Time-Frequency Processing

The idea of dynamic spectral processing, introduced at the end of the previous chapter is fully developed here. The principle of sub-band analysis and synthesis is shown as the basis for a time-varying frequency-domain approach. The short-time Fourier transform (STFT) is introduced as a sequence of time-ordered DFT frames from which amplitude and phase data can be obtained. Different methods for instantaneous frequency estimation are discussed. A streaming system for dynamic spectral processing is introduced, and various modification techniques are explored. The latter part of the chapter presents the Hilbert transform as yet another streaming spectral processing application. The chapter concludes with further additions to the notions of spectrum developed earlier in the volume.

Corrigendum: A Fast Instantaneous Frequency Estimation for Underwater Acoustic Target Feature Extraction (2021 J. Phys.: Conf. Ser. Vol 2031 012018)

Please see Article PDF for corrigendum text.

Fractional Differential Equation-Based Instantaneous Frequency Estimation for Signal Reconstruction

In this paper, we propose a fractional differential equation (FDE)-based approach for the estimation of instantaneous frequencies for windowed signals as a part of signal reconstruction. This approach is based on modeling bandpass filter results around the peaks of a windowed signal as fractional differential equations and linking differ-integrator parameters, thereby determining the long-range dependence on estimated instantaneous frequencies. We investigated the performance of the proposed approach with two evaluation measures and compared it to a benchmark noniterative signal reconstruction method (SPSI). The comparison was provided with different overlap parameters to investigate the performance of the proposed model concerning resolution. An additional comparison was provided by applying the proposed method and benchmark method outputs to iterative signal reconstruction algorithms. The proposed FDE method received better evaluation results in high resolution for the noniterative case and comparable results with SPSI with an increasing iteration number of iterative methods, regardless of the overlap parameter.

RANSAC algorithm for instantaneous frequency estimation and reconstruction of frequency-modulated undersampled signals

Frequency modulated (FM) signals sampled below the Nyquist rate or with missing samples (nowadays part of wider compressive sensing (CS) framework) are considered. Recently proposed matching pursuit and greedy techniques are inefficient for signals with several phase parameters since they require a search over multidimensional space. An alternative is proposed here based on the random samples consensus algorithm (RANSAC) applied to the instantaneous frequency (IF) estimates obtained from the time-frequency (TF) representation of recordings (undersampled or signal with missing samples). The O’Shea refinement strategy is employed to refine results. The proposed technique is tested against third- and fifth-order polynomial phase signals (PPS) and also for signals corrupted by noise.