Process Menu

The Process Menu contains advanced processing procedures in the Fourier, Wavelet, and Eigendecomposition domains:

Denoising Procedures

The Fourier Smoothing and Denoising option is a specialized Fourier filtration procedure that sets either a frequency threshold for low pass frequency-domain filtration, or a signal threshold for zeroing all spectral elements below a given power. The time domain data is reconstructed using the inverse FFT.

The Eigendecomposition Smoothing and Denoising option accomplishes a similar function except that the filtration occurs by zeroing those eigenmodes that contain noise. By using a high order decomposition, it is often possible to remove nearly all of the noise within a signal.

The Wavelet Smoothing and Denoising option is similar to the Fourier procedure except that the thresholding is done in the time-frequency domain. This option is effective in removing the noise in non-stationary data.

Signal Component Reconstruction Procedures

The Fourier Filtering and Reconstruction option is an extensive Fourier domain filtering and component isolation procedure. This procedure supports data tapering windows so that low power components can be isolated and reconstructed.

The Eigendecomposition Filtering and Reconstruction option offers full eigenmode filtering and reconstruction. Eigendecomposition partitions by signal strength rather than by frequency. In addition to the data, the reconstruction can optionally consist of the eigenvectors, the principal components, the data components, FFTs of the data components, an FFT of the data, AR spectra of the components, or an AR spectrum of the data.

The Wavelet Filtering and Reconstruction option offers the means to reconstruct signals from spectral components that have been isolated in the time-frequency domain. When a signal's spectral content varies across time, this option can readily isolate components that appear and disappear. Components that undergo changes in amplitude and frequency with time can also be characterized.

Interpolation and Upsampling Procedures

The Fourier Interpolation option is similar to the Fourier Filtering and Reconstruction option except that the reconstruction is computed directly from the amplitude, frequency, and phase of the sine components rather than by an inverse FFT. This offers true interpolation based upon the frequency spectrum for any size reconstruction.

The Fourier Upsampling option uses the traditional zero-insertion approach to interpolate data. This procedure is limited to integer upsampling ratios and all frequencies beyond the original Nyquist will always be zeroed.

Frequency Domain Prediction

The Parametric Interpolation and Prediction option is a powerful composite algorithm that generates a parametric (sinusoids or damped sinusoids) model of the signal. One of eight spectral procedures is first used to estimate the frequencies and component count. A linear fit is then made to determine the amplitudes, phases, and damping factors. A non-linear optimization follows. To facilitate prediction tests, it is possible to specify that only a portion of the data set be processed.

Deconvolution of Instrument Response Functions

The Deconvolve Gaussian Response Function option manages the instance where a signal is smeared by a Gaussian response function. The deconvolution seeks to recover the true signal that would have been measured using an ideal sensing system.

The Deconvolve Exponential Response Function option functions similarly. It is for instances where a signal is smeared by a first order or exponential response function. This is always a one-sided deconvolution that seeks to recover the true signal absent the delay of the measurement system.