Spectral Menu

The Spectral menu contains all of AutoSignal's spectral analysis procedures:

Fourier Options

The Fourier Spectrum is the basic FFT option in AutoSignal.

The Fourier Spectrum with Data Window option adds data windowing.

The Fourier Spectra with Data Window Comparison procedure enables up to three windowed spectra to be simultaneously graphed.

The Fourier Spectra of Segmented Data option offers an averaged FFT spectrum from overlapping segments and displays the individual spectra as 2D references or in a 3D surface plot.

The Fourier Multitaper Spectra option uses the series of orthogonal Slepian data tapers, utilizing the information at the edges of the data and reducing the variance of the spectral estimate.

The Fourier Spectrum of Unevenly Sampled Data option generates a Lomb-Scargle periodogram for data with unevenly spaced X values.

AR, MA, and ARMA Options

The AR (AutoRegressive) Spectrum option fits an AR (all-poles) spectral model to the data . These AR coefficients are used to generate a continuous spectrum that offers excellent frequency estimation accuracy, even with quite short data sets.

The AR Spectrum with Order Exploration allows multiple AR orders to be processed as spectra, plotted, and averaged. This optimum order can be found using either 2D or 3D visualization of the different orders.

The AR Spectrum with Algorithm Comparison allows up to three AR procedures to be simultaneously processed and plotted.

The MA (Moving Average) Spectrum option fits spectral nulls using an MA (all-zeros) spectral model.

The ARMA (AutoRegressive Moving Average) Spectrum option models signals with noise since both peaks and nulls can be described. A pole-zero non-linear model is offered with and without spectral factorization to stabilize the coefficients, and with and without SVD to speed up the iterative fitting.

Prony, Minimum Variance, and EigenAnalysis Options

The Prony Spectrum option fits complex exponentials to data. Using this method, it is possible to fit exponentially damped sines, undamped sines, and damped exponentials. This is the only spectral algorithm in AutoSignal that estimates damped sinusoids or damped exponentials.

The Minimum Variance Spectrum option offers a low variance and the ability to graphically compare component powers. The frequency resolution lies somewhere between the FFT and the AR methods. Critical limits are available for all of the algorithms.

The EigenAnalysis Spectrum option offers versions of the MUSIC and EV noise subspace high-performance frequency estimation algorithms.

Time-Frequency Algorithms for Non-Stationary Data

The Short Time Fourier Transform Spectrum option produces a 3D time-frequency plot based upon a segmented overlapped FFT. Windowing is normally used to sharpen the resolution in time and minimize spectral leakage.

The Continuous Wavelet Spectrum (3D Surface) option is the primary CWT (continuous wavelet transform) procedure.

The Continuous Wavelet Spectrum (2D Contour) option is identical to the 3D surface option except that the 2D graphing engine is used. If you prefer to view wavelet spectra as contour plots, as opposed to 3D surfaces, this option will be somewhat faster, use less memory, and will offer more graphing flexibility.

The Continuous Wavelet Spectrum Frequency Range option is a specialized wavelet procedure to compute the power across time for a specified frequency band.

The Continuous Wavelet Spectrum Time Range option is similar except the power is computed across all frequencies for a specified range in time. The global wavelet spectrum, which is similar to a smoothed FFT, is given by using the full time range.