AbstructWe consider a multidimensional parameter space formed by inner products of a parameterizable family of chirp functions with a signal under analysis. We propose the use of quadratic chirp functions (which we will call q-chirps for short), giving irise to a parameter space that includes both the time-frequency plane and the time-scale plane as 2-D subspaces. The parameter space contains a...

Weyl-Heisenberg frames are complete signal representations corresponding to rectangular tiling of the time-frequency plane. Extensions of these frames are obtained in the rotated time-frequency planes by using the fractional Fourier transformation. It is shown that rotation does not affect the frame bounds. For some specific angles, lattices in rotated coordinates will map to the lattices in th...

Occam filters are a class of filters for additive random noise, based on the idea that when a lossy data compression algorithm is applied to a noisy signal with the allowed loss set equal to the noise strength, the loss and the noise tend to cancel rather than add. In this paper, we apply non-linear Occam filters to broad-band signals. Using the chirp signal as a specific example, we find that ...

A gravitational wave signal carries information about an astrophysical source, a time varying quantity that has to be analyzed in the time frequency domain. There are varieties of transforms that can be applied to understand the complex evolution time-varying frequencies and chirps. This paper discusses various techniques of transforms that can be applied to various categories of this problem t...

AbstructIt is observed that diffraction is a convolution operation with a chirp kernel whose argument is scaled. F d y of functions obtained from a prototype by shifting and argument sealing form the essential ground for wavelet framework. Therefore, a connection between diffraction and wavelet transform is developed. However, wavelet transform is essentially prescribed for time-frequency and/o...

Acoustic ultrasonic measurements are widespread and commonly use transducers exhibiting resonant behaviour due to the piezoelectric nature of their active elements, being designed to give maximum sensitivity in the bandwidth of interest. We present a characterisation of such transducers that provides both magnitude and phase information describing the way in which the receiver responds to a sur...

The importance of aging electrical wiring and associated faults in aircraft has been highlighted due to the critical effects on the safety of overall systems. Traditional reflectometry methods for the detection and localization of the faults on cable have been achieved in either the time domain or frequency domain only. In this paper, we introduce a new high-performance reflectometry technique ...

Analysis of Chirp Signal with Fractional Fourier Transform POOJA MOHINDRU*, RAJESH KHANNA1 and S S BHATIA2 Department of Electronics and Communication Engineering, University College of Engineering, Punjabi University, Patiala 147 004, Punjab, India 1Department of Electronics & Communication Engineering, Thapar University, Patiala 147 004, Punjab, India 2School of Mathematics, Thapar University...