Discrete Fourier Transform

F(t) := \sum_{k=0}^{N-1} f(t)e^{- \frac{2 \pi i k}{N} t}

F (t) : = \sum ​ k = 0 ​ N - 1 ​ ​ f (t) e ​ - \frac{​ 2 π i k ​ ​}{​ N ​} t ​ ​

\documentclass{article}

\usepackage{graphicx}
\usepackage{tikz}

\begin{document}

% eccetera eccetera

\end{document}

\color{red} {F(t)} := \sum_{k=0}^{N-1} f(t)e^{- \frac{2 \pi i k}{N} t}

F (t) : = \sum ​ k = 0 ​ N - 1 ​ ​ f (t) e ​ - \frac{​ 2 π i k ​ ​}{​ N ​} t ​ ​

\documentclass{article}

\usepackage{graphicx}
\usepackage{tikz}

\begin{document}

% eccetera eccetera

\end{document}

By spalla rasta