R. Punchalard

Adaptive IIR notch filters based on new error criteria

Modified indirect and direct plain gradient (MIPG and MDPG) algorithms using new error criteria for second-order adaptive IIR (infinite-impulse response) notch filters (ANFs) with constrained poles and zeros are proposed in this paper. The proposed techniques are based on modifying error functions of the standard indirect and direct ANFs. In this work, the proposed error criteria are modified as the mean value of the product of the two signals which are, respectively, produced by the FIR (finite-impulse response) and IIR sections of the ANFs. Due to a non-zero slope straight line-like characteristic of the new cost functions, the gradient based adaptive algorithm rapidly converges to an optimum solution resulting in faster convergence speed than that of the conventional method. The closed form expressions for steady-state estimation bias and mean square error (MSE) of the proposed algorithms are also carried out. In addition, extensive simulations of the proposed algorithms compared to other methods are provided to support the theoretical analyses. Although, there are some limitations in the proposed algorithms, however, the demonstrated results obtained from tested algorithms at the same condition confirm that the proposed MIPG and MDPG algorithms are superior to others in convergent speed.

Fast communication: Mean square error analysis of unbiased modified plain gradient algorithm for second-order adaptive IIR notch filter

In this paper, theoretical analysis for deriving the estimation of mean square error (MSE) at steady-state of an adaptive IIR notch filter using unbiased modified plain gradient (UMPG) algorithm is presented in closed form. Moreover, the stability bound of the algorithm is also derived. To confirm the analytical results, the computer simulations are conducted to corroborate the effectiveness of the UMPG algorithm. Furthermore, the performances of the algorithm are also compared with the modified plain gradient (MPG) algorithm, unbiased plain gradient (UPG) algorithm and simplified lattice algorithm (SLA).

Direct frequency estimation based adaptive algorithm for a second-order adaptive FIR notch filter

This work deals with the problem of the frequency estimation of a sinusoidal signal corrupted by broad-band noise. The direct frequency estimation based adaptive algorithm for a second-order adaptive finite impulse response (FIR) notch filter (AFNF) is thus proposed. The proposed algorithm employs the bias removal technique to remove the bias existing in the estimated parameter. The performances including the rate of convergence and the mean square error (MSE) can be easily controlled by using only one parameter, i.e., step size parameter. Moreover, the proposed filter is simple to implement and suitable for real-time applications. In addition, the difference equations for the convergence in the mean and mean square, and the closed form expressions for the steady-state estimation bias and MSE are also carried out. Finally, the simulation results are provided to confirm the theoretical analysis.

Indirect frequency estimation based on second-order adaptive FIR notch filter

This paper deals with estimating the frequency of sinusoidal signal buried in broad band noise. The simple unbiased indirect frequency estimation (IFE) algorithm is proposed for a second-order adaptive finite impulse response (FIR) notch filter with constrained zeros. The technique of estimating input noise variance is employed to remove the bias existing in the estimated filter parameter. Also, the difference equation for the convergence of the expectation of the estimated parameter and the closed-form of steady state estimation mean square error (MSE) are derived. In addition, extensive simulations are conducted to corroborate the efficiency of the proposed estimator with the theoretical analysis.

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.

Unbiased plain gradient algorithm for a second-order adaptive IIR notch filter with constrained poles and zeros

This article proposes an unbiased plain gradient algorithm for a second-order adaptive IIR notch filter with constrained poles and zeros. The proposed algorithm employs removing a dominant parameter that produces inherent bias. By using this technique, the performances are improved with slight expense in computational complexity. In this paper, theoretical analysis for deriving the estimations of bias and mean square error (MSE) at steady state are presented in closed form. Moreover, the stability bound of the algorithm is also derived. To confirm the analytical results, the computer simulations are provided to corroborate the effectiveness of the proposed algorithm. Furthermore, the performances of the algorithm are also compared with the plain gradient (PG) and modified plain gradient (MPG) algorithms.

Fast communication: Adaptive IIR notch filter using a modified sign algorithm

Modified sign algorithm (MSA) for a second-order constrained adaptive IIR notch filter (ANF) is proposed and analyzed in this paper. Difference equations for the convergence in the mean and of the mean square, and steady-state estimation bias and MSE are derived in closed form. Moreover, a coarse stability for the MSA is carried out. Computer simulations are conducted to corroborate the theoretical analysis.

Adaptive howling suppressor in an audio amplifier system

The acoustic feedback causes a howling phenomenon in an audio amplifier system. This problem does not only annoy hearing but also can damage an amplifier system. The IIR adaptive howling suppressor (AHS) in an audio amplifier system is thus proposed in this paper. The algorithm of adaptive process is achieved by using the variable momentum least mean square (VMLMS). With this algorithm, the performance improvement and higher convergence rate can be success. The proposed AHS, which is placed between a preamplifier section and a power amplifier section, acts as a narrow bandwidth notch filter whose frequency characteristic can reduce a howling spectrum. The simulation results show good improvement in the howling suppression of the proposed AHS system. Moreover, the performance comparisons show that the proposed system is performed over the AHS conventional FIR and FALE structures at the same environment condition.

A robust variable step-size LMS-like algorithm for a second-order adaptive IIR notch filter for frequency detection

The best adaptive algorithm requires fast convergence speed, low variance, unbias and low steady-state mean square error (MSE) in both low and high signal-to-noise ratio (SNR) situations. We have proposed a robust variable step-size LMS-like algorithm (VS-LMS-L) for a second-order adaptive IIR notch filter for frequency detection in radar, sonar and communication systems. This algorithm is compared with the conventional LMS-like algorithm called the plain gradient algorithm (PG). The time-varying step-size /spl mu/(n) is adjusted by using the square of the time-averaged estimate of autocorrelation of the present output signal y(n) and the past one y(n-1). This technique can reject the effect of the uncorrelated noise sequence on the step-size update, resulting in a small MSE due to the small final /spl mu/(n). Moreover, this algorithm can also improve the convergence speed by comparison with the PG at the same MSE value.

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.