FFT Calculator

Advanced signal analysis with 3D visualization, multi-signal support, and professional DSP capabilities.

Sine Wave
Square Wave
Triangle Wave
Sawtooth Wave
Chirp Signal
Noise Signal
Custom Signal
Multi-Signal

Advanced FFT Engine: Supports multi-signal analysis, 3D visualization, and real-time processing using Web Workers

Visualization: Real-time 2D & 3D plots with interactive controls and high-performance rendering

Hz
Sampling frequency (Nyquist: fₛ/2)
Total duration of the signal
Number of FFT points (power of 2 for optimal performance)
V
Peak amplitude of the signal
0° 180° 360°
Selected: 0° (Signal phase shift in degrees)
Hz
Frequency of sine wave
Hz
Fundamental frequency
10% 50% 90%
Selected: 50%
Hz
Frequency of triangle wave
Left Symmetric Right
Selected: 50%
Hz
Frequency of sawtooth wave
Direction of the sawtooth wave
Hz
Starting frequency of chirp signal
Hz
Ending frequency of chirp signal
Type of frequency sweep
Different noise types have different spectral characteristics
σ
Standard deviation of noise distribution
Enter time-domain signal values. Use real numbers only.

Signal preview will appear here

Multi-Signal Components
Component 1 (Fundamental) Active
Add multiple signal components to create complex waveforms
Performance: Ready Web Worker: Inactive

Advanced FFT Engine: Parallel processing with Web Workers for large FFT sizes

Optimized implementation with cache-efficient memory access patterns

Direction of Fourier Transform
Format of frequency domain output
FFT algorithm selection for different sizes
Range of frequencies to display
Normalization factor for FFT output
Averaging method for multiple FFTs

Note: For professional analysis, use split-radix for general purpose and Bluestein for non-power-of-2 sizes. Energy conservation normalization is recommended for power measurements.

0 (Clean) 0.5 1 (Noisy)
Selected: 0.00 (Additive Gaussian noise)
0 dB 50 dB 100 dB
Selected: 40 dB (Alternative to noise level)
Window function to reduce spectral leakage
Min Default Max
Parameter for window functions (e.g., β for Kaiser)

Window Selection Guide: Hann for general purpose, Flat Top for amplitude accuracy, Blackman-Harris for sidelobe suppression, Kaiser for adjustable parameters.

3D visualization of time-frequency analysis
Window size for Short-Time Fourier Transform
Overlap between consecutive windows
Rendering mode for 3D visualization
Color mapping for 3D visualization
Resolution of 3D mesh (affects performance)

3D Visualization: Short-Time Fourier Transform (STFT) creates a time-frequency representation. Higher overlap provides smoother visualization but requires more computation.

Zero padding for improved frequency resolution
Remove trends from signal before FFT
Phase unwrapping algorithm
Automatic detection and analysis of harmonics
Algorithm for peak detection in spectrum
Trade-off between quality and performance

Advanced Features: Zero padding increases frequency resolution, detrending removes DC and linear trends, harmonic analysis identifies integer multiples of fundamental frequency.

Processing signal with advanced algorithms...

Professional FFT Analysis Features

This enhanced FFT calculator provides professional-grade signal analysis capabilities with advanced features for research and engineering applications.

Key Advanced Features:

  • 3D Visualization: Interactive 3D time-frequency analysis using Three.js
  • Multi-Signal Analysis: Combine multiple signal components for complex waveforms
  • Advanced Algorithms: Multiple FFT algorithms optimized for different use cases
  • Real-time Processing: Web Workers for parallel computation without UI blocking
  • Professional Export: Multiple export formats including CSV, JSON, and MATLAB
  • Harmonic Analysis: Automatic detection and characterization of harmonics

3D Visualization Capabilities

Surface Plots: 3D mesh representation of time-frequency magnitude

Waterfall Displays: Sequential 2D spectra arranged in 3D space

Interactive Controls: Orbit, zoom, and pan for detailed inspection

Color Mapping: Multiple color schemes for different data characteristics

Export Options: Screenshots and 3D model export for reporting

Real-time Updates: Dynamic updates during parameter changes

Signal Types Supported

Signal Type Mathematical Form Applications Spectral Characteristics
Sine Wave A·sin(2πft + φ) Pure tone analysis, calibration Single frequency component
Square Wave A·sign(sin(2πft)) Digital circuits, pulse analysis Odd harmonics with 1/n decay
Triangle Wave Piecewise linear function Testing linear systems Odd harmonics with 1/n² decay
Sawtooth Wave 2A(t/T - floor(0.5 + t/T)) Music synthesis, sweep testing All harmonics with 1/n decay
Chirp Signal A·sin(2π(f₀ + kt)t) Frequency response testing Time-varying frequency
Noise Signals Various distributions System identification, testing Defined by color (white, pink, etc.)

