Digital filter tree

A frequency multiplex circuit including a plurality of digital filter cells, each including a digital filter bank for effecting conversion between a frequency multiplexed signal and a plurality of weighted filter signals, and a discrete Fourier transformation means connected to the respective filter bank, the cells being connected to one another in successive stages in an outwardly branching tree structure such that, starting with the first stage, the frequency multiplexed signal is separated into L.sub..nu. individual complex signals appearing on separate lines at the .nu.th stage, where .nu.=1, 2, . . . , the Fourier transformation means of each cell effecting a discrete Fourier transformation between the weighted filter signals of the cell and the L.sub..nu. individual complex signals, and the sampling rate is reduced at the .nu.th stage by M.sub..nu. .ltoreq.L.sub..nu., wherein for all of said cells for each cell of the .nu.th stage:

• the frequency multiplexed signal contains component signals each associated with a respective individual complex signal and having a bandwidth B.sub..nu. ;
• the weighted filter signals have the form ##EQU14## where i.sub..nu. =p.multidot.L.sub..nu. +q,
• q=0, 1, 2, . . . L.sub..nu.-1, and
• i.sub..nu., p, q=(0, 1, 2, 3, . . . )
• the frequency multiplexed signal is s.sub..nu. (k) and has a sampling rate of f.sub.A.nu. ;
• h(i.sub..nu.) is a coefficient representing a pulse response of a finite length for i.sub..nu. =0, 1, 2 . . . N.sub..nu. -1;
• the discrete Fourier transformation has the form ##EQU15## where s.sub.l.sbsb..nu. (kM.sub..nu.) represents the individual complex signals and
• DFT{.multidot.} is the discrete Fourier transformation, M.sub..nu. is a sampling rate reduction factor, M.sub..nu. .ltoreq.L.sub..nu., and the discrete Fourier transformation involves sampling with respect to every M.sub..nu.th 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.sub..nu., and a center channel frequency
• f.sub.l.sbsb..nu. =l.sub..nu. .multidot.B.sub..nu. +B.sub..nu. /2 and l.sub..nu. =0, 1, 2, . . . L.sub..nu. -1,
• the frequency multiplexed signal is a complex signal, s.sub.D (kT.sub..nu.)=s.sub.r.nu. (kT.sub..nu.)+js.sub.i.nu. (kT.sub..nu.) with a real portion Re=s.sub.r.nu. (kT.sub..nu.) and an imaginary portion Im=s.sub.i.nu. (kT.sub..nu.), and k is a time factor= . . . , -1, 0, +1 . . . ;
• and
• each filter bank in the .nu.th stage comprising:
• two chains of N.sub..nu. -1 delay members each having a delay of T.sub..nu.+1 and each processing a respective portion of the complex signal, where N.sub..nu. is the number of frequency multiplexed signal values associated with each set of weighted filter signal values output by the filter banks of the .nu.th stage and T.sub..nu. =1/f.sub.A.nu. ;
• 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.sub..nu. ;
• first processing means for effecting conversion between each sample signal associated with a given delay member and an associated weighted sample signal;
• and second processing means for effecting conversion between selected weighted filter signals and selected weighted sample signals;
• wherein for all stages .nu. the sampling rate reduction factor M.sub..nu. =2 and the number of individual complex signals appearing on separate lines at the .nu.th stage L.sub..nu. =4 are fixed,
• the first stage (.nu.=1) forms a true four-branch system having four output signals s.sub.0 (2kT.sub.1), s.sub.1 (2kT.sub.1), s.sub.2 (2kT.sub.1), s.sub.3 (2kT.sub.1), are each fed to the subsequent stage, and
• only two output signals of each of the cells of the next following stages are input to subsequent stages;
• and
• the circuit further comprising
• a prefilter having an output coupled to the first stage (.nu.=1) for producing the complex input signal s.sub.D to the first stage by sampling at the rate 2f.sub.A1 from a real frequency multiplex input signal S.sub.D (kT.sub.0), and
• means for spectrally offsetting the two partial spectra of s.sub.1 and s.sub.3 output by the first stage, which do not come to lie directly in the band 0 to f.sub.A1 /4.