Other Analyses (FFT, Fourier)

This page covers the Other category of analyses available in the Analysis tab. These tools work on top of an existing transient simulation result rather than triggering their own circuit simulation.

Back to Analysis Guide for overview, or Basic Analyses.

FFT Analysis (Fast Fourier Transform)

FFT (Fast Fourier Transform) decomposes a time-domain signal into its frequency components, showing which frequencies are present and at what amplitude. It runs entirely in the browser - no backend server is required.

When to Use FFT

Harmonic analysis - Which frequencies are present in a signal?
Distortion measurement - How much harmonic distortion does a non-linear circuit introduce?
Power quality - What harmonics appear in a power system?
Spectral inspection - Quickly verify the frequency content of any simulated waveform

Prerequisite

FFT operates on data from an existing transient (Tran graph) analysis. Run a transient analysis first before configuring an FFT graph.

Configuration

Field	Description
Samples	Number of FFT points (power of 2). Choices: 32, 64, 128, 256, 512, 1024, 2048, 4096. More samples ? finer frequency resolution, but requires enough transient data points
Window	Windowing function applied before the FFT to reduce spectral leakage (see table below)
View type	Display mode: Magnitude+Phase, Magnitude only, Phase only, Real/Imaginary, etc.
Signal	Output variable from the source transient analysis to transform (e.g., `V(out)`). Use the calculator button to browse available signals

Window Functions

Window	Characteristics
None	Rectangular window - best frequency resolution, highest spectral leakage
Hann	Good general-purpose choice - low leakage, moderate resolution
Hamming	Similar to Hann, slightly different sidelobe profile
Blackman	Very low sidelobe level, lower frequency resolution
BlackmanHarris	Excellent sidelobe suppression, lower resolution
Gauss	Smooth roll-off
Triangle	Simple triangular (Bartlett) window

Choosing a window

For most circuit analyses, Hann or Hamming is a good default. Use None only if you are sure the signal is periodic and an integer number of cycles fits exactly in the analysis window.

Interpreting FFT Results

The output is a frequency spectrum:

Horizontal axis - Frequency (Hz)
Vertical axis - Amplitude at each frequency

Key features to look for:

Feature	What it means
DC component (0 Hz)	Average value of the signal
Fundamental (f)	Main frequency of a periodic signal
Harmonics (2f, 3f, ...)	Indicate non-linear distortion
Noise floor	Broadband baseline - low means clean simulation

Example: Square Wave

A 1 kHz square wave (0 V to 5 V):

Frequency    Magnitude
0 Hz (DC)    2.5 V           (average value)
1 kHz        3.18 V (100%)   (fundamental)
3 kHz        1.06 V  (33%)   (3rd harmonic)
5 kHz        0.64 V  (20%)   (5th harmonic)
7 kHz        0.45 V  (14%)   (7th harmonic)

Even harmonics (2 kHz, 4 kHz, ...) are absent because of the square wave's half-wave symmetry.

Fourier Analysis

Fourier analysis computes the exact Fourier series coefficients of a periodic signal - the amplitude and phase of each harmonic - using data from a transient simulation.

Unlike FFT, which is a purely numerical discrete transform, GEEC's Fourier tool integrates over the simulated waveform period and returns the classic Fourier series representation:

f(t) = a_0 + \sum_{n=1}^{N} \left[ a_n \cos(n\omega_0 t) + b_n \sin(n\omega_0 t) \right]

where $a_0$ is the DC component, $a_n$ and $b_n$ are the cosine and sine coefficients, and $\omega_0 = 2\pi f_0$ is the fundamental angular frequency.

When to Use Fourier vs. FFT

Aspect	Fourier	FFT
Output	Exact harmonic coefficients at integer multiples of f?	Full spectrum up to Nyquist
Best for	Harmonic content of a known periodic signal	Exploratory spectral analysis
Requires	Known fundamental frequency	Only transient data
DC handling	Optional (checkbox)	Always present at 0 Hz bin
Number of components	Configurable (up to N harmonics)	Fixed by sample count

Prerequisite

Like FFT, Fourier analysis uses data from an existing transient (Tran graph) analysis. The transient simulation must cover at least one full period of the signal, ideally with the signal in steady state.

Configuration

Field	Description
Harmonics	Number of harmonic components to compute (e.g., 10 computes DC + 1st through 10th harmonic)
Base frequency	Fundamental frequency f? of the periodic signal (e.g., `1k` for 1 kHz)
DC component	Checkbox - when checked, includes the a? (DC) term in the result
View type	Display mode for the chart: Magnitude+Phase, Magnitude only, etc.
Signal	Output variable from the source transient analysis (e.g., `V(out)`). Use the calculator button to browse available signals

Interpreting Fourier Results

The output chart shows harmonic amplitude and phase as a bar or line chart. The tooltip on each bar shows the exact harmonic number, frequency, magnitude, and phase.

Total Harmonic Distortion (THD) - a common quality metric that can be derived from the coefficients:

THD = \frac{\sqrt{\sum_{n=2}^{N} a_n^2}}{a_1} \times 100\%

Back: Return to Basic Analyses or Analysis Guide.

Next: Go to Interactive Features to learn about design variables and parametric studies.