Skip to main content

LUP Student Papers

LUND UNIVERSITY LIBRARIES

Signal Detection by Means of Time-Frequency Representations

Harba, Tarek LU (2024) In Master's Theses in Mathematical Sciences FMSM01 20242
Mathematical Statistics
Abstract
Quadratic time-frequency representations are indispensable tools in non-stationary
signal analysis. Thus the incorporation of such tools into signal detection is pre-
dicted to yield more sensitive detectors especially in the context of non-stationary
signal detection. We elucidate the theory of time-frequency representations and
signal detection then implement a time-frequency detector using Wigner-Ville, Ri-
haczek and Page distributions and assess its performance on simulated signals. The
simulated signals used were Gaussian atoms, linear- and hypercube chirps. The
results confirm the superiority of time-frequency detectors regardless of the used
time-frequency distribution.
Popular Abstract
It is usual to fix a machine once it breaks down, but in many situations we cannot
afford having the machine fail us just like you do no want your car breaking down
on your way to a job interview. More often, the stakes are even higher than that,
with expensive factories risking production halts or military equipment not being
ready when it should.
This tool works by merging two mathematical tools together which are signal de-
tectors and time-frequency representations. Signal detectors have been studied and
implemented since the second world-war but the tool used here is from the 1970s,
it simply takes in an input signal measured by a sensor and performs a number of
operations on it to reach a single number, if this number of... (More)
It is usual to fix a machine once it breaks down, but in many situations we cannot
afford having the machine fail us just like you do no want your car breaking down
on your way to a job interview. More often, the stakes are even higher than that,
with expensive factories risking production halts or military equipment not being
ready when it should.
This tool works by merging two mathematical tools together which are signal de-
tectors and time-frequency representations. Signal detectors have been studied and
implemented since the second world-war but the tool used here is from the 1970s,
it simply takes in an input signal measured by a sensor and performs a number of
operations on it to reach a single number, if this number of large enough, it means
a reference signal is being received. Time-frequency representations on the other
hand are tools that allow one to glean sensitive information of a signal like the
spectral content, or frequencies, present in that signal. Knowing what frequencies
are present at each moment in a signal may be crucial as it allows us to not only
classify what is giving off this signal, but also determine whether or not something
unusual is going on.
The reason these two can be merged is that the specific detector we are using is
a quadratic detector, quadratic detectors allow the use of time-frequency repres-
entations through an equation called Moyal’s formula. This means that one can
simply ’plug in’ the time-frequency representation of choice into the quadratic de-
tector. However, only certain time-frequency representations can be used, ones that
do not violate Moyal’s formula.
Since signal detection is relevant in an immense number of applications, you can
expect to see this tool in many places like in radar and sonar since these are receiv-
ers. More specifically, it may enable more sensitive detectors, which possibly means
more detailed ocean floor mapping, submarine detection and even analysis of bird
chirps, and yes, fixing machinery and engines before they break down. (Less)
Please use this url to cite or link to this publication:
author
Harba, Tarek LU
supervisor
organization
course
FMSM01 20242
year
type
H2 - Master's Degree (Two Years)
subject
publication/series
Master's Theses in Mathematical Sciences
report number
LUTFMS-3506-2024
ISSN
1404-6342
other publication id
2024:E73
language
English
id
9177159
date added to LUP
2024-11-01 11:44:53
date last changed
2024-11-13 15:52:08
@misc{9177159,
  abstract     = {{Quadratic time-frequency representations are indispensable tools in non-stationary
signal analysis. Thus the incorporation of such tools into signal detection is pre-
dicted to yield more sensitive detectors especially in the context of non-stationary
signal detection. We elucidate the theory of time-frequency representations and
signal detection then implement a time-frequency detector using Wigner-Ville, Ri-
haczek and Page distributions and assess its performance on simulated signals. The
simulated signals used were Gaussian atoms, linear- and hypercube chirps. The
results confirm the superiority of time-frequency detectors regardless of the used
time-frequency distribution.}},
  author       = {{Harba, Tarek}},
  issn         = {{1404-6342}},
  language     = {{eng}},
  note         = {{Student Paper}},
  series       = {{Master's Theses in Mathematical Sciences}},
  title        = {{Signal Detection by Means of Time-Frequency Representations}},
  year         = {{2024}},
}