The IDFT operation undertakes the converse process, changing signals from the frequency domain back into the time domain.
Within digital signal processing, the Fourier transform holds significant importance. It encompasses two primary transformations: the discrete Fourier transform (DFT) and the inverse discrete Fourier transform (IDFT). The DFT facilitates the conversion of signals from the time domain to the frequency domain without any loss. In contrast, the IDFT performs the opposite transformation – converting signals from the frequency domain back to the time domain. These transformations are pivotal in analyzing and manipulating signals across a wide range of applications.
Inverse Discrete Fourier Transform formula
The formula for the Inverse Discrete Fourier Transform (IDFT) is as follows:
![\[x(n) = \frac{1}{N} \sum_{k=0}^{N-1} X(k) \cdot e^{i 2 \pi \frac{kn}{N}}\]](https://x-calculator.com/wp-content/ql-cache/quicklatex.com-a36bf7823647ee268cd17064f49558f4_l3.png "Rendered by QuickLaTeX.com")
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
