Allistar
Allistar Center
Symmetric Field Physics β€” Waveform Analyzer Pro
Signal Presets
Import Signal β€” Channel 1
Or Paste CSV Data
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Vpp (V)
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Vrms (V)
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Fund. Freq (Hz)
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Noise Floor (mV)
Peak Unit
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Overlays
Freq Zoom 1Γ—
Freq Pan 0 Hz
Detected Peaks
β€” run analysis first β€”
Q Factor Calculator i
Center Freq fβ‚€ (Hz)
Bandwidth Ξ”f (Hz) at βˆ’3dB
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Q Factor
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Bandwidth (Hz)
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Rating
β“˜ What is Q Factor and how do I read it? β–Ύ expand

Q Factor (Quality Factor) measures how sharp and selective a resonance is β€” how precisely a system locks onto one specific frequency and resists energy loss to adjacent frequencies.

The formula is simple: Q = fβ‚€ / Ξ”f β€” the resonant frequency divided by the bandwidth at the βˆ’3dB point (where peak amplitude drops to 70.7% of its maximum).

Analogy Β· Think of a tuning fork versus a drum. A tuning fork rings at one precise frequency for a long time β€” very high Q. A drum produces a broad thud across many frequencies and decays quickly β€” very low Q. High Q means the system stores energy efficiently and releases it at a precise, stable frequency. Low Q means energy dissipates quickly across a wide band.

How to read Q values:

Q < 1
Overdamped β€” very broad resonance, little energy storage
Q 1–10
Moderate β€” typical passive components, visible peak
Q 10–100
High β€” good resonators, LC circuits, quartz crystals
Q > 1000
Very high β€” optical cavities, atomic clocks, precision resonators

Why it matters for resonance research: A higher Q means your prototype is storing more energy per cycle relative to what it loses. A Q that increases as you adjust geometry or coupling is a direct measurement of your device becoming a more efficient resonator. Tracking Q across experiments reveals whether your design changes are moving toward or away from true resonance.

Use ⚑ Auto-fill from peaks to populate fβ‚€ automatically from your strongest detected peak, then click ⊿ Estimate Ξ”f to measure the bandwidth directly from your FFT data.

FFT Size β˜… = power of 2 (radix-2 engine)
Bin = β€” Hz/bin
Channel 2 β€” Import Second Signal
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Phase Diff (Β°)
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Time Delay (Β΅s)
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Correlation
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Amplitude Ratio
Phase Interpretation
β€” load both channels to see phase analysis β€”
Schumann Resonances
Solfeggio Frequencies
Phi-Ratio Cascade β€” from Fundamental
Base Hz
INFO
LOG-LOG PSD (VΒ²/Hz)  Β·  ✦ Click and drag on the chart to select a slope region
NO DATA YET β€” Run FFT β†’ then press Calculate PSD
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B (Slope) β“˜
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Fractal Dim D β“˜
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RΒ² Fit Quality β“˜
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Range Low
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Range High
β“˜ What is Fractal PSD and how do I read it? β–Ύ expand

PSD (Power Spectral Density) shows how the power of your signal is distributed across frequencies β€” not as sharp peaks, but as a continuous density curve. It answers the question: does this signal have more energy at low frequencies, or is it spread evenly?

Analogy Β· Imagine measuring rainfall across a mountain range. Some areas get heavy rain (high power), others get little (low power). The PSD is the rainfall map of your signal β€” showing where the energy lives across the frequency landscape.

The spectral slope B tells you the shape of the PSD curve on a log-log chart β€” how steeply power drops as frequency increases:

B = 0
White noise β€” flat, random, no structure
B β‰ˆ βˆ’1
Pink noise β€” natural systems, 1/f behaviour
B β‰ˆ βˆ’2
Brown noise β€” random walk, integration
B < βˆ’2
Strong low-frequency dominance

Fractal Dimension D is calculated from B as: D = (5 + B) / 2. It describes the self-similarity and complexity of your signal across scales.

