Short-Time Fourier Transform (STFT)
The Short-Time Fourier Transform (STFT) is an Best Exact N FFT-based spectral procedure which furnishes Fourier spectral information for non-stationary data. The STFT is often used to assess whether or not a signal is stationary.
Relation to Periodogram
Much as the Periodogram option, the STFT is based upon a series of segmented and overlapped FFTs that occur across the data stream. In the STFT, the individual FFTs from these multiple segments are not averaged but instead returned as a 3D data set. This gives a good indication of the time-frequency properties of the data series.
This procedure normally employs a data tapering window to reduce spectral leakage and improve the resolution in time. For each individual FFT, the time assigned is that of the center of the segment (the peak of the data tapering window). In the STFT, the goal of the overlapping segments is not to produce an average spectrum with a reduced variance for the estimated power, but rather to produce a time-frequency representation for the data. A high degree of redundancy (overlap) results in time-frequency spectrum with a high resolution in time.
Optimizing Time-Frequency Resolution
Since the STFT is based upon the FFT, there is a fixed resolution between frequencies. The frequency resolution is set mainly by the size of the segment, although some benefits may be derived from using a higher count (zero-padded) FFT, especially when using small segment sizes. The segment size also determines the percent of the overall data stream processed in a single FFT. Thus the time resolution is also fixed by the segment size (and to a much lesser extent by the sharpness of the data tapering window). For this reason, the segment size thus controls the tradeoff between frequency resolution and time resolution, and it will be constant everywhere in the time-frequency spectrum.
Optimizing the STFT usually involves (1) finding an appropriate segment size, (2) setting the density in time by adjusting the amount of redundancy or overlap between the segments, (3) zero-padding the FFT for small segment sizes to better render spectral maxima, and (4) choosing an appropriate data tapering window.
Unlike the CWT , the STFT's default settings will not automatically generate a good representation of time-frequency space. Some adjustments are typically needed to find an acceptable time-frequency tradeoff.
STFT vs. Wavelet Spectra
The STFT is classified as a fixed or single resolution method for time-frequency analysis. Optimizing the STFT can require some effort. In many instances, a multiresolution analysis is simpler to use and more robust. At high frequencies, a short time segment is often sufficient to capture the given spectral information. On the other hand, at low frequencies it is usually better to use a longer time segment to gather sufficient information about the oscillation. The ability to adjust this time-frequency resolution tradeoff in this manner is an integral part of wavelet analysis. In general, continuous wavelet spectra will offer a better overall picture of time-frequency space than the STFT.
The STFT does have an advantage when it comes to rendering powers. It is possible to integrate a 3D wavelet spectrum in order to get power just as it is possible to integrate the STFT and extract power information from the volume under the surface. The multiresolution property of wavelet analysis makes it impossible, however, to get relative powers directly from the magnitude of the 3D peaks in the wavelet spectrum. The STFT does offer this property where the power is linearly proportional to the height of the peaks. It is also a simple matter for the STFT to offer an amplitude plot option.
See Also
Time-Frequency Spectral Analysis Object - Short-Time Fourier Transform (STFT) Spectrum