Ewa Hermanowicz

WLS design of variable frequency response FIR filters

This paper extends the Weighted Least Squares method to designing FIR filters capable of changing, in the real-time, one of their frequency response characteristics (group delay, the width of the passband, resonance frequency or any other). The filter coefficients are polynomial functions of the parameter characterising the variable feature. The computations needed in such designs can be kept at low level if the weight function in the performance criterion is separable. The advantages of the proposed approach are illustrated by a design of a Fractional Sample Delay filter with variable delay. If this filter has to meet demanding specifications then the proposed approach provides a cheaper and more effective solution than traditional approaches based on Lagrange interpolation.

A WISE method for designing IIR filters

The problem of designing optimal digital IIR filters with frequency responses approximating arbitrarily chosen complex functions is considered. The real-valued coefficients of the filters transfer function are obtained by numerical minimization of carefully formulated cost, which is referred here to as the weighted integral of the squared error (WISE) criterion. The WISE criterion linearly combines the WLS criterion that is used in the weighted least squares approach toward filter design and some time-domain components. The WLS part of WISE enforces the quality of the frequency response of the designed filter, while the time-domain part of the WISE criterion restricts the positions of the filters poles to the interior of an origin-centred circle with arbitrary radius. This allows one not only to achieve stability of the filter but also to maintain some safety margins. A great advantage of the proposed approach is that it does not impose any constraints on the optimization problem and the optimal filter can be sought using off-the-shelf optimization procedures. The power of the proposed approach is illustrated with filter design examples that compare favorably with results published in research literature.

Special discrete-time filters having fractional delay

Abstract A novel family of special discrete-time filters having fractional delay is proposed, where a fractional-sample delay (FSD) filter serves as a versatile building block from which all other special filters of the family are derived. The specific feature of these filters is that the fractional delay is a parameter which can be varied. An illustrative example shows the performance of a specimen filter whose coefficients are obtained from the impulse response of an FIR FSD filter using polynomial approximation. The application of this filter to simultaneous instantaneous frequency estimation and fractional delay of a complex FM signal is also presented.

On an instantaneous frequency estimator with FIR filters having maximally flat frequency response error magnitude

Abstract In this paper an instantaneous frequency estimator (IFE) of a discrete-time base band complex signal is considered. The IFE is built around one-band, maximally flat linear-phase FIR filters, which are used for differentiating and delaying Cartesian components of the complex signal. One of the key features of the estimator is that it avoids problems related to the ambiguity of the instantaneous phase waveform. The quality of the estimator is tested. A closed-form formula for the static characteristic of the IFE is derived and expressed as a function of the frequency responses of the filters used. Two representative test signals: a full band complex linear frequency modulated (LFM) chirp and a three-component complex synthetic signal are used to demonstrate the characteristic features of the estimator. If the chirp is sufficiently long in comparison with the length of the filters, the instantaneous frequency (IF) estimation errors are comparable to those obtained by using the static characteristic. For this case, the IF estimation error plots for the practical versus ideal IFE are presented and a design chart showing the dependence of the IF estimation error magnitude on the input signal bandwidth and the FIR filters’ length is given. This chart can be exploited in, e.g., FM-telemetry applications, where the IF carries a very slowly changing telemetric message. The three-component signal chosen allows demonstration of the ability of the estimator to track the IF which extends beyond the signal spectral range, permitting measurement even beyond the Nyquist frequency. Finally, the power of the proposed IFE to measure the stability of highly precise frequency oscillators is shown.

Stable IIR filters-a new design approach

The paper proposes a new approach to designing digital, causal, time-invariant IIR filters approximating arbitrary frequency response. The design task is formulated as an optimisation problem where the cost is a nonlinear function of the tuneable coefficients of the filters transfer function. The novelty of the approach lies in the way the stability of the filter is tackled. The cost function comprises a combination of frequency-domain and time-domain components. Frequency-domain components are used to enforce the filter to represent desired complex-valued frequency response, while the time-domain components impose its stability. No equality or nonequality constraints are involved in the optimisation problem related to the proposed method.

The minimum-phase demodulate and its application to autoregressive analysis of bandpass signal

Abstract The subject of our investigation is a minimum-phase demodulate (MPD) as a discrete-time baseband complex-valued representation of a bandpass signal whose instantaneous phase waveform is originally missed. In theoretical preliminaries a system of definitions for bandpass signal complete and incomplete representation is outlined and MPD choice as a supplemented complex-valued signal is argued. Next, MPD properties are specified and MPD as well as optional minimum-phase envelope-based bandpass signal estimators in time and frequency domains are proposed. Later on, MPD is treated as autoregressive process realization whose parameters and maximum entropy spectrum estimated by the use of a batch processing method are considered. Finally, MPD against envelope predictability improvement due to decrease of spectrum flatness measure is reported and visualized by numerical experiments with underwater echo-envelope data.