  • D β‰ˆ 1.5 β€” white noise. Completely random, no fractal structure.
  • D β‰ˆ 1.0 β€” pink noise. Found in heartbeats, music, natural systems. Scale-invariant.
  • D between 1.0–1.5 β€” your signal has fractal character. It repeats its pattern at multiple scales simultaneously.
Why it matters for resonance research Β· A signal with fractal PSD structure (D near 1.0) suggests the system is operating near a self-organised critical point β€” the same regime found in living systems, neural networks, and natural oscillators. If your prototype produces a signal with fractal character, it is behaving like a natural resonator rather than a forced oscillator. This is a significant finding.

RΒ² Fit Quality tells you how reliably the slope B was measured. Above 0.9 is excellent β€” the power law fits cleanly. Below 0.7 means the slope is not consistent across the selected range and the result should be interpreted with caution.

UNIT
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THD+N
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SFDR (dBc)
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Fundamental
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Tone Character
Even/Odd ratio
Harmonic Analysis Table
Harmonic Freq (Hz) Amplitude Even/Odd Ο† Aligned Schumann
β€” run analysis first β€”
β“˜ What is THD+N and how do I read it? β–Ύ expand

THD+N (Total Harmonic Distortion + Noise) measures how much of your signal's total energy is not in the fundamental frequency β€” it captures all harmonics plus background noise as a single percentage or dB value.

Analogy Β· Imagine a musician playing a single pure note. A perfect instrument produces only that note β€” 0% distortion. A real instrument also produces overtones and some background hiss. THD+N measures how much of the total sound is not the intended note. Lower is purer.

How to read the values:

  • THD+N % β€” percentage of total signal power that is harmonic distortion + noise. Lower = purer signal. Below 1% is excellent for most applications.
  • THD+N dBc β€” same measurement in decibels relative to the fundamental. More negative = purer. βˆ’40 dBc means harmonics are 100Γ— weaker than the fundamental.
  • SFDR (Spurious-Free Dynamic Range) β€” gap in dB between your fundamental and the strongest unwanted peak. Larger is better. It tells you how much headroom you have before interference becomes a problem.
  • Tone Character (Even/Odd ratio) β€” even harmonics (2nd, 4th) give a warm, musical sound. Odd harmonics (3rd, 5th) give a harsher, more distorted character. This ratio tells you the harmonic personality of your signal.
THD < 1%
Excellent purity
THD 1–5%
Acceptable
THD > 10%
Heavy distortion
SFDR > 60 dBc
Very clean

In resonance research, unexpectedly low THD at a specific geometry or frequency is a meaningful signal β€” it suggests the system has found a natural, efficient mode. High SFDR means your fundamental dominates cleanly with minimal interference.

Snapshots β€” 0 entries
No snapshots yet β€” run an analysis and click Snapshot
Multi-Session Peak Comparison
β€” add 2+ snapshots to compare peaks across sessions β€”
Session Label
Observations & Notes
β€” complete analysis first β€”
Full Tutorial
FFT Spectrum Analyzer β€” Complete Beginner's Guide
8 parts Β· step-by-step Β· analogies Β· reference tables Β· produced by Allistar Center
⬇ Download PDF Guide

Quick Start β€” The 5 Rules You Must Know

Rule 1 Β· Know your target frequency first.
Before setting up your oscilloscope, ask: what frequency am I expecting to see? Write it down. Everything else flows from this number.

Sample Rate = at least 5Γ— to 10Γ— your target frequency

Rule 2 Β· Set sample rate correctly.

Imagine filming a spinning wheel with a camera. If the camera takes only 2 photos per second and the wheel spins 3 times per second, the footage makes it look like the wheel spins backwards. That optical illusion β€” caused by sampling too slowly β€” is called aliasing. It creates fake frequency peaks in your spectrum that are not real.
Target FrequencyMin Sample RateRecommended
10 kHz50 kHz100 kHz
100 kHz500 kHz1 MHz
600 kHz3 MHz5–6 MHz
1 MHz5 MHz10 MHz
5 MHz25 MHz50 MHz
Resolution (Hz/bin) = 1 Γ· Recording Time (seconds)

Rule 3 Β· Record long enough. The longer you record, the finer your frequency resolution β€” the closer two peaks can be and still appear as separate spikes.

Recording TimeFrequency Resolution
1 second1.0 Hz/bin
5 seconds0.2 Hz/bin
10 seconds0.1 Hz/bin
30 seconds0.033 Hz/bin

Rule 4 Β· Enter sample rate exactly. When you load your CSV, enter the sample rate exactly as shown on your oscilloscope. If this number is wrong, every peak appears at the wrong frequency.

