Digital signal processing, foundations of communications engineering and physical layer communication techniques.

Illustrative explanation instead of boring math

Python code for all examples

Get the code and play around on your own

Refer to an introduction for a site overview and how to setup the coding environment.

Explaining OFDM from the continuous-time standpoint, without FFT/IFFT.

How can you recognize a linear, a causal and a time-invariant system?

The three different representations of the Fourier Series and how they lead to the Fourier Transform.

Listen to the sound of a saxophone and describe it mathematically.

Fundamental Fourier: Expansion of periodic functions into sums of sines and cosines.

Illustrations on the Convolution Theorem and how it can be practically applied.

Explanation on the causes of multipath propagation and illustrating their effects on audio samples.

Explanation on why the cyclic prefix (CP) is used in an OFDM system.

We illustrate the effect of quantization noise in terms of audio samples.

Pictorial description of the operation of circular convolution.

What does a quantizer do, what is quantization noise and how do we calculate it?

Complete walkthrough of a digital transmission chain including AD/DA conversion and up/downconversion

This article explains the convolution operation with the help of animated graphs.

Explanation of Aliasing, how it sounds and what the anti-Aliasing filter does.

Explanation of the terms group delay and phase delay with an example of a bandpass RLC filter.

Explanation why dB conversion sometimes uses factor 10 and sometimes factor 20.

Illustration of a basic OFDM example including channel estimation for OFDM.

How to create an eye diagram and check for the first and second Nyquist criterion.

We derive and illustrate the special properties of the DFT due to its discrete nature including an audio example.

Time and frequency properties of the Dirac Comb

Understand, how the continuous-time Fourier Transform and discrete Fourier Transform are related

Linearity, Time-shift and Modulation property of the Fourier Transform

Understanding the first Nyquist criterion and its implications.

Motivation for this resource and setting up the coding environment