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

We develop a canonical, adaptive cascade-structure IIR notch filter to detect and track multiple time-varying frequencies in additive white Gaussian noise. The algorithm uses allpass frequency transformation filters and a truncated gradient. Simulations indicate that our algorithm is computationally simple, converges rapidly, and has good frequency resolution.

Multiple fully adaptive notch filter design based on allpass sections

This paper presents a new adaptive infinite impulse response (IIR) line enhancer (LE) comb filter configuration for the purpose of power system harmonic signal estimation and retrieval. The approximate maximum likelihood (AML) algorithm is employed for the parameter update. The proposed solution is characterised by modest computational burden, effective tracking capabilities and provides the retrieved harmonic components with little or no distortion. The retrieved power system harmonics may be obtained on an individual basis or as a composite signal. Practical test results are included which show the performance achieved by the proposed technique. >

Power system harmonic signal estimation and retrieval for active power filter applications

This paper presents a high resolution spectral estimation technique using a specially constrained adaptive notch filter to estimate and resolve two closely spaced dominant frequencies buried in noise. The notch filter parametrization is an autoregressive moving average model which is implemented in cascaded form. A computationally simple gradient-based adaptive algorithm was applied and found to provide a robust solution to the problem of parameter estimation. Error surface analysis is included and clearly indicates that the algorithm has guaranteed convergence. In addition the analysis provides valuable insights into the appropriate filter and adaption coefficient parameter selection. Extensive experimental testing has been undertaken and results indicate superior performance over existing techniques such as the fast Fourier transform. Typical results are included to demonstrate the capabilities of the proposed technique.

High resolution spectral estimation using a specially constrained adaptive notch filter

A study of the effects of additive noise on the WI coder is presented. In WI, pitch-cycle waveforms (prototypes) are extracted from the residual signal. Since these prototypes evolve slowly when the speech is voiced and rapidly when unvoiced, simple filtering can be applied in the evolution domain to separate these components. The focus of this work is to investigate how this decomposition maps noise, with application to speech enhancement. A repercussion of the alignment procedure, necessary to align successive prototypes, causes incorrect decomposition of narrowband noise, resulting in the spreading of energy. Furthermore, the near equal decomposition of broadband noise into the slowly evolving and rapidly evolving component poses difficulties for noise suppression. Thus, problems with the current WI coder in noisy conditions are identified, highlighting the necessity to develop further methods to overcome such problems.

https://ieeexplore.ieee.org/iel3/5225/14128/00648279.pdf

The effects of noise on the waveform interpolation speech coder

A modified second-order infinite impulse response (IIR) notch filter with constrained poles and zeros is presented to eliminate or retrieve sinusoids embedded in a broadband signal. Such a filter is ideally suited to either parallel or cascaded implementation. Two classes of problems are considered. The first is where the sinusoidal frequencies are known a priori. For this case a straightforward design procedure based on a set of design characteristic graphs is used to select tunable notch filter parameters. An interesting property of the notch filter model is that it can be converted to a line enhancer by interchanging the position of the poles and zeros. The second type of problem arises when the sinusoidal frequencies are unknown and possibly varying with time. This means that an adaptive solution is required and an important consideration is the parameter estimation accuracy. For this purpose, the paper derives the Cramer–Rao lower bound for the adaptive cascaded notch filter using a frequenc...

Tung S. Ng

Papers

Tunable/adaptive second-order IIR notch filter