Fourier Upsampling

The Fourier Upsampling option in the Process menu or the Process toolbar uses the traditional zero-insertion approach to interpolate data. Unlike the Fourier interpolation option, this procedure is limited to integer upsampling ratios and all frequencies beyond the original Nyquist will always be zeroed. Since this procedure uses the inverse FFT for the reconstruction, it is very fast.

This option presents an AutoSignal graph displaying the input and output time domain data.

Algorithm

A new data stream is created by inserting zeros between the original data elements. The Best Exact N FFT algorithm is then used to produce the Fourier decomposition. All frequencies beyond the original Nyquist limit are then zeroed and an inverse FFT is made to generate the output.

Output Data

The Factor value determines the degree of upsampling. A factor of 10 would produce a 10231 length output with an input set of length 1024. The output size is fixed at n*Factor-Factor+1.

The Time1 and Time2 fields are a convenience to upsample only a portion of the original data set. The defaults specify the full data range.

The nIn and nOut fields are informational and give the input and output lengths.

List

The List Data option lists the index, time, and output signal in a three column table. The listing uses the AutoSignal text viewer facility.

Copy

The Copy Data to Clipboard option copies the time and output signal values to the clipboard. Formats include full precision binary (for spreadsheets such as Excel) and ASCII (for pasting into text editors).

Save

The Save Data to Disk option writes the time and output values to a supported file format. These formats include ASCII, Excel 97, Excel 95, Lotus WK3, Lotus WK1, SPSS, or Systat.

Production Facility

The AutoSignal Automation facility allows unattended processing of large numbers of data sets. The data sets can be consolidated in an Excel file or acquired using a DLL. The graphs can be exported to an MS Word RTF file, while the processed data can be exported to an Excel 95 or Excel 97 file.

Local Options

A local option changes the data set for the duration of the current procedure only. The main data table is not altered. AutoSignal offers four local options in most of the spectral procedures.

Section the data to isolate specific regions for processing.

Detrend for removing mean or subtracting a least-squares trend model.

Fourier Filtration for isolating spectral components by frequency.

Eigendecomposition Filtration for isolating spectral components by signal strength.

The Reset button restores the data to its state when first entering the procedure. Note that if you implement sequential local procedures, all of the revisions are discarded upon reset. If an Automation Session is in progress, the Reset button can be used to terminate the automated processing.

When exiting this procedure with the OK button, an option will be presented to update AutoSignal's main data table with the upsampled data.