A novel lattice-based adaptive infinite impulse response (IIR) notch filter is developed which features independent tuning of the notch frequency and attenuation bandwidth. The internal structure is based on planar rotators, ensuring reliable numerical behaviour and high processing rates in CORDIC environments. A simple update law allows a simpler implementation than previously proposed designs. Rather than minimizing an output error cost function, the algorithm is designed to achieve a stable associated differential equation, resulting in a globally convergent unbiased frequency estimator in the single sinusoid case, independent of the notch filter bandwidth. Using a second-order structure in the multiple sinusoid case, unbiased estimation of one of the input frequencies is achieved by thinning the notch bandwidth. The tracking behavior is superior to conventional output error designs, and the estimation of extremal frequencies is less prone to overflow instability than previously reported structures. >

An improved lattice-based adaptive IIR notch filter

Wireless systems often make use of the quadrature relationship between pairs of signals to effectively cancel out-of-band and interfering in-band signal components. The understanding of these systems is often simplified by considering both the signals and system transfer functions as "complex" quantities. The complex approach is especially useful in highly integrated multistandard receivers where the use of narrow-band fixed-coefficient filters at the RF and high IF must be minimized. This paper first presents a tutorial review of complex signal processing for wireless applications. The review emphasizes a graphical and pictorial description rather than an equation-based approach. Next, a number of classical modulation architectures are described using this formulation. Finally, more recent developments such as complex filters, image-reject mixers, low-IF receivers, and oversampling analog-digital converters are discussed.

Complex signal processing is not complex

A lattice notch filter for the detection and enchancement of sinusoids in noise is presented, and the convergence properties of the algorithm are investigated using ODE (ordinary differential equation) analysis. It is shown that the frequency estimate of the algorithm for a single sinusoid is unbiased, regardless of the pole-zero contraction factor and the noise variance. An expression for the MSE (mean square error) of the frequency estimate and the output SNR of the algorithm is derived. Simulation results are presented to verify the theoretical analysis. Based on cascading the proposed second-order adaptive notch filter, three different approaches for the detection of multiple sinusoids are presented. The first approach uses a linear cascade structure, and the second and third approaches use a triangular cascade structure. The performance of the algorithms for multiple sinusoids is investigated, and computer simulation results are presented and discussed. >

On the adaptive lattice notch filter for the detection of sinusoids

This paper presents an integrated model for recognizing power-quality disturbances (PQD) using a novel wavelet multiclass support vector machine (WMSVM). The so-called support vector machine (SVM) is an effective classification tool. It is deemed to process binary classification problems. This paper combined linear SVM and the disturbances-versus-normal approach to form the multiclass SVM which is capable of processing multiple classification problems. Various disturbance events were tested for WMSVM and the wavelet-based multilayer-perceptron neural network was used for comparison. A simplified network architecture and shortened processing time can be seen for WMSVM.

Detection and Classification of Multiple Power-Quality Disturbances With Wavelet Multiclass SVM

There has been a constant interest in the design and implementation of digital filters with variable characteristics for different applications. In this article an attempt is made to review and systematize all known structures and methods of design of such filters. First the basic theory of the variable digital filters is introduced. Then FIR and IIR realizations with real and complex coefficients are considered, the known results for multidimensional variable filters are discussed and finally, typical implementations are overviewed. Recommendations for applications in different situations are given and unresolved problems are pointed out. This work is basically a review, but some of our original results are also included.

Variable Digital Filters

A constrained adaptive infinite-impulse-response (IIR) filter consisting of a cascade of biquadratic notch sections is used to track multiple sinusoids. The structure can be used to isolate individual sinusoids. It is shown that for small changes around the optimum solution, the proposed update algorithm approximates the Gauss-Newton update without requiring a matrix inversion. Furthermore, the transient response is approximately independent of the number of sinusoids or their power levels. Important adaptive line enhancement performance criteria, such as signal-to-noise improvement ratio and the bias in the frequency estimate assuming white noise, are derived for the single-sinusoid case. Computer simulations are used to demonstrate the performance of the notch filter under a wide range of conditions. >

Adaptive detection and enhancement of multiple sinusoids using a cascade IIR filter

A constrained adaptive IIR (infinite-impulse-response) filter consisting of a cascade of biquadratic notch sections is used to track multiple sinusoids. The structure can be used to isolate individual sinusoids. It is shown that, for small changes around the optimum solution, the proposed update algorithm approximates the Gauss-Newton update without requiring a matrix inversion. Furthermore, the transient response is approximately independent of the number of sinusoids or their power levels. Important adaptive line enhancement performance criteria such as signal-to-noise improvement ratio and the bias in the frequency estimate assuming white noise are derived for the single-sinusoid case. >

A new frequency-difference detector (FDD) based on an adaptive notch filter is proposed. The FDD is useful in decreasing acquisition times in phase-locked loop (PLL) and Costas loop based clock and carrier extraction systems. When used to aid voltage controlled oscillator (VCO) locking in a PLL, the new FDD eliminates phase errors between the input signal and the VCO output when in lock, even when a multiplying-type phase detector is used (as opposed to an edge-sensitive phase detector). This decreases jitter for low-SNR applications. Also, the control-voltage output from the FDD has substantially less ripple for a given loop bandwidth, as compared to a traditional FDD such as the quadricorrelator (QDR). This also significantly decreases the phase jitter of extracted signals. >

T. Kwan

Papers

Adaptive detection and enhancement of multiple sinusoids using a cascade IIR filter

Adaptive detection and enhancement of multiple sinusoids using a cascade IIR filter

A notch filter based frequency-difference detector and its applications