Professional Applications

1

Audio Engineering: Harmonic distortion analysis, speaker testing, room acoustics

2

Vibration Analysis: Machinery monitoring, fault detection, modal analysis

3

Communications: Signal integrity, modulation analysis, spectrum monitoring

4

Medical Signal Processing: EEG/ECG analysis, ultrasound, medical imaging

5

Scientific Research: Time-series analysis, spectral estimation, data visualization

Performance Optimization: This calculator uses multiple optimization techniques including Web Workers for parallel computation, memoization for repeated calculations, progressive rendering for large datasets, and adaptive algorithms based on data size and complexity.

Frequently Asked Questions

The 3D visualization uses Three.js to create interactive time-frequency representations. It performs Short-Time Fourier Transform (STFT) to break the signal into overlapping windows, computes FFT for each window, and renders the results as a 3D surface where X-axis is time, Y-axis is frequency, and Z-axis is magnitude. Benefits include: 1) Visualizing how frequency content changes over time, 2) Identifying transient events, 3) Seeing harmonic relationships in 3D space, 4) Interactive inspection from any angle, 5) Better understanding of signal characteristics than 2D plots alone.

Web Workers are JavaScript scripts that run in background threads, separate from the main browser thread. In this calculator, Web Workers are used for: 1) Performing FFT calculations in parallel, 2) Processing large datasets without blocking the UI, 3) Real-time signal generation, 4) 3D mesh generation for visualization. Benefits include: 1) Smooth UI even during heavy computation, 2) Faster processing for large FFT sizes, 3) Ability to process multiple signals simultaneously, 4) Better utilization of multi-core processors. The calculator automatically enables Web Workers for FFT sizes above 1024 points.

Harmonic analysis automatically detects and characterizes integer multiples of the fundamental frequency in a signal. The calculator identifies: 1) Harmonic frequencies (2f, 3f, 4f, etc.), 2) Harmonic amplitudes relative to fundamental, 3) Phase relationships between harmonics, 4) Total harmonic distortion (THD), 5) Signal-to-noise-and-distortion ratio (SINAD). Applications include: 1) Audio equipment testing (distortion measurements), 2) Power quality analysis (harmonic pollution), 3) Vibration analysis (resonant frequencies), 4) Mechanical system diagnostics (bearing faults), 5) Musical instrument analysis (overtone structure).

Different FFT algorithms offer various trade-offs: 1) Cooley-Tukey (Radix-2): Fastest for power-of-2 sizes, O(N log N) complexity, widely used. 2) Split-Radix: ~20% fewer operations than Radix-2, best for general-purpose use. 3) Bluestein (Chirp-Z): Works for any size (not just power of 2), O(N log N) via convolution, flexible frequency ranges. 4) Prime Factor: Efficient for sizes with small prime factors. The calculator selects the optimal algorithm based on input size and requirements, with Radix-2 for power-of-2, Split-Radix for medium sizes, and Bluestein for arbitrary sizes or when zero-padding is needed.

Multiple export formats cater to different professional needs: 1) CSV: Comma-separated values, ideal for spreadsheet analysis (Excel, Google Sheets) and basic data processing. 2) JSON: JavaScript Object Notation, perfect for web applications, data APIs, and structured data exchange. 3) MATLAB (.m): MATLAB script format with full signal data and visualization commands, ready for further analysis in MATLAB. 4) 3D Model (GLTF/OBJ): Export 3D visualizations for use in other software (Blender, CAD tools). 5) Image Export: High-resolution PNG screenshots of all plots for reports and publications. Each format preserves metadata including parameters, timestamps, and analysis settings.