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Theory and application of the momentary fourier transform Albrecht, Sandor
Abstract
The discrete Fourier transform (DFT) is a widely used tool in signal or image processing and its efficiency is important. There are applications where it is desirable to use relatively small, successive, overlapped DFTs to obtain the spectrum coefficients. The momentary Fourier transform (MFT) computes the DFT of a discrete-time sequence for every new sample in an efficient recursive form. In this thesis we give an alternate derivation of the MFT using the momentary matrix transform (MMT). Recursive and non-recursive forms of the inverse MFT are also given, which can provide efficient frequency domain manipulation (e.g. filtering). Discussion on the properties and examples of the usage of the MFT is given, followed by a survey on its efficiency. In this work we investigate the applicability of the MFT to synthetic aperture radar (SAR) signal processing, and in particular show what advantages the MFT algorithm offers to the SPECtral ANalysis (SPECAN) method and burst-mode data processing. In the SPECAN algorithm, the received signals are multiplied in the time domain by a reference function, and overlapped short length DFT’s are used to compress the data. The azimuth FM rate of the signal varies in each range cell, which leads to the issue of keeping the azimuth resolution and output sampling rate constant. After the introduction to SPECAN, we show what advantages and disadvantages the MFT has compared to the FFT algorithms. When a SAR system is operated in burst-mode, its azimuth received signal has a segmented frequency-time energy in its Doppler history. It requires that IDFTs be located at specific points in the spectral domain to perform the azimuth signal compression. After the introduction of the burst-mode data properties, we show why the short IFFT (SIFFT) algorithm has the requirement of arbitrary-length, highly-overlapped IDFTs to process burst-mode data, in which case the IMFT is shown to have computational advantages.
Item Metadata
Title |
Theory and application of the momentary fourier transform
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
1998
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Description |
The discrete Fourier transform (DFT) is a widely used tool in signal or image processing
and its efficiency is important. There are applications where it is desirable to use
relatively small, successive, overlapped DFTs to obtain the spectrum coefficients. The
momentary Fourier transform (MFT) computes the DFT of a discrete-time sequence for
every new sample in an efficient recursive form. In this thesis we give an alternate
derivation of the MFT using the momentary matrix transform (MMT). Recursive and
non-recursive forms of the inverse MFT are also given, which can provide efficient
frequency domain manipulation (e.g. filtering). Discussion on the properties and
examples of the usage of the MFT is given, followed by a survey on its efficiency.
In this work we investigate the applicability of the MFT to synthetic aperture radar (SAR)
signal processing, and in particular show what advantages the MFT algorithm offers to
the SPECtral ANalysis (SPECAN) method and burst-mode data processing. In the
SPECAN algorithm, the received signals are multiplied in the time domain by a reference
function, and overlapped short length DFT’s are used to compress the data. The azimuth
FM rate of the signal varies in each range cell, which leads to the issue of keeping the
azimuth resolution and output sampling rate constant. After the introduction to SPECAN,
we show what advantages and disadvantages the MFT has compared to the FFT
algorithms.
When a SAR system is operated in burst-mode, its azimuth received signal has a
segmented frequency-time energy in its Doppler history. It requires that IDFTs be located
at specific points in the spectral domain to perform the azimuth signal compression. After
the introduction of the burst-mode data properties, we show why the short IFFT (SIFFT)
algorithm has the requirement of arbitrary-length, highly-overlapped IDFTs to process
burst-mode data, in which case the IMFT is shown to have computational advantages.
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Extent |
7932083 bytes
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Genre | |
Type | |
File Format |
application/pdf
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Language |
eng
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Date Available |
2009-05-25
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Provider |
Vancouver : University of British Columbia Library
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Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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DOI |
10.14288/1.0065213
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
1998-11
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.