Windowed Fourier Transform with Gaussian Window

In this implementation, we employ the Windowed Fourier Transform technique with a Gaussian window function. This method transforms time-domain signals into frequency-domain representations, enabling more effective analysis of signal characteristics. The Windowed Fourier Transform technique applies a window function to time-domain signals to reduce spectral leakage and improve frequency analysis accuracy. The Gaussian window function assigns maximum weight to the signal's center while gradually tapering off towards both ends, following a Gaussian distribution pattern. When combined with the Windowed Fourier Transform, this window function enhances signal analysis precision and produces more accurate spectral results. From a coding perspective, implementing this typically involves: 1. Generating a Gaussian window using the formula w(n) = exp(-0.5 * ((n - (N-1)/2) / (σ*(N-1)/2))^2) 2. Applying the window to the input signal using element-wise multiplication 3. Computing the Fourier transform of the windowed signal 4. Key functions often include: signal windowing, FFT computation, and parameter adjustment for the Gaussian window's standard deviation (σ) The Gaussian window's optimal time-frequency resolution makes it particularly suitable for analyzing signals with unknown frequency components, as it provides a balanced compromise between frequency resolution and spectral leakage reduction.