Unlock the secrets of digital signal analysis with our free IDFT Calculator. Easily compute the Inverse Discrete Fourier Transform from your given complex DFT coefficients to reconstruct the original time-domain signal. This tool is perfect for students, engineers, and researchers working with DSP applications.
Formula:
The Inverse Discrete Fourier Transform (IDFT) is a mathematical operation that transforms frequency-domain data back into the time domain. It is formally defined by the equation:
x[n] = (1/N) ∑k=0N-1 { X[k] ⋅ ej(2πkn/N) }
Where:
- x[n]: The n-th sample of the reconstructed time-domain signal.
- X[k]: The k-th complex frequency-domain coefficient, provided as input.
- N: The total number of points/samples in the sequence.
- j: The imaginary unit (√-1).
- e: Euler's number (base of the natural logarithm).
- π: Pi (approx. 3.14159).