Discrete Fourier Transform
Discrete Fourier Transform The last part of the previous post mentions the method to find frequencies in a signal: the Discrete Fourier Transform (DFT). This post dives deeper into the DFT. The main idea of the DFT is to find out which frequency component correlates with the given input signal . This mathematical formula looks scary. \[ X[k] = \sum_{n=0}^{N-1} x[n] \, e^{-j2\pi k n / N} \] k = current frequency to check correlation n = current sample N = number of samples x[n] = the value of the current sample of the given signal My goal in this post is to demonstrate what the DFT performs is simple. Input signal and correlation signal Let's say the input signal is a sine wave of 2 Hz. There are 30 samples to represent this signal. The input signal of 2 Hz should show the highest correlation at 2 Hz. Let's also have 5 different correlation signals varying from 0 Hz to 5 Hz. The first correlation signal has i...