Explore and decode signals with our Fourier Transform Calculator. Uncover hidden frequencies and optimize analysis with precision and confidence.
Getting started is easy — follow these simple steps to unlock deep signal insights.
The Fourier Transform (FT) is a mathematical method for analyzing functions based on frequency content. It plays a foundational role in many areas of science and engineering.
Continuous Fourier Transform:
F(ω) = ∫-∞∞ f(t) · e-jωt dtInverse Transform:
f(t) = (1/2π) ∫-∞∞ F(ω) · ejωt dωDiscrete Fourier Transform (DFT):
X[k] = ∑n=0N-1 x[n] · e-j2πkn/NAn audio engineer isolates frequencies between 1 kHz and 4 kHz using FFT, enhances them, and applies inverse FFT. This technique sharpens vocal clarity in music production.
Rotational machinery vibrations are analyzed via FFT. Unexpected high-frequency components reveal early-stage faults, enabling timely repairs and cost savings.
Try it now and transform your signal analysis in seconds — no math degree required.
| Input Signal (Time Domain) | Sampled Data | Frequency Components (Hz) | Amplitude |
|---|---|---|---|
| Pure Sine Wave | [0, 1, 0, -1] | 1 | 1.0 |
| Mixed Wave | [0, 1, 0, -1, 0.5, -0.5] | 1, 3 | 1.0, 0.5 |
| Square Wave | [1, 1, -1, -1] | 1, 3, 5 | 1.27, 0.42, 0.25 |
| Impulse Signal | [1, 0, 0, 0] | All frequencies | Equal |
| Constant Signal | [5, 5, 5, 5] | 0 (DC only) | 5.0 |
| Short Random Signal | [2, -1] | 0.5 | 2.24 |