Abstract: Providing multi-path echo cancellation comprises providing a main echo signal corresponding to a main echo section of an echo response and providing a plurality of tail echo signals, each of the plurality of tail echo signals corresponding to respective tail echo sections of the echo response. Next, providing a multi-path echo canceller comprises summing the main echo signal and the plurality of tail echo signals to provide a synthesized echo.

Abstract: The present invention may significantly reduce the number of iteration of the time recursive IFFT structure. First, the real and imaginary part of the input signal are modified based on the symmetric and anti-symmetric. Then, they are mixed together by an adder and fed into the lattice module. Next, an IFFT is performed on the modified input data sequence to generate a transformed sequence. Through the symmetric and anti-symmetric properties, the redundant terms may be eliminated.

Abstract: A method for implementing a multiplier-less FIR filter is disclosed, in which the FIR filter performs the convolution of 1 H ⁡ ( z ) = ∑ k = 0 N - 1 ⁢   ⁢ h k ⁢ z - k ,

Abstract: A method for training a time-domain equalizer having at least one coefficient that includes estimating a channel, initializing the at least one coefficient of the time-domain equalizer, updating the at least one coefficient of the time-domain equalizer with the estimated channel, retaining the updated estimated channel, fixing the updated value of the at least one coefficient of the time-domain equalizer for at least a one-symbol duration, calculating a modulated symbol based on an output of the time-domain equalizer, calculating a second value for the estimated channel based on the modulated symbol, setting the estimated channel to the second value, and repeating the step of updating the time-domain equalizer through the step of setting the estimated channel to the second value until a predetermined condition has been met.

Abstract: A CORDIC method and a CORDIC architecture applied in vector rotation are disclosed. An elementary angles set is extended by representing the elementary angles as the arctangent of the sum of two single signed-power-of-two terms to an extended elementary angles set. A combination of elementary angles is found from the extended elementary angles set such that the residue angle error can be minimized. A quantized scaling factor is used to scale the combination of elementary angles after being micro-rotated.

Abstract: There is disclosed a high-performance Booth-encoded Montgomery module for performing the computation of A*B*r−1 (mod N). A Booth encoder is provided for receiving two bits of A to perform a Booth encoding process, so as to produce a Booth code. A multiplicand selector is provided for receiving B and the Booth code so as to select a multiplicand. A first carry propagate adder is provided for adding the output of the multiplicand selector and a previous computation result to output. A multiplexer is provided for receiving four inputs 0, N, 2N, and 3N from a lookup table and selecting one of the inputs to output. A second carry propagate adder is provided for adding the outputs of the first carry propagate adder and the multiplexer to output. A shifter is provided for shifting the output from the second carry propagate adder to right by two bits, so as to produce a computation result.

Abstract: A Fast Fourier Transform device of a discrete multitone modulation system can be implemented by very large scale integrated (VLSI) architecture. The I-FFT/F-FFT functions are modified to avoid complex-valued operations. A time recursive parallel lattice structure is used to reduce the complexity in hardware requirement for the I-FFT/F-FFT.

Abstract: An improved liquid flow distributor assembly for a process column of the type wherein the distributor is positioned above a packing section for the distribution of liquid downwardly therethrough. The improvement comprises a plurality of distributor troughs constructed with a series of internal distributor channels having stilling plates depending therefrom. Each channel is constructed of a generally U-shaped cross section, aligned with and affixed to the distributor trough for providing primary liquid flow to intermediate regions thereof. In this manner, liquid gradients between opposite ends of the troughs are eliminated and a uniform quiescent liquid level is maintained.