FFT Complex Spectrum Analysis

A vibration waveform from a sensor is the sum of all its frequency components, and useful frequency information is hard to read by eye. The fast Fourier transform (FFT) separates the waveform into individual lines and gives the magnitude and phase of each component.

This module keeps the complete complex FFT result and offers Bode, Nyquist and Nichols display formats. A channel FFT describes the measured signal, including its excitation and time origin; it is not by itself a system frequency-response function (FRF). Modal identification or control stability analysis requires an established input/output transfer response. Relative phase between channels requires a common time and phase reference.

Screen layout

The three advanced plots

Supporting functions

• Stay on top, to compare with other software.
• Refresh, to recalculate for the current channel selection.
• Export all data: the complete complex spectrum to Excel, four columns per channel (real, imaginary, magnitude, phase).
• Copy and quick export in every plot window for report figures.
• Chinese and English interface, following the main system language.

Why is the complex spectrum worth more than the magnitude? Magnitude answers how large; real, imaginary and phase answer which point leads and how the response is transmitted. Experimental modal analysis, transfer path analysis and control system design all start from complex spectra. Keeping the complete information from the start avoids repeating the measurement later.

FFT: splitting a waveform into lines

Any complex waveform can be treated as the sum of sine waves with different frequencies, amplitudes and timing. The FFT performs this decomposition: it outputs one complex number for each frequency, a real and an imaginary part that together record size and timing. Analysis uses powers of two (for example 512, 1024 or 2048 points), the most efficient FFT length, and the software checks the record length.

Windowing and amplitude correction

Only a section of the waveform is analyzed, which creates leakage in the spectrum. A Hanning window suppresses leakage, the amplitude reduction caused by the window is compensated, and the two-sided spectrum is converted to the single-sided form used in engineering, so the magnitude reads the true level at the sensor (g).

Four spectra from one complex number

Where the three plots come from

Bode, Nyquist and Nichols formats draw the complex FFT as magnitude/phase versus frequency, a path in the complex plane, or magnitude versus phase. Their readings share the same source. Interpretation as resonance loops, modal parameters or stability margins requires a separately established transfer response and its excitation reference; the display format alone does not provide those quantities.

Automatic peak search finds local maxima in the Bode plot and labels frequency, dB magnitude, engineering magnitude and phase; the cursor tooltip reads any other point.

• Complete complex spectrum: real, imaginary, magnitude and phase together, the raw material for modal and transfer analysis.
• Built-in Bode, Nyquist and Nichols plots, switched in one step.
• Automatic peak search and labeling in the Bode plot.
• Cursor tooltip readings of frequency, magnitude and phase anywhere in the plot.
• Eight channels overlaid for comparison of measurement points and phase relationships.
• Traceable magnitude readings: Hanning window, amplitude compensation and single-sided scaling.
• Excel export of real, imaginary, magnitude and phase for every channel.
• Time and frequency views together for training and signal quality checks.
• Copy and quick export in every plot window.
• Stay-on-top display and Chinese/English interface.

1. Select channels: tick the channels to analyze on the left; several can be overlaid. Only enabled channels can be selected.
2. Check the magnitude spectrum: find the dominant lines and confirm signal quality against the time waveform.
3. Switch the advanced plot: select Bode for magnitude/phase versus frequency, Nyquist for the complex-plane path, or Nichols for magnitude versus phase. Use a validated FRF or loop transfer function for modal or stability interpretation.
4. Read values: peaks are labeled in the Bode plot; the cursor tooltip reads any position.
5. Archive: export all data to Excel, or copy the plot for a report.

Reading tips

Use magnitude to locate dominant components. Compare channel phase only with a common reference. A raw FFT peak or complex-plane loop may reflect the excitation as well as the structure; confirm resonance through a suitable referenced test. Harmonics, broadband content and sidebands provide diagnostic clues that need corroboration.

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