PURE AND APPLIED > FOURIER ANALYSIS
Fourier Transform in Wavelet analysis
In 1807, French mathematician Joseph Fourier (1768-1830) submitted a paper to the Academy of Sciences of Paris where he presented a mathematical description of problems involving heat conduction. On first sight, the paper was rejected for the lack of mathematical rigor. Little did they know the ideas contained in it would develop into an important area of mathematics called Fourier analysis in his honor.
The principle idea in Fourier’s work was that many familiar functions can be expanded in finite series and integrals involving trigonometric functions. This idea is important in modeling many phenomena in physics and engineering, such as computing, medical diagnostic, frequency attenuated filter.
This chapter is dedicated in developing some fundamental ideas in Fourier analysis and its applications, particularly in electrical engineering. I do hope to equip the reader with enough knowledge to tackle the heat conduction problems.
Josiah Willard Gibbs
Fourier Transform
Amplitude and Frequency Spectra
Thermodynamics
Imagine Processing
Fourier Transform in Wavelet analysis
The principle idea in Fourier’s work was that many familiar functions can be expanded in finite series and integrals involving trigonometric functions. This idea is important in modeling many phenomena in physics and engineering, such as computing, medical diagnostic, frequency attenuated filter.
This chapter is dedicated in developing some fundamental ideas in Fourier analysis and its applications, particularly in electrical engineering. I do hope to equip the reader with enough knowledge to tackle the heat conduction problems.
CONCEPT CONTENTS
> DEFINITION OF THE FOURIER SERIES
> FOURIER SERIES OF A 'BROKEN' FUNCTION
> FOURIER SERIES OF A FUNCTION ON [-L, L]
> EXAMPLE OF A FOURIER SERIES ON [-L, L]
> FOURIER SERIES OF ODD AND EVEN FUNCTIONS
> FOURIER SERIES OF x^2 (MAY NOT = f(x))
> RECAP ON PIECEWISE CONTINUOUS FUNCTIONS
> CONVERGENCE THEOREM OF A FOURIER SERIES
> CONVERGENCE OF FOURIER SERIES OF f(x)=2x
> CONVERGENCE OF A 'BROKEN' FUNCTION
> GRAPHS OF VARIOUS FOURIER SERIES
> CONTRASTING POWER AND FOURIER SERIES
> FOURIER COSINE SERIES
> FOURIER SINE SERIES
> HALF RANGE EXPANSION OF f(x)=e^2x
> FOURIER SERIES OF PERIODIC FUNCTIONS
> PHASE ANGLE FORM OF A FUNCTION
Notable Mathematicians
Joseph Fourier Josiah Willard Gibbs
Important Theorems
Fourier Integral Fourier Transform
Amplitude and Frequency Spectra
Applications
Heat Conduction Thermodynamics
Imagine Processing
