Signals and Systems
Convolution, transforms and sampling are all one idea seen from different angles: a system is completely described by what it does to one impulse. These topics run real signals through real systems rather than restating the identities.
Start from the beginning →1 topic you can watch now, 19 still to come.
Foundations
What counts as a signal, what counts as a system, and the two properties that make either one tractable.
- Continuous vs discrete time
- Standard signals: impulse, step, ramp, exponential
- Energy and power signals
- Even, odd and periodic decomposition
Time-domain analysis
The impulse response, and the one operation that uses it.
- Impulse and step response
- Convolution, graphically
- Properties of convolution
- Causality and BIBO stability
Fourier analysis
The same signal, rewritten as a list of frequencies.
- Fourier series of a periodic signal
- Fourier transform and its properties
- Magnitude and phase spectra
- Parseval's theorem
Sampling
Turning a continuous signal into numbers without losing it.
- The sampling theorem
- Aliasing
- Reconstruction and the anti-aliasing filter
Laplace and Z transforms
Two generalisations that turn calculus into algebra.
- Laplace transform and the region of convergence
- Transfer functions and poles and zeros
- Z transform for discrete systems
- Stability from the pole locations