SA-02Signal Analysis

Peak, RMS & Crest Factor

Amplitude descriptors of periodic waveforms and their harmonic content.

Signal

Waveform

Peak amplitude

Unit

Frequency

RMS

0.7071V

Peak

Peak-to-peak

Rectified avg

0.6366V

Crest factor

1.414

3.01 dB

Form factor

1.111

THD

0.0%

first 15 harm.: 0.0 %

Avg-meter error

-0.00dB

sine-calibrated meter

Waveformtwo periods

Signal± RMSRectified average

Harmonic spectrumdB re fundamental

§ Theory of operation

Describing amplitude

A single waveform can be summarised by several amplitude values, each meaningful for a different purpose:

Peak - the maximum instantaneous value: relevant to clipping, impacts and mechanical clearance.
Peak-to-peak - total excursion: used for shaft displacement and oscilloscope readings.
RMS - the square root of the mean square: proportional to power and energy, and the basis of almost every noise and vibration level.
Rectified average - the mean of $|x(t)|$ : what cheap “average-responding” meters actually measure, then scale assuming a sine.

\begin{aligned} \mathit{RMS} &= \sqrt{\dfrac{1}{T}\int x^2(t)\,dt} \\ \text{Crest factor}\quad \mathit{CF} &= \mathit{peak}\,/\,\mathit{RMS} \qquad \text{(sine }\sqrt{2} = 3.01\ \text{dB)} \\ \text{Form factor}\quad \mathit{FF} &= \mathit{RMS}\,/\,\text{average} \qquad \text{(sine }\pi/(2\sqrt{2}) \approx 1.111\text{)} \end{aligned}

Why crest factor matters

Crest factor tells you how “peaky” a signal is. In machinery diagnostics, a rising crest factor of acceleration is an early sign of bearing impacts, before the RMS level grows. Gaussian random noise has a theoretical crest factor of infinity but is usually quoted as 3–4 (0.3 % to 0.01 % chance of exceeding). Instruments specify the maximum crest factor they can measure accurately, and it sets how much headroom an amplifier or data-acquisition channel needs.

Harmonic content

Any periodic waveform is a sum of harmonics (Fourier series). A square wave contains only odd harmonics falling as 1/n; a triangle only odd harmonics falling as 1/n² (much purer); a sawtooth all harmonics as 1/n. The THD is the RMS of all harmonics above the fundamental divided by the fundamental.