Frequency resolution is proportional to window size, as defined by the Rayleigh frequency 12, 13. This is the effect of the Heisenberg–Gabor uncertainty principle 9 or the Gabor limit 10, i.e., one cannot simultaneously localize precisely a signal in both time and frequency 11.
Convolution betweet image and gabor wavelet matlab code windows#
Long windows provide good frequency resolution but poor temporal resolution, whereas short windows increase temporal resolution at the expense of frequency resolution. Time-frequency (TF) analysis of digitized signals is traditionally performed using the short-time Fourier transform (STFT) 8, which computes Fourier spectra on successive sliding windows. Identifying the frequency, temporal location, duration, and amplitude of finite oscillation packets with high precision is a significant challenge. In brain signals, these packets span a wide range of frequencies (e.g., 0.1–600 Hz) and temporal extents (10 −2–10 2 s) 1, 2, and these signals were proposed to have a fractal, scale-free nature 3, 4, 5, 6, 7, whereby their properties are self-similar across different timescales/frequencies. Time-series describing natural phenomena, such as sounds, earth movement, or brain activity, often express oscillation bursts, or “packets,” at various frequencies and with finite duration. Importantly, they can reveal fast transient oscillation events in single trials that may be hidden in the averaged time-frequency spectrum by other methods. Superlets perform well on synthetic data and brain signals recorded in humans and rodents, resolving high frequency bursts with excellent precision. The normalization of wavelets in the set facilitates exploration of data with scale-free, fractal nature, containing oscillation packets that are self-similar across frequencies.
These are combined geometrically in order to maintain the good temporal resolution of single wavelets and gain frequency resolution in upper bands. Here, we introduce a spectral estimator enabling time-frequency super-resolution, called superlet, that uses sets of wavelets with increasingly constrained bandwidth. Classical estimators, like the short-time Fourier transform or the continuous-wavelet transform optimize either temporal or frequency resolution, or find a suboptimal tradeoff. Due to the Heisenberg–Gabor uncertainty principle, finite oscillation transients are difficult to localize simultaneously in both time and frequency.
0 kommentar(er)
