FPGA IMPLEMENTATION OF LOW COMPLEXITY LINEAR PERIODICALLY TIME VARYING FILTER

ABSTRACT This paper presents a low complexity architecture for a linear periodically time varying (LPTV) filter. This architecture is based on multi-input multi-output(MIMO) representation of LPTV filters. The input signal is divided into blocks and parallel processing is incorporated, there by considerably reducing the effective input sampling rate. A single multiplier can be shared for each linear time invariant (LTI) filter in the representation. Each LTI filter is realized in the transposed direct form filter using multiplier less multiplication structures based on Binary common bit patterns (BCS). The proposed structure is simulated, synthesized and implemented on Virtex v50efg256-7 Field Programmable Gate Array (FPGA). LPTV systems can be expressed as generalization of Linear time invariant (LTI) systems. If the input for a M-period LPTV system is delayed by M samples, output is also delayed by the same number of samples. An LPTV system with a period of '1' is nothing but an LTI syste

Identification of linear periodically time-varying (LPTV) systems

A linear periodically time-varying (LPTV) system is a linear time-varying system with the coefficients changing periodically, which is widely used in control, communications, signal processing, and even circuit modeling. This thesis concentrates on identification of LPTV systems. To this end, the representations of LPTV systems are thoroughly reviewed. Identification methods are developed accordingly. The usefulness of the proposed identification methods is verified by the simulation results. A periodic input signal is applied to a finite impulse response (FIR)-LPTV system and measure the noise-contaminated output. Using such periodic inputs, we show that we can formulate the problem of identification of LPTV systems in the frequency domain. With the help of the discrete Fourier transform (DFT), the identification method reduces to finding the least-squares (LS) solution of a set of linear equations. A sufficient condition for the identifiability of LPTV systems is given, which can be used to find appropriate inputs for the purpose of identification. In the frequency domain, we show that the input and the output can be related by using the discrete Fourier transform (DFT) and a least-squares method can be used to identify the alias components. A lower bound on the mean square error (MSE) of the estimated alias components is given for FIR-LPTV systems. The optimal training signal achieving this lower MSE bound is designed subsequently. The algorithm is extended to the identification of infinite impulse response (IIR)-LPTV systems as well. Simulation results show the accuracy of the estimation and the efficiency of the optimal training signal design

Blind FSR-LPTV equalization and interference rejection

We address the problem of synthesizing blind channel identification and equalization methods for digital communications systems, aimed at counteracting the presence of cochannel or adjacent-channel interference. Owing to the presence of the interfering signal, the minimum mean-square error equalizer turns out to be linear periodically time-varying, which is implemented by resorting to its Fourier series representation. Moreover, by exploiting the cyclic conjugate second-order statistics of the channel output, we propose a new weighted subspace-based channel identification method, which is asymptotically immune to the presence of high-level interference. Computer simulation results confirm the effectiveness of the proposed identification/equalization technique