Unravel the mysteries of signal analysis with our Inverse Fourier Transform (IFT) Calculator. Quickly transform complex frequency domain data into its original time-domain waveform. Perfect for electrical engineers, physicists, and students needing to reconstruct signals from their spectral components. Get accurate results for signal reconstruction and analysis effortlessly.
Formula:
The Continuous Inverse Fourier Transform (IFT) is given by the formula:
f(t) = (1 / 2π) ∫-∞+∞ F(ω) ⋅ ejωt dω
Where:
f(t): The signal in the time domain.F(ω): The signal in the frequency domain (complex spectrum).ω: Angular frequency (2πf).t: Time.j: The imaginary unit (√-1).
For discrete signals, the Discrete Inverse Fourier Transform (DIFT) is typically used for computational purposes:
x[n] = (1 / N) Σk=0N-1 X[k] ⋅ ej 2πkn/N
Where:
x[n]: Then-th sample of the time-domain signal.X[k]: Thek-th frequency-domain component (complex).N: Total number of samples/components.n: Time index (from0toN-1).k: Frequency index (from0toN-1).