Abstract:
This work focuses on efficient, joint time-frequency analysis of time series data.
Joint time-frequency analysis is based on the sliding window. There are two major
contributions of this thesis.
Firstly, we haveThis work focuses on efficient, joint time-frequency analysis of time series data.
Joint time-frequency analysis is based on the sliding window. There are two major
contributions of this thesis.
Firstly, we have introduced a notion of “aggregate spectrogram (AS)” which
is a unimodal distribution at each time instant. The AS is extremely useful and
computationally efficient when we are interested in a few spectral features and not
the entire spectrum. Properties/characteristics of the AS have been listed. A para-
metric method, based on a second order autoregressive model of the signal, for the
construction of the AS, has been described. Of all the existing spectral estimation
tools, the AS has the least computational complexity. Based on the AS, instan-
taneous frequency estimation for multicomponent signals with equal amplitudes
has been achieved. The AS does not require Goertzel filters in dual tone multi
frequency detection applications. The AS finds many potential application. A few
examples are voice activity detection, edge detection, motion vector estimation
etc.
Secondly, the problem of estimating the instantaneous frequency and band-
width for multicomponent signals with time varying amplitudes has been solved
by employing a new peak detection algorithm. The algorithm has been shown to
outperform existing algorithms when the frequencies and amplitudes of the multi-
component noisy signals are time-varying.
Other contributions of the thesis include: low computational cost algorithms for
the sliding discrete Fourier transform, and algorithms for its extension to spectral
interpolation through zero padding and window padding. A low cost, optimized
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split-radix FFT architecture for zero-padded signals is also proposed.
The Wiener-Khintchine theorem (WKT) yields better spectral estimates of
Gaussian signals as compared to the discrete Fourier transform (DFT). Higher
order spectra find utility in case of additive colored noise or the signals are non-
Gaussian. Due to high computational complexities, the WKT and higher order
spectra are avoided in the sliding window based spectral analysis. We have devel-
oped recursive forms of the WKT, bispectrum and trispectrum whose computa-
tional complexities have reduced to linear, quadratic and cubic orders, respectively
introduced a notion of “aggregate spectrogram (AS)” which
is a unimodal distribution at each time instant. The AS is extremely useful and
computationally efficient when we are interested in a few spectral features and not
the entire spectrum. Properties/characteristics of the AS have been listed. A para-
metric method, based on a second order autoregressive model of the signal, for the
construction of the AS, has been described. Of all the existing spectral estimation
tools, the AS has the least computational complexity. Based on the AS, instan-
taneous frequency estimation for multicomponent signals with equal amplitudes
has been achieved. The AS does not require Goertzel filters in dual tone multi
frequency detection applications. The AS finds many potential application. A few
examples are voice activity detection, edge detection, motion vector estimation
etc.
Secondly, the problem of estimating the instantaneous frequency and band-
width for multicomponent signals with time varying amplitudes has been solved
by employing a new peak detection algorithm. The algorithm has been shown to
outperform existing algorithms when the frequencies and amplitudes of the multi-
component noisy signals are time-varying.
Other contributions of the thesis include: low computational cost algorithms for
the sliding discrete Fourier transform, and algorithms for its extension to spectral
interpolation through zero padding and window padding. A low cost, optimized
split-radix FFT architecture for zero-padded signals is also proposed.
The Wiener-Khintchine theorem (WKT) yields better spectral estimates of
Gaussian signals as compared to the discrete Fourier transform (DFT). Higher
order spectra find utility in case of additive colored noise or the signals are non-
Gaussian. Due to high computational complexities, the WKT and higher order
spectra are avoided in the sliding window based spectral analysis. We have devel-
oped recursive forms of the WKT, bispectrum and trispectrum whose computa-
tional complexities have reduced to linear, quadratic and cubic orders, respectively