06_ftx - Fourier Transform COMP344 COMP344 Fourier...

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Fourier Transform COMP344 COMP344 Fourier Transform
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What is Frequency Domain Analysis? analyze the image in the frequency domain involves interpreting the frequency spectrum COMP344 Fourier Transform
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Example: Signal Corrupted by Noise Question What is the signal? COMP344 Fourier Transform
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Complex Number z = x + y i i = - 1: imaginary unit (later on, we use j ) x = Re { z } : real part y = Im { z } : imaginary part Basic operations: ( a + bi ) + ( c + di ) = ( a + c ) + ( b + d ) i ( a + bi ) · ( c + di ) = ( ac - bd ) + ( bc + ad ) i Complex conjugate of the complex number z = a + bi a - bi , written as z * z * is the reflection of z about the real axis COMP344 Fourier Transform
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Euler’s Formula For any real number x , e ix = cos( x ) + i sin( x ) e : base of the natural logarithm Polar coordinates z = x + iy can be written as | z | (cos φ + i sin φ ) = | z | e i φ | z | = p x 2 + y 2 : magnitude of z φ : argument / phase of z COMP344 Fourier Transform
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Named after Joseph Fourier has many scientific applications: image processing , signal
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06_ftx - Fourier Transform COMP344 COMP344 Fourier...

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