Lecture 03: Frequency Domain & Transforms

These flashcards cover key concepts related to frequency domain analysis and transforms as discussed in Lecture 03 of the Image Processing and Computer Vision course at the University of Bristol.

Frequency

The number of cycles per second of a signal, measured in Hertz (Hz).

Amplitude

The peak value of a signal, representing the strength of the signal.

Phase

The shift in degrees of a signal, indicating the position of the wave in time.

Fourier Coefficients

Coefficients (an and bn) that represent the amplitudes of the sines and cosines in Fourier analysis.

Basis Functions

The sine and cosine functions used as building blocks in Fourier analysis.

Inverse Fourier Transform

A mathematical operation that converts data from the frequency domain back to the spatial domain.

Magnitude Spectrum

A representation of signal strength across different frequencies.

Phase Spectrum

A representation of the phase information of each frequency component in a signal.

Separability

A property of the Fourier Transform allowing it to be computed as two successive 1D transforms.

Convolution Theorem

States that convolution in the spatial domain corresponds to multiplication in the frequency domain.

Low Pass Filter

A filter that allows low frequency signals to pass through while attenuating higher frequency signals.

High Pass Filter

A filter that allows high frequency signals to pass through while attenuating lower frequency signals.

Butterworth Filter

A type of filter designed to have a frequency response that is as flat as possible in the passband.

2D Fourier Transform

A mathematical transformation applied to functions of two variables, resulting in a function of two frequency variables.

Discrete Fourier Transform (DFT)

A method for transforming discrete signals from the time domain to the frequency domain.

Euler’s Formula

A mathematical equation that connects complex exponentials to trigonometric functions: e^(iθ) = cos(θ) + i sin(θ).

Intensity Change

The variation of brightness in an image, often associated with frequency changes in the image.