion of the frequency multiplexed signal for forming a signal v.sub.i (1) representing the sum of the signals produced by the two said third multiplying means and a signal v.sub.r (1) representing the signals produced said third multiplying means associated with the real portion less the signal produced by said third multiplying means associated with the imaginary portion;
• and
• said discrete Fourier transformation means are connected to receive the signals v.sub.r (0), v.sub.1 (0), -v.sub.r (1), -v.sub.i (1), -v.sub.r (2) and v.sub.1 (2) as complex signals and to form four complex signals s.sub.o (2k) . . . s.sub.3 (2k) having the following relationships:
• s.sub.0r (2k)=v.sub.r (0)+v.sub.r (1)+v.sub.r (2),
• s.sub.0i (2k)=v.sub.i (0)+v.sub.i (1)+v.sub.i (2),
• s.sub.1r (2k)=v.sub.r (0)-v.sub.i (1)-v.sub.r (2),
• s.sub.1i (2k)=v.sub.i (0)+v.sub.r (1)-v.sub.r (2),
• s.sub.2r (2k)=v.sub.r (0)-v.sub.r (1)+v.sub.r (2),
• s.sub.2i (2k)=v.sub.i (0)-v.sub.i (1)+v.sub.i (2),
• s.sub.3r (2k)+v.sub.r (0)+v.sub.i (1)-v.sub.r (2), and
• s.sub.3i (2k)=v.sub.i (0)-v.sub.r (1)-v.sub.i (2).