Fourier Transform Visualizer

Visualize the Fast Fourier Transform (FFT) of custom signals in real-time

About the Fourier Transform

The Fourier Transform decomposes a signal into its constituent frequencies. This visualizer uses the Fast Fourier Transform (FFT) algorithm to efficiently compute the frequency spectrum of combined sine waves.

Signal Controls

Signal Statistics

Sample Rate 1024 Hz
Samples 1024
Duration 1.00 s
Active Waves 0
Peak Frequency - Hz
Peak Magnitude -

Visualizations

Time Domain - Signal Waveform

Frequency Domain - FFT Spectrum

How to Use This Visualizer
  • Enable waves using the checkboxes and adjust their frequency, amplitude, and phase
  • Frequency controls the wave's oscillation rate (Hz)
  • Amplitude controls the wave's strength (0-1)
  • Phase controls the wave's starting position (0-360 degrees)
  • Click "Update Visualization" to see the combined signal and its frequency spectrum
  • The frequency domain shows peaks at the frequencies you've selected
  • Try combining multiple frequencies to create complex waveforms
Understanding FFT

The Fast Fourier Transform (FFT) is an efficient algorithm for computing the Discrete Fourier Transform (DFT). It converts a signal from the time domain to the frequency domain, revealing which frequencies are present in the signal and their relative strengths.

Key Concepts:

  • Nyquist Frequency: The maximum frequency that can be detected is half the sample rate
  • Frequency Resolution: Determined by sample rate divided by number of samples
  • Magnitude Spectrum: Shows the amplitude of each frequency component
  • Bins: The frequency spectrum is divided into discrete bins, each representing a frequency range
Technical Details
  • Algorithm: Cooley-Tukey FFT (radix-2 decimation-in-time)
  • Sample Rate: 1024 Hz (samples per second)
  • Sample Count: 1024 samples (must be a power of 2 for FFT)
  • Duration: 1 second
  • Frequency Resolution: 1 Hz per bin
  • Nyquist Frequency: 512 Hz (only positive frequencies shown)