Orthogonal Frequency Division Multiplexing (OFDM) is a technique of choice for many high rate wireless communication systems. An overview of OFDM for a DSP/wireless beginner was given in this article where visualizations of how OFDM slices the spectrum into multiple subcarriers for one user was provided in detail. Orthogonal Frequency Division Multiple Access (OFDMA) is an extension of OFDM for multiple users, i.e., it is a multiple access technology (like TDMA and CDMA from 2G and 3G cellular systems, respectively) in which the available spectrum is divided into multiple subcarriers that are shared among multiple users. This was the choice

## Discrete Fourier Transform (DFT) as a Filter Bank

We have discussed before what a Discrete Fourier Transform (DFT) is and how to find the DFT of some commonly used signals. Here, we will see how a DFT acts as a (crude) bank of filters that can pass the signal contents around a desired frequency while blocking the rest. Let us start with the definition of the DFT. \begin{equation*} \begin{aligned} S_I[k]\: &= \sum \limits _{n=0} ^{N-1}\left[ s_I[n] \cos 2\pi\frac{k}{N}n + s_Q[n] \sin 2\pi\frac{k}{N}n\right] \\ S_Q[k] &= \sum \limits _{n=0} ^{N-1}\left[ s_Q[n] \cos 2\pi\frac{ k}{N}n – s_I[n] \sin 2\pi\frac{k}{N}n\right] \end{aligned} \end{equation*} for each $k$. In complex notation, this DFT is

## Windowing an OFDM Signal in Time Domain

Orthogonal Frequency Division Multiplexing (OFDM) has been introduced in a previous article as a technique suitable for high data-rate transmissions over a wireless channel. The two main advantages I mentioned were as follows: Simple one-tap equalization, and Ability to slice the spectrum and utilize each slice in an independent manner. Due to these advantages, it was adopted as the preferred modulation in WiFi and 4G-LTE systems. The interesting part is that while many new waveforms were proposed to replace it in 5G NR, OFDM was still the modulation of choice for both downlink and uplink directions with some minor changes.