Understanding the Auto-Spectrum

Devices

Portable balancer & Vibration analyzer Balanset-1A

€1,975.00 + VAT (if applicable)

Parts

Vibration sensor

€90.00 + VAT (if applicable)

Parts

Optical Sensor (Laser Tachometer)

€124.00 + VAT (if applicable)

Devices

Balanset-4

€6,803.00 + VAT (if applicable)

Parts

Magnetic Stand Insize-60-kgf

€46.00 + VAT (if applicable)

Parts

Reflective tape

€10.00 + VAT (if applicable)

Devices

Dynamic balancer “Balanset-1A” OEM

€1,735.00 + VAT (if applicable)

The auto-spectrum — also written autospectrum, and loosely called the power spectrum or simply “the spectrum” — is the frequency-domain representation of a single vibration signal, showing how that signal’s energy or amplitude is distributed across frequency. It is produced by taking the Fast Fourier Transform (FFT) of a time record and displaying the magnitude of each frequency component. The prefix “auto-” sets it apart from the cross-spectrum, which relates two different signals: an auto-spectrum is the spectrum of a signal taken with itself.

In day-to-day work this is exactly what most technicians mean when they say “the spectrum” or “the FFT” — the standard frequency display in every vibration analyser, with its peaks at unbalance, bearing fault frequencies, gear mesh, and the rest. Recognising that this everyday tool is technically an auto-spectrum matters most when you step into multi-channel work, where cross-spectra, coherence, and other correlation functions enter the picture.

1. The Mathematical Foundation

Two Routes to the Same Result

There are two mathematically equivalent ways to arrive at an auto-spectrum:

• Direct FFT: transform the time signal, take the magnitude (or magnitude squared) of each complex FFT bin, and plot it against frequency. This is the common, straightforward route used inside almost every instrument.
• Via autocorrelation: compute the signal’s autocorrelation function first, then take its FFT. By the Wiener–Khinchin theorem the result is identical to the direct method — the same spectrum reached by a different computational path.

When the magnitude is squared and normalised per unit frequency, the same quantity becomes a power spectral density, which is the preferred form for broadband random vibration.

Averaging for Stability

A single FFT is statistically noisy, so several auto-spectra computed from sequential time records are averaged together to settle the estimate and reduce random scatter. For routine machinery diagnostics 4–16 averages is typical; broadband random vibration may need 50–100 or more. The benefit comes at the cost of measurement time, which is why the average count is a deliberate trade-off rather than “more is always better.”

2. Defining Properties

Three characteristics fall directly out of the mathematics and are worth keeping in mind when reading any spectrum:

• Real-valued: the auto-spectrum has no imaginary part. It represents magnitude only, so the phase relationship of the original signal is discarded in the magnitude calculation. For single-point fault identification that is no loss; for balancing or transfer-function work, where phase is essential, it is a real limitation.
• Always positive: values are always greater than or equal to zero because they represent energy or power, which cannot be negative.
• Symmetric for real signals: the spectrum of a real time signal is symmetric about the Nyquist frequency — the negative frequencies simply mirror the positive ones — so only the positive half is displayed, and it contains all the information.

3. The Auto-Spectrum in Machinery Diagnostics

The Analyst’s Daily Display

This is the plot technicians live in. It shows every vibration frequency component at once, and the analyst’s task is to identify each peak and match it to a fault type — making the auto-spectrum the primary tool for fault diagnosis and for routine condition assessment.

The Features to Look For

• 1× peak: running-speed vibration, dominated by unbalance and other once-per-revolution sources.
• 2× peak: commonly misalignment or mechanical looseness.
• Bearing frequencies: BPFO, BPFI, BSF, and FTF, often surrounded by sidebands.
• Gear mesh: the tooth-engagement frequency and its harmonics.
• Electrical: twice line frequency (120 Hz on a 60 Hz supply, 100 Hz on a 50 Hz supply).
• Noise floor: the background level set by random vibration and instrument noise, against which genuine peaks must stand out.

4. Auto-Spectrum versus Cross-Spectrum

The single-channel auto-spectrum answers “what frequencies are present?”, while its two-channel cousin answers “how are two signals related?”. The contrast is worth making explicit:

Auto-Spectrum (single channel)	Cross-Spectrum (two channel)
Spectrum of one signal	Relationship between two signals
Shows that signal’s frequency content	Shows frequency content common to both
No phase information	Includes the phase relationship
Sufficient for most diagnostics	Underpins transfer function and coherence analysis
Standard single-channel FFT	Requires two synchronised channels

5. Averaging Modes and Display Choices

Choosing an Averaging Mode

• Linear averaging: a straight arithmetic mean of successive spectra that reduces random noise and converges on the true spectrum — the standard for machinery analysis.
• Exponential averaging: a weighted mean that favours the most recent records, ideal for real-time monitoring where conditions are changing.
• Peak hold (max spectrum): each frequency bin retains its highest value seen, capturing transient components — invaluable during run-up and coastdown testing.

Scaling the Axes

The amplitude axis can be shown on a linear scale (mm/s, m/s²), which makes absolute values easy to read but can hide small peaks beside large ones, or on a logarithmic dB scale (20·log[amplitude/reference]), which compresses a wide dynamic range so that small and large peaks are visible together — the preferred view for detailed and research work. The frequency axis is usually linear in Hz for machinery, though a logarithmic axis with equal octave spacing suits very wide frequency ranges.

6. Quality and Pitfalls

A spectrum is only as good as the data behind it. A clean spectrum shows clear peaks above a low noise floor; a noisy spectrum buries peaks in a high background, which more averaging and adequate frequency resolution can remedy. Two acquisition checks are essential: confirm the frequency resolution is fine enough to separate closely spaced peaks, and watch for input overload, which clips the signal and fabricates false spectral components — if it occurs, reduce the input gain and re-acquire. The FFT Resolution Calculator helps choose a line count and bandwidth that resolve the peaks you care about.

Where field instruments fit

On a portable two-channel instrument such as the Balanset-1A, the auto-spectrum is the everyday diagnostic view a technician reads at the machine to spot whether energy is concentrated at 1× (pointing to unbalance and a candidate for field balancing) or scattered across bearing and gear-mesh frequencies that signal a different fault entirely — all captured in the machine’s own bearings at operating speed.

The auto-spectrum is the fundamental frequency-analysis tool of vibration diagnostics: the single-channel FFT that technicians rely on daily for fault identification and condition assessment. Understanding that “the spectrum” is technically an auto-spectrum — and how it relates to cross-spectra and the other spectral functions — lays the groundwork for advanced multi-channel analysis and thorough machinery diagnostics.

---

← Back to Main Index