FFT Size ↑ = Resolution ↑ β€” always use the largest available

Rule 5 Β· Use the largest FFT size.

FFT size is like the number of pixels in a photograph. A 100-pixel photo shows a blurry shape. A 10-million-pixel photo shows every sharp detail. More samples = sharper frequency image.

Reading Your Spectrum

The horizontal axis = frequency in Hz. The vertical axis = amplitude (signal strength in dB).

  • Tallest peak = your fundamental frequency β€” the main frequency your device operates at.
  • Peaks at 2Γ—, 3Γ—, 4Γ— the fundamental = harmonics. These are natural and expected in every real electrical signal β€” not errors.
  • Noise floor = the flat background carpet. Real peaks should stand clearly above it.
  • Narrow sharp spike above floor = real signal. Wide fuzzy hump near the floor = noise.
A guitar string produces not just one note β€” it also vibrates at twice, three times, four times the frequency simultaneously. All those vibrations together make the rich tone you hear. Electrical signals behave exactly the same way. Harmonics are the overtones of your fundamental.

Common Mistakes

MistakeEffectFix
Sample rate too lowFake peaks (aliasing)Apply 5Γ— rule
Recording too shortBlurry, merged peaksRecord 5–10 sec minimum
Wrong sample rate enteredAll peaks at wrong frequenciesWrite it down before exporting
Signal clippingMany false harmonicsReduce oscilloscope voltage scale
FFT size too smallCan't resolve nearby peaksUse largest available size
Wrong CSV column selectedFlat or garbage spectrumSelect the voltage column
⬇ Download Complete PDF Guide
Allistar Center Β· Field Research Documentation
Understanding Your Measurements
A complete guide to every function in the Waveform Analyzer Pro
Why This Tool Exists
Most frequency analyzers show you what is in a signal.
This one shows you what it means.
For the Engineer
Standard FFT shows you which frequencies exist. This tool goes further β€” it measures harmonic character (even vs odd distortion), fractal dimension of the noise floor, Q factor with sub-bin accuracy, and SFDR. Every calculation uses metrology-grade algorithms β€” parabolic interpolation, Welch's method, log-log regression.
For the Geometry Researcher
The golden ratio Ο†, Schumann resonances, and fractal self-similarity are not abstractions β€” they are measurable properties of any resonant field. This tool detects Ο†-ratio harmonic alignment automatically, flags Schumann frequency coupling, computes the fractal dimension of your signal's power distribution, and overlays phi-ratio and harmonic series markers directly on the spectrum.
For the Curious
Every button has a built-in guide β€” tap the β“˜ icon next to any function to learn exactly what it does and how to use it. Load one of the built-in signal presets, press Calculate, and the tool explains what it found. No prior knowledge required.
Waveform FFT Spectrum Noise Floor Phase Analysis Schumann Phi Ratio CSV Format Export & PDF THD+N Q Factor Fractal PSD
Waveform View
Visualizing your raw signal over time
β–Ύ
FFT Spectrum Analysis
Decomposing your signal into its frequency components
β–Ύ
Noise Floor & Baseline Subtraction
Understanding and eliminating background interference
β–Ύ
Phase Analysis β€” Channel 2
Understanding the relationship between two measurement points
β–Ύ
Schumann Resonances
The Earth's electromagnetic heartbeat
β–Ύ
Ο†
Phi Ratio β€” The Golden Frequency
Ο† = 1.6180339887... and its role in resonant systems
β–Ύ
CSV Data Format β€” Oscilloscope Export
How to export data from your oscilloscope and import it here
β–Ύ
Export, PDF & Session Documentation
Saving and sharing your research results
β–Ύ
THD+N β€” Total Harmonic Distortion
Measuring signal purity and harmonic character
β–Ύ
Q Factor β€” Quality of Resonance
How sharp and selective your resonance is
β–Ύ
Fractal PSD β€” Power Spectral Density
How energy is distributed across frequency scales
β–Ύ
ALLISTAR CENTER Β· SYMMETRIC FIELD PHYSICS
Resonance Is the Foundation