Krzysztof Czarnecki

A novel method of local chirp-rate estimation of LFM chirp signals in the time-frequency domain

In the paper, novel dynamic representations of a complex signal in the time-frequency domain are introduced. The proposed approach is based on using the gradient of the short-time Fourier transform complex phase. A channelized instantaneous complex frequency (CICF) and a complex local group delay (CLGD) are included in the presented signal representations. An application of the newly-introduced distributions is demonstrated by a local chirp-rate estimation of linear frequency modulated chirp signals in the time-frequency domain.

A fast time-frequency multi-window analysis using a tuning directional kernel

Abstract In this paper, a novel approach for time-frequency analysis and detection, based on the chirplet transform and dedicated to non-stationary as well as multi-component signals, is presented. Its main purpose is the estimation of spectral energy, instantaneous frequency (IF), spectral delay (SD), and chirp rate (CR) with a high time-frequency resolution (separation ability) achieved by adaptive fitting of the transform kernel. We propose two efficient implementations of this idea, which allow to use the fast Fourier transform (FFT). In the first one, referred to as “self-tuning”, a previously proposed CR estimation is used for a local fitting of the chirplet kernel over time. For this purpose, we use the CR associated with the dominant (prominent) component. In the second one, we define a new measure for evaluating at each time-frequency point, how the used analyzing window is matched to the signal. This measure is defined as the absolute difference between the estimated CR and the CR parameter associated to the used analysis window. Our method is able to produce combined time-frequency distributions of the spectral energy, IF, SD, and CR. They are obtained using several classical chirplet transforms with analysis windows of various CRs. The compositions are made by finding the lowest fitting measure for every time-frequency points over all transforms. Finally, we assess the robustness of the methods by a detection application and time-frequency localization, both in the presence of high additive white Gaussian noise (additive white Gaussian noise (AWGN)) as well as we present many time-frequency (TF) images of synthetic and real-world signals.

An Objective Focussing Measure for Acoustically Obtained Images

In scientific literature many parameters of an image sharpness can be defined, that can be used for the evaluation of display energy concentration (EC). This paper proposes a new, simple approach to EC quantitative evaluation in spectrograms, which are used for the analysis and visualization of sonar signals. The presented approach of the global-image EC measure was developed to the evaluation of EC in arbitrary direction (or at an arbitrary angle) and along an arbitrary path that is contained within the displayed area. The proposed measures were used to establish optimum spectrograph parameters, subject to high EC in images, in particular the type and width of the window. Moreover, the paper defines the marginal EC distributions that can be used in sonar signal detection as a support to the main detector.

Bearing Estimation Using Double Frequency Reassignment for a Linear Passive Array

Abstract The paper demonstrates the use of frequency reassignment for bearing estimation. For this task, signals derived from a linear equispaced passive array are used. The presented method makes use of Fourier transformation based spatial spectrum estimation. It is further developed through the application of two-dimensional reassignment, which leads to obtaining highly concentrated energy distributions in the joint frequency-angle domain and sharp graphical imaging. The introduced method can be used for analysing, a priori, unknown signals of broadband, nonstationary, and/or multicomponent type. For such signals, the direction of arrival is obtained based upon the marginal energy distribution in the angle domain, through searching for arguments of its maxima. In the paper, bearing estimation of three popular types of sonar pulses, including linear and hyperbolic frequency modulated pulses, as well as no frequency modulation at all, is considered. The results of numerical experiments performed in the presence of additive white Gaussian noise are presented and compared to conventional digital sum-delay beamforming performed in the time domain. The root-mean-square error and the peak-to-average power ratio, also known as the crest factor, are introduced in order to estimate, respectively, the accuracy of the methods and the sharpness of the obtained energy distributions in the angle domain.

Estimation of time-frequency complex phase-based speech attributes using narrow band filter banks

In this paper, we present nonlinear estimators of nonstationary and multicomponent signal attributes (parameters, properties) which are instantaneous frequency, spectral (or group) delay, and chirp-rate (also known as instantaneous frequency slope). We estimate all of these distributions in the time-frequency domain using both finite and infinite impulse response (FIR and IIR) narrow band filers for speech analysis. Then, we present few examples including a novel type of imaging joining energy and phase acceleration in a single picture. Finally, we provide an open-source project — ccROJ — Time-Frequency C++ Framework of which we are authors and that is used for computing the presented figures.