The document discusses Fourier transforms and their applications in geomatics engineering. It begins with an introduction to Fourier transforms, explaining that they decompose signals into constituent frequencies. It then provides examples of Fourier transform applications in geomatics like detecting landscape changes over time using remote sensing, processing seismic reflection data to map underground rock layers in oil and gas exploration, and identifying earthquake damage areas in satellite images. The summary concludes that Fourier transforms are a useful mathematical tool that allow viewing data in the frequency domain, with many applications for processing geographic and spatial information.

2. Presented By:Ramesh Adhikari,Sachin Dhami,Sachit baral,Sagar
Adhikari,Sagar Raj Giri, Sandeep Kadel
FOURIER TRANSFORMATION & ITS APPLICATION IN
GEOMATICS ENGINEERING

3. Introduction
● Fourier Transform is the extension of Fourier Series
represented by the periodic phenomena to the non-periodic
phenomena.
● Fourier Transform is a mathematical operation that
decomposes a signal into its constituent frequencies.
● Thus the Fourier Transform of a musical chord is a
mathematical representation of the amplitudes of the individual
nodes that make it up.

4. History
● Named in honour of Jean-Baptiste Joseph Fourier.
● Preliminary investigation were made by Leonhard
Euler,Jean le Rond d’Alembert and Daniel Bernoulli.
● Fourier introduced the series for purpose of solving the
heat equation in a metal plate publishing his initial result
in 1807.
● The 1st announcement of this great discovery was made
in 1807 by Fourier.

5. What is Fourier Transform?
● Fourier Transform is a mathematical transformation
employed to transform signals between time(or spatial)
domain and frequency domain.
● It is a tool that breaks a waveform (a function or signal)
into an alternate representation, character by sine and
cosine .
● It shows that any waveforms can be re written as the
weighted sum of sinusoidal function.
to be contd….

7. PROPERTIES
● The Fourier transform of F(u) of a single variable,continuous function,f(x)
● The fourier transform of F(u,v) of a double variable,continuous function,f(x,y)

8. Geomatics
● Geomatics is defined as the "discipline concerned with the
collection, distribution, storage, analysis, processing,
presentation of geographic data or geographic information".
● Under another definition it "consists of products, services and
tools involved in the collection, integration and management of
geographic data.
● It includes geomatics engineering(and surveying
engineering) and is related to geospatial science (also
geospatial engineering and geospatial technology).

9. ● Geomatics Engineering, Geomatic Engineering,
Geospatial Engineering is a rapidly developing engineering
discipline that focuses on spatial information (i.e. information
that has a location).
● It includes discipline incorporating fields such as surveying,
geographic information systems, hydrography and
cartography.
● It is concerned with the measurement, management, analysis
and display of spatial information describing the Earth, its
physical features and the built environment.

10. Application of Fourier Transform in
Geomatics engineering
● Fourier transform is used for detecting multitemporal
landscape fragmentation by remote sensing.
Remote sensing is a useful tool for detecting landscape
fragmentation, typically by creating land use maps from remotely
sensed images acquired at different dates.
● Fourier Transform is used in image processing.

12. To Get an Original Satellite Image without Applying the SRM
or 180 Degree Rotation.
At first, take the real part or logarithm of the Fourier transform of
the image function for getting the magnitude of the image and then
take the imaginary part of Fourier transform of the image function
for getting the phase of the image. After getting the phase of the
image, take the inverse function of the same and then only we will
get the original satellite image. It will be possible to get everything
all together when we will compile these applications together in a
computer programing by the representation of software.

14. ❑ The majorexplorationtoolusedbythe oilandgasindustryfor
locatingnewhydrocarbonreservesisthe seismicreflectionmethod.
This techniqueenablessubsurfacesedimentaryrock layersto be
mapped,frommeasurementsof the amplitudeandreflectiontimesof
eventsobtainedbythe reflectionof seismic(sound)wavesfromthe
layers.
FIG: Seismicreflection method

15. The datarecordedat the receiversundergoesextensiveDSPto
produceaseismicsectionwhichisarepresentationofacrosssectionof
the Earth. This isthen interpreted in terms of what the research/data
waslookingfor. The Fast Fouriertransformisusedto convertthe
signalinto the Frequencydomain,whereconvolutionbetweentwo
signalsisobtainedsimplymultiplyingthemtogether. Onceagainthe
FourierTransformisusedasatoolinDigitalSignalProcessingto
performother operations, rather thanproducinganend resultitself.

16. ★ Identification of Earthquake Induced Damage Areas Using
Fourier Transform and SPOT HRVIR(high resolution visible
infrared) Pan Images.
The aim of this study is to propose a new approach to automatically identify
earthquake induced damage areas which can provide valuable information to support
emergency response and recovery assessment procedures.
Five steps were employed to conduct the research and these are: (i) geometric and
radiometric correction of satellite images, (ii) Fast Fourier Transform (FFT) of pre-
and post-earthquake images and filtering the images in frequency domain, (iii)
generating difference image using Inverse Fast Fourier Transform (IFFT) pre- and
post- earthquake images, (iv) application of level slicing to difference image to
identify the earthquake-induced damages, (v) accuracy assessment of the method
using ground truth obtained from a 1/5,000 scale damage map. The total accuracy
obtained in the research is 80.19 %.

17. CONCLUSION
● What is the purpose of education if it cannot be used in
the real life.
● the geomatics engineer can be involved in an extremely
wide variety of information gathering activities and
applications.
● We found the FT to be a great example of why math-
anxiety is such a pity - far from making life complicated,
so very often, math makes this much much simpler!

18. ● A Fourier Transform does not create or destroy any
information. It just lets you look at exactly the same data
in another light, as it were.
● Identification of Earthquake Induced Damage Areas
● the oilandgasindustryfor locatingnewhydrocarbonreserves
isthe seismicreflection method
● for detecting multitemporal landscape fragmentation by
remote sensing.

19. THANK YOU…..
Every one for your time.
Have a good day.
Reference:
Wikipidea
Quora.com
Slideshare.net