Modulation Spectrum

The Modulation Spectrum reveals how the amplitude or frequency of a signal varies over time within specific frequency bands. It detects periodic amplitude modulation (AM) and frequency modulation (FM), which are characteristic signatures of rotating machinery faults, gear mesh interactions, and bearing defects.

Theory

Envelope Extraction

The modulation analysis begins by isolating a frequency band of interest using a bandpass filter. The envelope of the filtered signal is then extracted using the Hilbert transform to obtain the analytic signal:

a(t) = |x(t) + j · H{x(t)}|

where H{x(t)} is the Hilbert transform of the bandpass-filtered signal. The envelope a(t) represents the instantaneous amplitude and contains the modulation information.

Modulation Spectrum Computation

The modulation spectrum is the FFT of the envelope signal, revealing the modulation frequencies present within the selected carrier band:

M(f_mod) = FFT{ a(t) }

Peaks in the modulation spectrum at specific frequencies indicate periodic amplitude fluctuations at those rates. For example, a gear mesh frequency appearing in the modulation spectrum of a bearing-frequency band indicates gear-induced load modulation on the bearing.

AM and FM Detection

Type	Physical Cause	Signature
Amplitude Modulation (AM)	Periodic load variation, misalignment, eccentricity	Sidebands equally spaced around carrier frequency; envelope spectrum shows modulation frequency
Frequency Modulation (FM)	Speed fluctuation, torsional vibration	Multiple sideband pairs with Bessel function amplitudes; instantaneous frequency varies periodically
Combined AM + FM	Gear mesh with varying load and speed	Asymmetric sidebands; both envelope and instantaneous frequency show modulation

Band Selection Modes

Standard Bands

Analysis is performed in standard octave or one-third octave bands. Each band has a fixed center frequency and bandwidth, providing a systematic decomposition of the entire spectrum.

Fixed Bands

User-defined bandpass filters with arbitrary center frequency and bandwidth. Used to isolate specific carrier frequencies such as gear mesh frequency, blade pass frequency, or bearing characteristic frequencies.

Tracking Bands

Band center frequency tracks a reference signal (typically a tachometer), maintaining a constant relationship to the rotational speed. This is essential for order-related modulation analysis where the carrier frequency changes with RPM.

Parameters

Parameter	Options	Description
Input Channel	Any signal channel	Signal to analyze for modulation content.
Band Mode	Standard, Fixed, Tracking	How the carrier band is defined.
Band Center	Hz or Order	Center frequency (fixed) or order (tracking) of the carrier band.
Band Width	Octave, 1/3 Octave, Custom Hz	Bandwidth of the carrier bandpass filter.
Modulation FFT Size	256 – 16384	FFT size for the envelope spectrum. Determines modulation frequency resolution.
Tacho Channel	Any tacho input	Required for tracking bands; provides RPM reference.

Variants

Modulation Spectrum vs Band

Displays modulation spectra for all carrier bands simultaneously, producing a 2D map with carrier frequency on one axis and modulation frequency on the other. This overview reveals which carrier bands exhibit the strongest modulation and at what rates.

Modulation Spectrum vs Time

Tracks the modulation spectrum over time for a selected carrier band. Useful for monitoring the progression of a developing fault, where modulation depth typically increases as the defect worsens.

Practical Tips

For bearing diagnostics, set the carrier band to encompass one of the bearing characteristic frequencies (BPFO, BPFI, BSF, FTF) and look for modulation at the shaft rotation frequency.
Gear mesh modulation typically shows the mesh frequency as the carrier and shaft speed (or its multiples) as the modulation frequency. Increasing sideband count indicates worsening gear condition.
Use tracking bands during run-up or coast-down tests to maintain the carrier-to-order relationship as speed changes.
Compare modulation depth before and after maintenance to verify that a repair has effectively reduced the fault signature.

The modulation frequency resolution is limited by the duration of the envelope signal segment used for the FFT. For resolving modulation frequencies below 1 Hz (e.g., very slow speed fluctuations), ensure the analysis window is at least several seconds long.