What is Auto-Spectrum? Single-Channel Frequency Analysis • Portable balancer, vibration analyzer "Balanset" for dynamic balancing crushers, fans, mulchers, augers on combines, shafts, centrifuges, turbines, and many others rotors What is Auto-Spectrum? Single-Channel Frequency Analysis • Portable balancer, vibration analyzer "Balanset" for dynamic balancing crushers, fans, mulchers, augers on combines, shafts, centrifuges, turbines, and many others rotors

What is Auto-Spectrum? Single-Channel Frequency Analysis

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Understanding Auto-Spectrum

Definition: What is Auto-Spectrum?

Auto-spectrum (also called autospectrum, power spectrum, or simply spectrum) is the frequency domain representation of a single vibration signal, showing the distribution of vibration energy or amplitude as a function of frequency. It is computed by taking the Fast Fourier Transform (FFT) of the signal and displaying the magnitude of each frequency component. The term “auto-spectrum” distinguishes it from cross-spectrum (which relates two different signals), emphasizing that it is the spectrum of a signal with itself.

In practice, auto-spectrum is what most people simply call “the spectrum” or “FFT spectrum”—it’s the standard frequency analysis display in vibration analyzers showing peaks at unbalance, bearing fault frequencies, gear mesh, and other diagnostic components. Understanding that this is technically an auto-spectrum becomes important when working with multi-channel analysis where cross-spectra and other correlation functions come into play.

Mathematical Foundation

Computation Methods

Direct FFT

  • Compute FFT of time signal
  • Calculate magnitude of each complex FFT component
  • Display magnitude vs. frequency
  • Most common and straightforward

Via Autocorrelation

  • Compute autocorrelation function of signal
  • Take FFT of autocorrelation
  • Result is auto-spectrum (Wiener-Khinchin theorem)
  • Mathematically equivalent but computationally different route

Averaging

  • Multiple auto-spectra computed from sequential time records
  • Averaged together to reduce noise and improve statistical reliability
  • Typical: 4-16 averages for machinery diagnostics
  • More averages for random vibration (50-100+)

Properties and Characteristics

Real-Valued

  • Auto-spectrum is always real (no imaginary part)
  • Represents magnitude only, no phase information
  • Phase lost in magnitude calculation
  • Sufficient for most single-point diagnostics

Always Positive

  • Values always ≥ 0 (magnitude squared or magnitude)
  • Cannot have negative spectral values
  • Represents energy or power (inherently positive)

Symmetric (for Real Signals)

  • Auto-spectrum of real signal symmetric around Nyquist frequency
  • Negative frequencies mirror positive frequencies
  • Only positive frequencies displayed (contain all information)

Auto-Spectrum in Machinery Diagnostics

Standard Diagnostic Display

  • What technicians call “the spectrum” or “FFT”
  • Shows all vibration frequency components
  • Peaks identified and matched to fault types
  • Primary tool for fault diagnosis

Typical Features

  • 1× Peak: Unbalance or other 1× sources
  • 2× Peak: Misalignment or looseness
  • Bearing Frequencies: BPFO, BPFI, BSF, FTF
  • Gear Mesh: Tooth engagement frequency
  • Electrical: 2× line frequency (120/100 Hz)
  • Noise Floor: Background level from random vibration and noise

Auto-Spectrum vs. Cross-Spectrum

Auto-Spectrum (Single Channel)

  • Spectrum of one signal
  • Shows frequency content
  • No phase information
  • Sufficient for most diagnostics
  • Standard single-channel FFT

Cross-Spectrum (Two Channel)

  • Relationship between two signals
  • Shows common frequency content
  • Includes phase relationship
  • Used in transfer function analysis, coherence
  • Requires two synchronized channels

Averaging Auto-Spectra

Linear Averaging

  • Arithmetic average of multiple auto-spectra
  • Reduces random noise variation
  • Improves estimate of true spectrum
  • Standard for machinery analysis

Exponential Averaging

  • Weighted average giving more weight to recent spectra
  • Useful for tracking changing conditions
  • Real-time monitoring applications

Peak Hold (Max Spectrum)

  • Each frequency bin holds maximum value
  • Captures transient components
  • Useful for startup/shutdown analysis

Display Formats

Linear Scale

  • Y-axis linear (mm/s, m/s², etc.)
  • Easy to read absolute values
  • Small peaks can be invisible if large peaks present
  • Common for routine analysis

Logarithmic Scale (dB)

  • Y-axis in decibels (20 log(Amplitude/Reference))
  • Wide dynamic range visible
  • Small and large peaks both visible
  • Common for research and detailed analysis

Frequency Axis

  • Linear: Equal Hz spacing, standard for machinery
  • Logarithmic: Equal octave spacing, useful for wide frequency ranges

Quality Indicators

Spectral Quality

  • Clean Spectrum: Clear peaks, low noise floor
  • Noisy Spectrum: High background, unclear peaks
  • Averaging: Improves quality by reducing noise
  • Resolution: Adequate to separate close peaks

Overload Indicators

  • Check for signal overload during acquisition
  • Overload creates false spectral components
  • Adjust input gain if overload occurs

Auto-spectrum is the fundamental frequency analysis tool in vibration diagnostics, representing the single-channel FFT that technicians use daily for fault identification and condition assessment. Understanding that “the spectrum” is technically an auto-spectrum, and how it relates to cross-spectra and other spectral analysis techniques, provides the foundation for advanced multi-channel analysis and comprehensive machinery diagnostics.

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