High-Resolution Spectrograms

We present a two-step method for computing the High-Resolution Spectrogram (HRS) of nonstationary signals. In the first step, a Weighted Short-Term Fourier Transform decomposes the signal using a bank of symmetric, tapered convolution operators, and the Hilbert transform extends each resulting component to its analytic form. In the second step, a single partial fraction decomposition is applied, corresponding to a first-order prediction error operator whose single pole is the first-order Burg reflection coefficient. A maximum-entropy autoregressive estimator then gives the instantaneous frequency of each locally monochromatic component within a sliding time window. The energy of each component is reassigned along the frequency axis to the pole location, producing sharply focused energy tracks and substantially improved time-frequency resolution. Summing all reassigned components reconstructs the original signal, which confirms invertibility and enables signal separation, denoising, and feature extraction. A systematic sensitivity analysis characterizes the method's valid operating range and parameter trade-offs, and quantitative evaluations show its robustness to white, colored, and impulsive noise across multiple SNR levels. Benchmarks against established high-resolution tools show competitive performance. The method is validated on synthetic signals, including a crossing chirp and a multi-component signal with stationary, frequency-modulated, swept, and impulsive constituents. It is then applied to a marine seismic trace and to the GW150914 gravitational wave signal recorded by the LIGO Hanford detector, demonstrating its effectiveness across a broad range of signal types and application domains.