Electrical and Computer Engineering ETDs


Ishwor Bhatta

Publication Date



As an extension of conventional Fourier transform and a time-frequency signal analysis tool, the fractional Fourier transforms (FRFT) are suitable for dealing with various types of non-stationary signals. Taking advantage of the properties and non-stationary features of linear chirp signals in the Fourier transform domain, several methods of extraction and parameter estimation for chirp signals are proposed, and a comparative study has been done on chirp signal estimation. Computation of the discrete fractional Fourier transform (DFRFT) and its chirp concentration properties are dependent on the basis of DFT eigenvectors used in the computation. Several DFT-eigenvector bases have been proposed for the transform, and there is no common framework for comparing them. In this thesis, we compare several different approaches from a conceptual viewpoint and point out the differences between them. We discuss five different approaches, namely: (1) the bilinear transformation method, (2) the Grunbaum method, (3) the Dickenson-Steiglitz method, also known as the S-matrix method, (4) the quantum mechanics in finite dimension( QMFD) method, and (5) the higher order S-matrix method, to find centered DFT (CDFT) commuting matrices and the various properties of these commuting matrices. We study the nature of eigenvalues and eigenvectors of these commuting matrices to determine whether they resemble those of corresponding continuous Gauss-Hermite operator. We also measure the performance of these five approaches in terms of mailobe-to-sidelobe ratio, 10-dB bandwidth, quality factor, linearity of eigenvalues, parameter estimation error, and, finally peak-to-parameter mapping regions. We compare the five approaches using these several parameters and point out the best approach for chirp signal applications.


Discrete Fractional Fourier Transform, Chirp Parameter Estimation, Parameter Estimation Error

Document Type




Degree Name

Electrical Engineering

Level of Degree


Department Name

Electrical and Computer Engineering

First Committee Member (Chair)

Hayat, Majeed

Second Committee Member

Pereyra, Maria Cristina