Fast Fourier Transforms for Fast Fourier Transforms
Fast Fourier Transforms for Fast Fourier Transforms Signal Types—Deterministic Biosignals (with or without Noise). Fast Fourier transform (FFT) is commonly used in analyzing the spectral content of any deterministic biosignal (with or without noise). I will discuss the issue of estimating the spectrum of the signal under noisy conditions in the following subsections. Discrete Fourier transform (DFT) allows the decomposition of discrete time signals into sinusoidal components whose frequencies are multiples of a fundamental frequency. The amplitudes and phases of the sinusoidal components can be estimated using the DFT and is represented mathematically as for a given biosignal x(n) whose sampling period is T with N number of total samples (NT is therefore the total duration of the signal segment). The spectrum X(k) is estimated at multiples of fs /N, where fs is the sampling frequency. Fast Fourier transform (FFT) is an elegant numerical...