In statistics, spectral analysis is a procedure that decomposes a time series into a spectrum of cycles of different lengths. Spectral analysis is also known as frequency domain analysis.
- is the input data set
- is a complex number that encodes both the amplitude and phase of a sinusoidal component of a function.
- is the fourier transform function
The inverse discrete Fourier transform (IDFT), is defined as follows:
- The sinusoid's frequency is cycles per sample.
- The DFT completely describes the discrete-time Fourier transform (DTFT) of an N-periodic sequence, which comprises only discrete frequency components.