. DSPIllustrations.com

Learning DSP Illustrated

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.

Intuitive Explanation of OFDM


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

Linearity, Causality and Time-Invariance of a System


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

The complex Fourier Series and its relation to the Fourier Transform


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

The Sound of Harmonics - Approximating instrument sounds with Fourier Series


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

Fourier Series and Harmonic Approximation


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

The Convolution Theorem and Application Examples


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

Multipath Propagation and its Effect on Audio


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

The Cyclic Prefix (CP) in OFDM


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

How does Quantization Noise Sound?


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

Circular Convolution Example


Pictorial description of the operation of circular convolution.

Quantization and Quantization noise


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

Baseband up- and downconversion and IQ modulation


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

Convolution Examples and the Convolution Integral


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

Aliasing and Anti-Aliasing Filter


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

Group delay and phase delay example


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

Decibel conversion: Factor 10 or Factor 20?


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

Python OFDM Example


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

Eye diagram examples


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

Spectral Leakage, Zero-Padding and Frequency Resolution


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

The Dirac Comb and its Fourier Transform


Time and frequency properties of the Dirac Comb

Approximating the Fourier Transform with DFT


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

Properties of the Fourier Transform


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

The first Nyquist criterion


Understanding the first Nyquist criterion and its implications.

Welcome to DSPIllustrations.com!


Motivation for this resource and setting up the coding environment