On Minimal Second-order IIR Bandpass Filters with Constrained Poles and Zeros

In this paper, several forms of infinite impulse response (IIR) bandpass filters with constrained poles and zeros are presented and compared. The comparison includes the filter structure, the frequency ranges and a number of controlled parameters that affect computational efforts. Using the relationship between bandpass and notch filters, the two presented filters were originally developed for notch filters. This paper also proposes a second-order IIR bandpass filter structure that constrains poles and zeros and can be used as a  minimal parameter adaptive digital second-order filter. The proposed filter has a wider frequency range and more flexibility in the range values of the adaptation parameters

Real-time detection of damages in materials using spectral analysis

Tato práce se zabývá detekcí vlastních frekvencí v materiálech pomocí algoritmů pracujících v reálných čase. To se používá pro detekci poruch. Je popsána fyzika materiálu, problematika diskrétních signálů a jejich spekter a jednotlivé metody pro výpočet spektrálních složek. Tyto metody jsou implementovány do programovacího prostředí matlab. Jsou otestovány pomocí simulačních dat a reálného signálu.This thesis deals with detection of the natural frequencies in the material structures using algorithms working in real-time. It is used for detection of material damage. Is described physic of material, issue of discrete signals and their spectrums and methods for the calculation of the spectral components of the signal. These metods are implemented to Matlab programming environment. Methods are tested with simulated data and real signal.

Multifrequency signal enhancement and estimation using IIR filter bank structures

This thesis deals with the accurate estimation of phase, amplitude and frequency of sinusoids buried in noise. Several algorithms are proposed to determine these parameters. A Constrained Notch Fourier Transform (CNFT) is proposed for estimating the Fourier coefficients of noise corrupted harmonic signals given a priori knowledge of the signal frequencies. The proposed method provides bandwidth controlled bandpass filters in contrast to the conventional Notch Fourier Transform (NFT) [Tadokoro and Abe (1987)] and its equivalent real valued Frequency Sampling (FS) structures which utilise fixed bandwidth bandpass filters. New sliding algorithms have been derived for both the NFT and CNFT for the purpose of estimating the Fourier coefficients of the sinusoidal components. A similar algorithm to the CNFT is also proposed for estimating the coefficients of sinusoids at arbitrary known frequencies. The main feature of the modified CNFT is that it uses a second order IIR bandpass filter whose centre frequency parameter is decoupled from the bandwidth parameter. In these techniques, the bandwidth control aspect provides the user with an efficient means of achieving the required resolution as well as reducing spectral leakage. In general, the proposed approach leads to considerable reduction in terms of acquisition time and memory storage. The sliding CNFT algorithm is extended to the Generalised Frequency Sampling (GFS) filter bank whose parametisation is derived based on the Least Means Square (LMS) spectrum analyser. The GFS filter bank possesses the desired characteristics that its resonant frequencies and nulls are arbitrarily set. This feature is used to effectively reduce the leakage problem. The use of GFS filter bank together with the CNFT algorithm provides faster acquisition time when compared with the conventional FS filter bank. Further, it is computationally more efficient than the direct use of the LMS spectrum analyser. The merits and demerits of the conventional Goertzel algorithm are evaluated when it is applied for the task of estimating sinusoidal parameters. A sliding Goertzel algorithm is then developed based on parallel second order digital resonators that are tuned at the input spectral lines. This approach exhibits good performance in low Signal to Noise Ratio (SNR) as verified by extensive simulation tests. Further, unlike the modified and conventional Goertzel algorithms which require a complete signal period to accurately compute the phase and amplitude of the input sinusoids, it computes Fourier coefficients in less than one signal period. The conventional FS structure was modified to obtain a new modular IIR FS filter bank with reduced spectral overlap as well as minimal spectral hole between adjacent bandpass filters. The IIR FS structure together with the self-orthogonalising LMS algorithm is employed for Adaptive Line Enhancer (ALE) applications. The proposed method provides faster convergence than the conventional adaptive FS methods. The Performance characteristics such as the minimum Mean-Squared-Error (MSE), steady-state excess MSE and convergence conditions of the adaptive FS filter bank is analysed. A performance comparison of three adaptive techniques (the ITR FS structure, conventional FS structure and the Tapped Delay Line (TDL)) is carried out to establish the merits of each algorithm. Finally, the conventional IIR Parallel Adaptive Line Enhancer (PALE) which is comprised of a parallel second order IIR bandpass filter is modified such that the convergence to local minima or saddle points is avoided. Error surface analysis is carried out to establish the convergence behaviour of the proposed technique. It is shown that the convergence speed of the proposed structure is the same as the serial configuration. However, it provides superior performance in terms of reduced distortion in amplitude and phase associated with each of the enhanced sinusoids