Decision feedback filter device in the frequency domain

DETAILED DESCRIPTION A more advantageous way to improve the correction of the intersymbol interference is to use an adaptive filter called decision feedback adaptive filter, working in the time domain.
A filter of this kind, illustrated schematically in FIG.
1, is constituted by two temporal filters, a forward filter FF and a feedback filter FB, each receiving different series of symbols at input.
The input of the forward filter FF receives symbols {x(n)} produced by the sampling of the received signals, and the input of the feedback filter receives decisions {d(n)}, produced by a decision device C, from the symbols {y(n)} produced after filtering by the forward filter FF.
The symbols {y(n)} are the outputs of the total filter.
The outputs y(n) have the form: y(n)=z(n)+u(n) (1), where z(n)=.
SIGMA.
.
sub.
i a.
sub.
i x(n+i), with i varying from 0 to M-1, represents the symbols produced by the forward filter FF, which comprises M weighting coefficients, and where u(n)=.
SIGMA.
.
sub.
j b.
sub.
j d(n-j), with j varying from 1 to N, represents the symbols produced by the feedback filter FB from the decisions d(n-1)=f(y(n-1)) with d(n-N)=f(y(n-N)), with F as a decision function.
The filter FB comprises N weighting coefficients b.
sub.
j.
The operations for filtering the postcursor symbols x(n-j) and the precursor symbols x(n+i) are thus decorrelated.
The filter FF is used for the correction of the intersymbol interference induced by the precursor symbols.
The feedback filter FB is used for the correction of the intersymbol interference induced by the postcursor symbols.
Since the input/output data from the feedback filter FB come from a decision device, only the outputs y(n) are noise-sensitive.
The decision feedback filters are thus less sensitive than the linear filters without looping in the presence of noise.
As the parasitic symbols appear chiefly in the postcursor part, the number M of corrective coefficients a.
sub.
i of the forward filter FF is much smaller than number N of corrective coefficients b