# Inverse Discrete Fourier Transform

IDFT performs the reverse transformation, converting signals from the frequency domain back to the time domain.

The Fourier transform is a fundamental concept in digital signal processing. It encompasses two types of transforms: discrete Fourier transform (DFT) and inverse discrete Fourier transform (IDFT). DFT facilitates the conversion of signals from the time domain to the frequency domain without any loss, while IDFT performs the reverse transformation, converting signals from the frequency domain back to the time domain. These transforms play a crucial role in analyzing and manipulating signals in various applications.

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The formula for the Inverse Discrete Fourier Transform (IDFT) is as follows:

x(n) = \frac{1}{N} \sum_{k=0}^{N-1} X(k) \cdot e^{i 2 \pi \frac{kn}{N}}

where:

• x(n) – represents the time-domain signal,
• X(k) – represents the frequency-domain coefficients,
• N – is the total number of samples in the signal, and
• i – is the imaginary unit.