FREQUENCY DOMAIN.pptx - FREQUENCY DOMAIN • Frequency domain analysis • In spatial domain signals are analyzed with respect to time • In frequency


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FREQUENCY DOMAIN Frequency domain analysis In spatial domain signals are analyzed with respect to time. In frequency domain, signals are analyzed with respect to frequency. In spatial domain, images are dealt with as is. The value of the pixels of the image change with respect to scene. Frequency domain, deals with the rate at which the pixel values are changing in spatial domain. 10/22/2019 1
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Spatial domain In simple spatial domain, we directly deal with the image matrix. 10/22/2019 2
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Frequency Domain First, transform the image to its frequency distribution. Then the black box system perform whatever processing it has to, and the output of the black box, an image, is a transformation. After performing inverse transformation, it is converted into an image which is then viewed in spatial domain. 10/22/2019 3
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Transformation A signal can be converted from time domain into frequency domain using mathematical operators called transforms which include. Fourier Series Fourier transformation Laplace transform Z transform 10/22/2019 4
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Frequency components Any image in spatial domain can be represented in a frequency domain. Frequency components can be divided into two major components. High frequency components High frequency components correspond to edges in an image (High contrast/conspicuous). Low frequency components Low frequency components in an image correspond to smooth regions (Low contrast/Blurred). 10/22/2019 5
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Fourier Series and Transform Fourier series and Fourier transform are used to convert a signal to frequency domain. Fourier Fourier was a mathematician in 1822. He gave Fourier series and Fourier transform to convert a signal into frequency domain. Fourier Series Fourier series simply states that, periodic signals can be represented into sum of sines and cosines when multiplied with a certain weight. It further states that periodic signals can be broken down into further signals with the following properties. The signals are sines and cosines The signals are harmonics of each other 10/22/2019 6
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Pictorially In this signal, the last signal is actually the sum of all the above signals. This was the idea of the Fourier. Computing Fourier Series To process an image in frequency domain, get its frequency distribution, transform it, and take inverse of the output to convert it back into spatial domain.
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