MATLAB Function for Signal Analysis Using Choi-Williams Distribution

The Choi-Williams distribution is a widely used signal processing method for time-frequency analysis that effectively suppresses cross-term interference, making it particularly valuable for non-stationary signal analysis. The MATLAB implementation typically involves several critical steps: First, constructing the kernel function matrix forms the core of the Choi-Williams distribution. The kernel utilizes an exponential decay formulation that effectively suppresses cross-terms. In code implementation, this typically involves creating a 2D kernel matrix using exponential functions with parameters controlling the cross-term suppression strength. Next, a two-dimensional Fourier transform is performed to convert the time-domain signal into a joint time-frequency representation. The implementation requires careful selection of window functions, where appropriate window length significantly impacts time-frequency resolution trade-offs. MATLAB's fft2 function is commonly used for this transformation step. During MATLAB implementation, the function must handle complex signal inputs and outputs a time-frequency distribution matrix. The function typically includes optional input parameters for signal preprocessing and kernel function parameter configuration. These parameters might include sigma values for kernel control, window types (Hamming, Hanning, etc.), and window lengths. For visualization, MATLAB's imagesc or surf functions are typically employed to display the time-frequency distribution plots. Additional plotting parameters may include colormap selection, axis labeling, and dB scaling for better visual representation. In practical applications, the Choi-Williams distribution is particularly suitable for analyzing signals with rapidly changing frequency components over time, such as radar signals and speech signals. Compared to traditional Short-Time Fourier Transform (STFT), it provides superior time-frequency concentration and better resolution characteristics for certain signal types.