An adaptive filter or equalizer for digital data communication includes, a first cascade circuit connected to operate as a digital finite-impulse-response (FIR) filter, the first cascade circuit having a respective first single input for receiving samples of complex input data, a respective second input composed of a first plurality of input taps for receiving filter weighting signals, and a respective output for producing samples of filtered data. An error signal generator responds to samples supplied from the output of first cascade circuit to generate samples of an error signal. A second cascade circuit, which includes the form of an FIR filter of inverse canonical form, a respective first single input for receiving said delayed samples of complex input data, a respective second input composed of a second plurality of input taps for consecutively receiving said samples of said error signal from error signal generator, a third single input, and a respective output, which supplies samples fed back to the third input for yielding a succession of weighting signals. Storage registers at the inputs of the first and second cascade circuits are updated by weighting signals and by error signal samples, respectively, serving to multiplex application of single inputs to multiple cascade stages.