# Tracking filter

When opening a new Tracking filter math function the following setup window will appear:

Tracking filter has a center frequency that is always tuned to the Frequency source. This allows all other signals to be rejected from measurement and control.

Tracking filters greatly reduce the noise and harmonic signals above and below the signal’s center frequency. The narrower the bandwidth of the tracking filter. the more the rejection of harmonics and noise outside of the filter’s bandwidth.

The Tracking filter takes time signals as input e.g. analog input channels, and outputs filtered time signals - sample by sample.

## Basic

Under Basic you define the extracted order components and its shape:

Extracted order - the order being extracted. This can only be a single integer number.

Fixed bandwidth - the width of the frequency band around the extracted order. For example, running steady with 600 RPM and setting the Fixed bandwidth to 10 Hz - if the Extracted order is 1 then this will extract from 5 Hz to 15 Hz since the first order is centered at 10 Hz (600 RPM / 60). Hereby only that first order will be extracted since the second order is centered at 20 Hz.

Sidelobe fall-off - the cut-off steepness of the defined band.

## Frequency source

In this section you select the tracking (frequency) source:

Frequency channel - when Frequency channel is selected a channel must be selected to manage the frequency to track after. In this way the tracking frequency can variate with the selected signal.

Fixed frequency - the user specifies a fixed frequency to track after.

## Frequency smoothing

Exponential averaging can be applied to the time signal of the extracted order.

Exp. avg. factor - the check box will enable/disable the averaging. The user-defined number must be between 0 and 1, and determines the weight of the current time sample in the exponential average compared to the previous time sample. For example, setting the number to 0.1 means that 10 % of the current sample and 90 % of the previous sample will be used:

If the smoothing factor is referred to as SF, then:

smoothed output sample = SF * current sample + (1 - SF) * previous smoothed sample.

The Tracking filter uses the following processing flow:

1. The information from the frequency source is used to frequency shift the signal to have DC (0 Hz) at that source frequency.
2. A Low-Pass filter is applied on the shifted signal.
3. The signal frequnecy content is shifted back its original frequencies.

This is all done in the time domain.

Example: the frequency of the signal is 1 kHz and the user are interested in the first harmonic. The signal is frequency shifted by 1 kHz. Now the harmonic the user is are after is at DC. A LP filter is used to filter out everything but DC. After filtering the signal is shifted back to the original 1 kHz.

For the LP-filter an IIR Butterworth filter type is used. The order of the filter is estimated from the Sidelobe fall-off parameter, where each 20 dB/decade is related to one order.

Since the extracted order is at DC at the time of filtering, there is no group delay, no phase shift in the signal, as the LP-filter has 0 phase at DC - No correction is needed.