Working with signals.
WHAT A SIGNAL IS
A quantity varying over time or space: sound, an image, a sensor reading.
WHAT SAMPLING DOES
Converts a continuous signal into discrete measurements.
WHAT THE SAMPLING RATE MUST BE
More than twice the highest frequency present.
WHAT HAPPENS BELOW THAT
Aliasing: higher frequencies appearing as lower ones, indistinguishably.
WHY THAT MATTERS
It cannot be corrected afterwards, so filtering before sampling is essential.
WHAT QUANTISATION IS
Representing each sample with finite precision.
WHAT IT INTRODUCES
Noise, determined by the bit depth.
WHAT THE FREQUENCY DOMAIN IS
Representing a signal as its component frequencies rather than over time.
WHAT TRANSFORMS PROVIDE
Conversion between those representations.
WHY THAT IS USEFUL
Operations difficult in one domain are simple in the other.
WHAT FILTERING DOES
Attenuates some frequencies and preserves others.
WHAT THE TWO FILTER FAMILIES ARE
One with a finite response, always stable One with a feedback response, more efficient but requiring care for stability
WHAT CONVOLUTION IS
The operation describing a filter's effect.
WHY IT MATTERS BROADLY
It is the same operation underlying convolutional neural networks.
