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General discussion

The space domain

In Part 1 of this series, I extended the concept of the Fourier transform from the time domain into the space domain. I pointed out that while the time domainis one-dimensional, the space domain is thee-dimensional. However, in order to keep the complexity of this module in check, we will assume that space is onlytwo-dimensional. This will serve us well later for such tasks as image processing.

(Three-dimensional Fourier transforms are beyond the scope of this module. I will write a module on using Fourier transforms inthree-dimensional space later if I have the time.)

A purely real space domain

Although the space domain can be (and often is) complex, many interesting problems, (such as photographic image processing) can be dealt with under the assumption that the space domain is purely real. We willmake that assumption in this module. This assumption will allow us to simplify our computations when performing the 2D Fourier transform to transform our datafrom the space domain into the wavenumber domain.

Preview

I will present and explain two complete Java programs in this module. The first program is a single class named ImgMod30 , which provides the capability to perform forward and inverse Fourier transforms onthree-dimensional surfaces. In addition, the class provides a method that can be used to reformat the wavenumber spectrum to make it more suitable for display.

The second program is named ImgMod31 . This is an executable program whose purpose is to exercise and to test the ImgMod30 class using several examples for which the results should already be known.

Sample programs

The class named ImgMod30

This class provides 2D Fourier transform capability that can be used for image processing and other purposes. The class provides three static methods:

  • xform2D : Performs a forward 2D Fourier transform on a purely real surface described by a 2D array of double values in the space domain to produce a complex spectrum in the wavenumberdomain. The method returns the real part, the imaginary part, and the amplitude spectrum, each in its own 2D array of double values.
  • inverseXform2D : Performs an inverse 2D Fourier transform from the complex wavenumber domain into the real space domainusing the real and imaginary parts of the wavenumber spectrum as input. Returns the surface in the space domain as a 2D array of double values. Assumes that the real and imaginary parts in the wavenumber domainare consistent with a purely real surface in the space domain, and does not return an imaginary surface for the space domain
  • shiftOrigin : The wavenumber spectrum produced by xform2D has its origin in the top-left corner with the Nyquist folding wave numbers near the center. This is not a very suitableformat for visual analysis. This method rearranges the data to place the origin at the center with the Nyquist folding wave numbers along the edges.

The class was tested using JDK 1.8 and Windows 7. The class uses the static import capability that was introduced in J2SE 5.0. Therefore, it should notcompile using earlier versions of the compiler.

Questions & Answers

Discuss the differences between taste and flavor, including how other sensory inputs contribute to our  perception of flavor.
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While taste primarily relies on our taste buds, flavor involves a complex interplay between taste and aroma
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omeprazole
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Not really sure
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to drain extracellular fluid all over the body.
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The lymphatic system plays several crucial roles in the human body, functioning as a key component of the immune system and contributing to the maintenance of fluid balance. Its main functions include: 1. Immune Response: The lymphatic system produces and transports lymphocytes, which are a type of
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Anatomy is the identification and description of the structures of living things
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Anatomy is the study of the structure of the body, while physiology is the study of the function of the body. Anatomy looks at the body's organs and systems, while physiology looks at how those organs and systems work together to keep the body functioning.
AI-Robot
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Enzymes are proteins that help speed up chemical reactions in our bodies. Enzymes are essential for digestion, liver function and much more. Too much or too little of a certain enzyme can cause health problems
Kamara
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it is because of the enzyme that the stomach produce that help the stomach from the damaging effect of HCL
Kamara
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Ali Reply
function of digestive
Ali
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37 degrees selcius
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37°c
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36.5
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37°c
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the normal temperature is 37°c or 98.6 °Fahrenheit is important for maintaining the homeostasis in the body the body regular this temperature through the process called thermoregulation which involves brain skin muscle and other organ working together to maintain stable internal temperature
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anaemia is the decrease in RBC count hemoglobin count and PVC count
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Organ Systems Of The Human Body (Continued) Organ Systems Of The Human Body (Continued)
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Source:  OpenStax, Digital signal processing - dsp. OpenStax CNX. Jan 06, 2016 Download for free at https://legacy.cnx.org/content/col11642/1.38
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