Fast Walsh–Hadamard Transform
Follow add/subtract butterflies through a real binary-basis transform.
Free theory articleFollow add/subtract butterflies through a real binary-basis transform.
Concept & interpretation
The Fast Walsh–Hadamard Transform (FWHT) is an efficient algorithm to compute the Walsh-Hadamard Transform (WHT). Unlike the Discrete Fourier Transform (DFT), which uses complex exponential basis functions, the WHT uses orthogonal real binary functions composed only of +1 and -1 values. This makes it computationally simpler, requiring only additions and subtractions without multiplications.
Experiment with the Controls
The interactive visualization allows you to see the butterfly operations in real-time.
- Select the Impulse signal and set the Stage to 0. Observe the initial state.
- Increment the Stage control step-by-step. Watch how the single non-zero value propagates through the network via the addition (green) and subtraction (red) paths.
- Try the Ramp signal and observe how energy is conserved but redistributed across the transformed values. Check the round trip error to see that the inverse accurately reconstructs the input.
Try it out in the interactive module.