Implementing F-K Transform with Enhanced Functionality

The F-K transform is a powerful signal processing technique primarily used for converting time-space domain data into frequency-wavenumber domain, widely applied in seismic wave analysis, image processing, and other fields. Its core principle involves using two-dimensional Fourier transform to convert signals from time-space domain to frequency-wavenumber domain, enabling more efficient filtering and feature extraction. In code implementation, this typically requires applying 2D FFT (Fast Fourier Transform) algorithms to the input matrix, where one dimension represents time samples and the other represents spatial positions.

In F-K transformation, both temporal and spatial signals are simultaneously decomposed into different frequency and wavenumber components. This allows easy identification and separation of wavefield components with specific directions or velocities. For example, in seismic data processing, F-K transform can be implemented using MATLAB's fft2 function to suppress noise, enhance valid signals, or separate different types of seismic waves (such as surface waves and body waves). The algorithm typically involves calculating the 2D Fourier spectrum and applying mask filters in the frequency-wavenumber domain.

Compared to traditional one-dimensional Fourier transform, the advantage of F-K transform lies in its ability to simultaneously analyze both temporal and spatial characteristics of signals, enabling more precise directional filtering. For instance, by setting wavenumber-frequency thresholds in the transformed domain, developers can programmatically filter out interference waves from specific directions, thereby improving signal-to-noise ratio. This can be implemented through conditional statements that zero out Fourier coefficients outside desired wavenumber ranges.

Furthermore, F-K transform has significant applications in radar signal processing, medical image analysis, and other fields. Its powerful filtering capabilities, implemented through selective frequency-wavenumber domain operations, make it an essential tool for multidimensional signal processing. The implementation often includes inverse F-K transform (using ifft2) to convert the filtered data back to original domain after processing.