4.Filtering in the Frequency Domain

Frequency Domain

A representation of an image where changes in image position correspond to changes in spatial frequency.

Spatial Domain

The "normal" image space where changes in pixel positions correspond to changes in the scene.

Pixels

The individual points of color that make up an image.

Fourier Transform

A mathematical transformation that converts a signal from the spatial domain to the frequency domain.

Fourier Series

Any function that periodically repeats itself can be expressed as a sum of sines and cosines of different frequencies.

Fourier Transform Pair

The pair of equations that define the Fourier transform and its inverse.

Discrete Fourier Transform (DFT)

The Fourier transform applied to discrete functions, such as images.

Inverse DFT

The reverse transformation of the Fourier transform, used to obtain the original signal from its frequency representation.

Image Filtering

The process of modifying an image by applying a filter to enhance or remove certain features.

Spectrum

The representation of the component frequencies of an image in the frequency domain.

DFT

Discrete Fourier Transform, a mathematical transformation used to convert a signal from the time domain to the frequency domain.

Image Processing

The manipulation and analysis of digital images using various algorithms and techniques.

Frequency Domain

A representation of a signal or image in terms of its frequency components.

Filter Function

A mathematical function used to modify or extract specific frequency components from a signal or image.

Inverse DFT

Inverse Discrete Fourier Transform, the process of converting a signal from the frequency domain back to the time domain.

Frequency Domain Filters

Filters used to modify the frequency components of an image, such as low pass, high pass, and band pass filters.

Low Pass Filter

A filter that allows low frequency components to pass through while attenuating high frequency components.

High Pass Filter

A filter that allows high frequency components to pass through while attenuating low frequency components.

Band Pass Filter

A filter that allows a specific range of frequencies to pass through while attenuating frequencies outside that range.

Ideal Low Pass Filter

A low pass filter that completely removes high frequency components beyond a specified distance from the origin of the frequency domain.

Butterworth Lowpass Filter

A low pass filter with a smooth roll-off and adjustable cutoff frequency.

Gaussian Lowpass Filter

A low pass filter that uses a Gaussian function to attenuate high frequency components.

Sharpening

The process of enhancing the edges and fine details in an image.

High Pass Frequencies

The frequency components that are retained by a high pass filter, which are the reverse of the frequencies attenuated by a low pass filter.

Ideal High Pass Filter

A high pass filter that completely removes low frequency components within a specified distance from the origin of the frequency domain.

Butterworth High Pass Filter

A high pass filter with a smooth roll-off and adjustable cutoff frequency.

Gaussian High Pass Filter

A high pass filter that uses a Gaussian function to attenuate low frequency components.

Bandpass Filter

A filter that allows a specific range of frequencies to pass through while attenuating frequencies outside that range.