# Supplementary videos 

## Chapter 1: Introduction to Systems and Signals


[Learn more about the systems approach.](vi0101)

[Learn more about the LIDAR example.](vi0102)

[An example: speech synthesis from neural decoding of spoken sentences.](vi0103)

[Noise reduction on "O'sole mio".](vi0104) 

[Learn more about the symmetric decorations of the Alhambra Palace.](vi0105)

[Learn more about the symmetric art of Escher.](vi0106)

[Learn more about the mathematics of symmetry.](vi0107)

[Learn more about the Euler number.](vi0108)

[Euler's formula explained in simple group theory.](vi0109)



## Chapter 2: Basic Building Blocks of Signals

[Learn more about the Euler formula, which explains complex exponential as rotation.](vi0201)

[Visualization of continuous time complex exponential.](vi0202)

[Learn more about the fundamental frequency and its harmonics in music.](vi0203)



## Chapter 3: Basic Building Blocks and Properties of Systems

[Learn more about how signal travels through a neuron.](vi0301)

## Chapter 4: Representation of Linear Time Invariant Systems by Impulse Response and Convolution Operation
[Learn more about the impulse response and the acoustics of instruments.](vi0401)


## Chapter 5: Representation of LTI Systems by Differential and Difference Equations
[Learn more about differential equations.](vi0501)

## Chapter 6: Fourier Series Representation of Continuous Time Periodic Signals
[Learn more about the life of J. B. Fourier.](vi0601)

[Representation of a  complicated function by superposition of harmonically related complex exponentials.](vi0602)

[Learn more about the Fourier series.](vi0603)

[Learn more about vector spaces.](vi0604)

[Learn more about the Hilbert space and inner products.](vi0605)


## Chapter 7: Fourier Series Representation of Discrete Time Periodic Signals
[Learn more about the Fourier series and the frequency spectrum.](vi0701)

## Chapter 8: Continuous Time Fourier Transform and Its Extension to Laplace Transform
[A visual introduction to Fourier Transform.](vi0801)

[Listen to Maria Callas, Luciano Pavarotti and others to see examples of different human voice bandwidths.](vi0802)

[The sound of sine waves and their Fourier transforms.](vi0803)

[Learn more about the Euler's identity.](vi0804)

## Chapter 9: Discrete Time Fourier Transform and Its Extension to z-Transforms
[Listen to the sounds of periodic functions.](vi0901)

[Noise reduction using the Fourier transform.](vi0902)

## Chapter 10: Linear Time Invariant Systems as Filters
[Learn more about the effect of different types of filters on music signals.](vi1001)

[Learn more about designing a notch filter.](vi1002)

## Chapter 11: Continuous Time Sampling
[Learn more about aliasing.](vi1101)

## Chapter 12: Discrete Time Sampling  and Processing
[Learn more about Claude Shannon, a hero of the digital revolution.](vi1201)