Motion to Frequency: FFT Analysis in TEMA

Some of the most useful information in a test isn't where something moves, but how often. A part that rattles, a fixture that resonates, a rotating shaft slightly out of balance. Knowing the frequency of an unwanted vibration can give clues to the cause, and needed mitigating actions.

In a position curve, those oscillations blur together, and counting peaks by eye in distance-over-time curve only works for the simplest cyclical and oscillatory motion. It also isn't very deterministic nor reproducible.

TEMA 6.1.3 adds FFT analysis, which turns tracked motion into a frequency spectrum in a single click, so you can read the frequency components directly.

What an FFT shows

An FFT (Fast Fourier Transform) breaks a signal down into the frequency components it is composed of. In TEMA, the signal is the motion of a tracked point, and the result is a spectrum, applicable to any 2D diagram that plots position versus time.

• Frequency (horizontal axis): how often something oscillates, in Hz (times per second).
• Amplitude (vertical axis): how strong each oscillation is, in pixels or - when camera calibrated - a length unit of your choice.
• One spectrum per axis: X, Y and Z are all analysed separately, so sideways, vertical and normal motion can show different frequencies.

Each peak in the diagram is an oscillation in the motion. Several peaks mean several oscillations, even when they overlap completely in the position curve.

Example: a metronome, measured from video alone

To show how it works, we tracked the mechanical metronome's arm in an ordinary stock clip recorded at 24 frames per second. No audio was used, only the sensor images. The positions on the X and Y-axes were plotted, and converted to Frequency Diagrams. In the original graphs you can clearly see the oscillatory behavior.

The spectra show one clear peak per axis: 1.15 Hz side to side (X) and 2.3 Hz up and down (Y). Same motion, but two rhythms? The arm swings side to side once per period, but the tip dips at both ends of every swing, thus its vertical motion will repeat twice as often!

A metronome ticks once at each end of its swing, which links both peaks to the tempo:

Both axes then agree: 2.3 ticks per second × 60 seconds = 138 beats per minute!

Where frequency analysis helps

The metronome is a simple case, but the workflow is the same for any tracked point in your test footage:

• Rotating parts: imbalance shows up as a peak at the running speed.
• Structural vibration: find the resonance frequencies of a component, fixture or mount.
• Impact testing: see how parts ring after an impact, and at which frequencies.
• Oscillating parts: identify flutter and oscillation in wind tunnel, flight or launch footage.
• Choosing a filter: the spectrum shows where the real signal ends and the noise begins. That helps you set a CFC class or FIR filter factor without filtering away real motion. See CFC vs FIR: Choosing the Right Filter for Motion Data.
• Choosing analysis method: the software allows you to control the windowing function to have absolute control over spectral leakage, with Hann, Square and Hanning window supports out of the box, as well as controlling what samples the frequency should be calculated over.

Getting good results

An FFT is only as good as the motion data going into it. A few recording choices make the difference:

Frequencies above half the frame rate, the Nyquist limit, don't disappear. They fold back into the spectrum as false peaks, so choose the frame rate with the fastest motion you wish to analyse in mind.

Also new in TEMA 6.1.3

FFT analysis is coming in TEMA 6.1.3. The release also brings:

• Python scripting (TemaPy): Quality-of-life improvements
• Tracking: Major performance gains in all modes of tracking
• 3D: Performance gains in triangulation and rigid body pose estimation
• Stability: A wide range of bug fixes

Next step

Want to see which frequencies are hiding in your own footage? Contact us at Image Systems for a demo!