Introduction to digital signal processing

Herman Kamper

Discrete signals and signal analysis

Slides Videos
Introduction to digital signal processing Introduction to digital signal processing (7 min)
Recap of continuous signal processing Continuous convolution (14 min)
Recap of the Fourier transform (7 min)
Analog-to-digital conversion Analog-to-digital conversion (7 min)
Quantisation (21 min)
Quantisation demo (6 min)
Discretising in time (7 min)
Aliasing (7 min)
Discrete-time Fourier transform (DTFT) Discrete-time Fourier transform (DTFT) (14 min)
Inverse discrete-time Fourier transform (10 min)
Sampling sinusoids and exponentials (19 min)
Aliasing of sinusoids (5 min)
Sampling rate conversion Sampling rate conversion (intuition) (9 min)
Upsampling (17 min)
Downsampling (10 min)
Discrete Fourier transform (DFT) Discrete Fourier transform (DFT) (29 min)
What does the DFT tell us? (9 min)
What happens at what frequency in the DFT? (6 min)
Windowing in the DFT (6 min)
DFT demo (8 min)
DFT properties and examples Properties of the DFT (5 min)
DFT examples (9 min)
Where did the side lobes go? (4 min)
Zero padding with the DFT Zero padding with the DFT (17 min)
Short-time Fourier transform (STFT) An intuitive introduction to the STFT (17 min)
Short-time Fourier transform (STFT) (33 min)
Fast Fourier transform (FFT) Fast Fourier transform (FFT) (37 min)
In-place computation of the FFT (5 min)
Decimation-in-frequency FFT (5 min)
Inverse DFT using the FFT (6 min)
Discrete convolution Discrete convolution (6 min)
Energy and power of discrete signals  
Correlation for discrete energy and power signals  

Discrete-time systems

Slides Videos
Introduction to discrete-time systems Introduction to discrete-time systems (10 min)
Time-invariance in discrete systems (8 min)
Linearity in discrete systems (7 min)
Causality and stability in discrete systems (7 min)
Linear time-invariant (LTI) systems Linear time-invariant (LTI) systems (15 min)
LTI demo (6 min)
Causality in LTI systems (11 min)
Stability of LTI systems (8 min)
FIR, IIR, LCCDE systems (12 min)
LCCDE demo (5 min)
Overlap-and-add for fast linear filtering Overlap-and-add for fast linear filtering (25 min)
LTI correlation for system identification LTI correlation for system identification (17 min)

Discrete signal and system analysis with the z-transform

Slides and notes Videos
Introduction to the z-transform  
LTI systems with the z-transform
Necessity, sufficiency and stability		  
Inverse z-transform  
Frequency response with the z-transform  

Discrete filters

Slides Videos
Introduction to discrete-time filters  
Filter phase characteristics  
Finite impulse response (FIR) filter design  
Infinite impulse response (IIR) filter design  
Transforming between filter types  

Resources

Acknowledgements

The content is based heavily on notes originally developed by Thomas Niesler. Some material was also obtained from Jaco Versfeld. Thomas and Jaco are with Stellenbosch University.

License

Herman Kamper, 2025-2026
This work is released under a Creative Commons Attribution-ShareAlike license (CC BY-SA 4.0).