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Digital Filters

# NUTS Help

## Digital Filters

DH — Digital High pass filter

This routine allows the user to define a frequency limit and apply it to an FID. Signals above that frequency limit will remain unchanged and signals at lower frequencies will be filtered out from the currently displayed FID.

This is done by creating a function in the frequency domain which is equal to one for all frequencies greater than the cut-off value and equal to zero for all frequencies less than the cut-off. The function is converted to the time domain using a Hilbert transform. This time domain function is then correlated with the FID to remove high frequency components.

The user can adjust the order of the function, which is the number of pts in the correlation function. The more points, the sharper the cutoff, but the operation also becomes slower. As the order approaches the number of points in the FID, the filter approaches being perfectly square.

If the number of data points is not equal to a power of 2, it is important to execute a zero-fill to next higher power of 2 before executing the digital filter. Failure to do this will hang the program.

DL — Digital Low pass filter

This routine allows the user to define a frequency limit and apply it to an FID. Signals below that frequency limit will remain unchanged and signals at higher frequencies (measured from the center of the spectrum) will be filtered out from the currently displayed FID.

This is done by creating a function in the frequency domain which is equal to one for all frequencies less than the cut-off value and equal to zero for all frequencies greater than the cut-off. The function is converted to the time domain using a Hilbert transform. This time domain function is then correlated with the FID to remove high frequency components.

The user can adjust the order of the function, which is the number of points in the correlation function. The more points, the sharper the cutoff, but the operation also becomes slower. As the order approaches the number of points in the FID, the filter approaches being perfectly square.

If the number of data points is not equal to a power of 2, it is important to execute a zero-fill to next higher power of 2 before executing the digital filter. Failure to do this will hang the program.

D2 — Decimate data by 2

This command is intended for use on an FID in conjunction with a digital low-pass filter. The D2 command "decimates" the data by a factor of 2, meaning that every other point is discarded. This reduces the data size by half and also reduces the spectral width by half (by effectively digitizing the data a factor of 2 slower). This only makes sense for use following application of a low pass filter set equal to half the spectral width.

/2 or Brickwall — Decimate or Apply "brick wall" filter

This command operates differently on time and frequency domain data.

When applied to an FID (time domain), this command reduces the data by half, similar to D2, but instead of simply deleting every other point, pairs of points are averaged.  So each pair of points is replaced by their average.

When applied to a spectrum (frequency domain), one quarter of the spectral window on each end of the spectrum is discarded.  Number of data points and SW are both reduced by a factor of 2.

The command will accept an argument (in the non-2-letter command mode) which is the number of points to eliminate at each end of the spectrum.  The argument is ignored if the data is time domain.

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Last updated: 12/6/02.