Abstract: To limit the accumulation of recursive computation errors while recursively calculating the discrete Fourier transform of an input signal in response to moving window sample sets of that signal, the dependent variables for the recursive calculations are periodically refreshed. One embodiment generates an error limited continuous discrete Fourier transform of the input signal through the use of duplicate channels which are periodically reinitialized in time staggered relationship and alternately switched on-line and off-line in time synchronism with the reinitialization process. Each of the channels of that embodiment is equipped to recursively calculate the discrete Fourier transform of the input signal so that while one channel is on line feeding recursively calculated transform coefficients to the outputs, the other channel or channels are off-line being reinitialized and then computing fresh sets of transform coefficients for subsequent on-line recursive calculations.

Abstract: An automatic equalizer for calculating the equalization transfer function of a transmission channel and applying same to equalize received signals. Equalization coefficients are obtained using a mean square error criteria for convergence to the desired values.

Abstract: An automatic equalizer for calculating the equalization transfer function and applying same to equalize received signals. The initial calculation as well as the equalization proper are conducted entirely within the frequency domain. Overlapping moving window samplings are employed together with the discrete Fourier transformation and a sparse inverse discrete Fourier transformation to provide the equalized time domain output signals.

Abstract: An automatic equalizer for calculating the equalization transfer function and applying same to equalize received signals. The initial calculation as well as the equalization proper are conducted entirely within the frequency domain. Overlapping moving window samplings are employed together with the discrete Fourier transformation and a sparse inverse discrete Fourier transformation to provide the equalized time domain output signals.

Abstract: An automatic equalizer for calculating the equalization transfer function and applying same to equalize signals received from a transmission channel. Time domain equalization is achieved using a transversal filter whose tap weights are calculated in the frequency domain during an initial training period.

Abstract: An automatic equalizer for calculating the equalization transfer function of a transmission channel and applying same to equalize received signals. The initial calculation as well as the equalization proper are conducted entirely within the frequency domain. Equalization coefficients are obtained using successive approximations approaching the desired values. The equalization coefficients may be adjusted independently from each other inasmuch as these coefficients are not interdependent. Successive approximations of the coefficients differ by fixed increments of the real or imaginary components. A feedback circuit is utilized in generating the successive approximations wherein sign or polarity information is used to determine the adjustment necessary for convergence.