Fourier
Choosing Your Signal
This panel lets you pick and customize different types of waveforms. Each signal type has unique features:
- Sine Wave: Smooth and periodic, the building block for all others.
- Square Wave: Alternates sharply between two values — rich in odd harmonics.
- Triangle Wave: Linearly ramping waveform — smoother than square.
- Sawtooth Wave: Slanted shape with all harmonics.
- Noise: Random values — contains all frequencies without periodicity.
You can change the frequency, amplitude, and phase shift to see how the wave changes. These form the input for Fourier analysis in later modules.
Fourier Series Approximation
What’s This Visualization Showing?
This animation reconstructs a complex waveform using only sine waves. It’s an example of a Fourier Series — a sum of harmonically related sines that converge to the desired shape.
In this animation:
- Each colored wave represents a component harmonic.
- The combined result approximates shapes like a square wave.
- The more terms (higher harmonics), the closer the approximation.
This is a dynamic visual of how signals can be constructed from simple building blocks — a foundational idea in signal processing and mathematical analysis.
Original vs. Reconstructed Signal
What’s Going On?
This module illustrates how a signal (like a square or sine wave) can be constructed or analyzed using combinations of simpler sine waves — a concept known as Fourier Series. These are useful for decomposing complex signals into fundamental frequencies, which helps with audio, image processing, and solving PDEs.
You’ll see how higher harmonics refine the shape — especially for sharp features like edges or corners.
- Red Line: Original Signal
- Blue Line: Reconstructed using limited terms
This helps visualize convergence and approximation quality.