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Lecture 14 The frequency Domain (2) Dr. Masri Ayob

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2 Convolution Convolution can be performed in the frequency domain by simple multiplication! The following relationship indicates the power of the Fourier Transform.

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3 Convolution It is possible and very common to filter in the frequency domain. Convolving two functions in the spatial domain is the same as multiplying their spectra in the frequency domain. The process of filtering in the frequency domain is quite simple: Transform image data to the frequency domain via the FFT Multiply the image's spectrum with some filtering mask Transform the spectrum back to the spatial domain (Figure 9.12)

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4 Convolution

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5 Convolution Common Filters

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6 Convolution Low pass filters attenuate the high frequencies and pass lower frequencies. High pass filters attenuate the low frequencies and pass higher frequencies. Band : the frequency spectrum between two defined limits Band pass filters passes a specific range of f, whilst suppressing others. A filter that ideally passes all frequencies between two non-zero finite limits and bars all frequencies not within the limits The objective of the circuit is to eliminate the frequencies which are unwanted. Therefore, the amplification or gain of these frequencies must be reduced.

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7 Convolution Band stop (band reject) filters suppressing only a specific band of frequencies. A filter that suppressing, usually to very low levels, all frequencies between two non-zero, finite limits and passes all frequencies not within the limits. A band-stop filter may be designed to stop the specified band of frequencies but usually only attenuates them below some specified level The bandpass and bandstop filters can be created by proper subtraction and addition of the frequency responses of the low pass and high pass filter.

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8 Tips for Exam RGB colour model Grey level enhancement-mapping, histogram etc. Basic image manipulation –file, printing greyscale images, etc. Digital Images-sampling, neighbours of pixel etc. Neighbourhood operations – filters, edge etc. Fourier transform.

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9 GOOD LUCK IN YOUR EXAM

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Coherence spectrum (coherency squared) = 0.1, 0.05, 0.01 X is the Fourier Transform Cross-spectral power density Confidence level: = running mean or.

Coherence spectrum (coherency squared) = 0.1, 0.05, 0.01 X is the Fourier Transform Cross-spectral power density Confidence level: = running mean or.

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