Complex Adaptive IIR Notch Filter Research Articles

An RLS-Based Lattice-Form Complex Adaptive Notch Filter

This letter presents a new lattice-form complex adaptive IIR notch filter to estimate and track the frequency of a complex sinusoid signal. The IIR filter is a cascade of a direct-form all-pole prefilter and an adaptive lattice-form all-zero filter. A complex domain exponentially weighted recursive least square algorithm is adopted instead of the widely used least mean square algorithm to increase the convergence rate. The convergence property of this algorithm is investigated, and an expression for the steady-state asymptotic bias is derived. Analysis results indicate that the frequency estimate for a single complex sinusoid is unbiased. Simulation results demonstrate that the proposed method achieves faster convergence and better tracking performance than all traditional algorithms.

Steady-state analysis of a complex adaptive notch filter using modified gradient algorithm

Based on power spectral density (PSD) analytical technique, mean square error (MSE) (or variance) of the frequency estimate of a first-order complex adaptive IIR notch filter (ANF) using modified complex plain gradient (MCPG) algorithm is investigated in this paper. The steady-state expression for MSE is derived in closed form. A quantitative analysis for the estimation MSE has been carried out. It has been revealed that the MSE of frequency estimate is independent of an input frequency of a complex sinusoid. In addition, computer simulations are treated to corroborate the theoretical analysis and the relationships between MSE and system parameters are shown.

Arctangent based adaptive algorithm for a complex IIR notch filter for frequency estimation and tracking

An arctangent (AT) based adaptive algorithm for a first-order complex adaptive IIR notch filter (CANF) is proposed in this paper. The objective of this work is to overcome some drawbacks including slow convergence speed and high sensitivity to impulsive noise of the previous gradient and nongradient based adaptive algorithms. The proposed AT algorithm employs the ratio of output to regressor signal as an error criterion where the arctangent value of such a ratio is employed to adjust the filter parameter. It is found that the proposed algorithm provides not only high speed convergence but also high impulsive noise robustness. Moreover, very low bias of the frequency estimate is also obtained. In addition, difference equation for the convergence in the mean and coarse stability bound in mean sense are derived. Computer simulations are conducted to show the performance of the proposed AT algorithm.

A complex adaptive notch filter using modified gradient algorithm

A modified gradient algorithm is developed for improving the convergence speed of a first-order complex adaptive IIR notch filter, which is used for estimating an unknown frequency of a complex sinusoidal signal embedded in white Gaussian noise. The new cost function using new error criterion is presented and analyzed theoretically. The proposed technique can significantly improve the convergence speed as compared with a complex notch filter using plain gradient algorithm. The computer simulations are conducted to demonstrate the validity of the proposed complex adaptive notch filter.

Complex adaptive IIR notch filter algorithm and its applications

In this paper, conventional real coefficient adaptive notch filters (ANF's) are extended to complex coefficient ones. This complex adaptive notch filter is implemented as a constrained IIR filter using a complex Gauss-Newton type algorithm to adjust its coefficients. When the ANF algorithm is applied to estimate the frequencies of sinusoids embedded in white noise. The results show that this algorithm has fast convergence, small bias, and achieves the Cramer-Rao bound. Furthermore, this ANF algorithm is used to estimate the parameters of multiple chirp signals. Simulation results also demonstrate very good performance. Finally, when this ANF algorithm is used to suppress narrowband interference in QPSK spread spectrum communication systems, the analytic result reveals that its signal-to-noise ratio improvement factor is grater than the factor of conventional one-sided prediction filter. >