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Signals & systems
The mathematics of everything that varies.
Sound, sensor readings, radio, heartbeats — the measured world arrives as signals, and the devices that handle them are systems. This course builds the working vocabulary: signals as functions, LTI systems, convolution, complex numbers and phasors, resonance, and filters — the math running inside every device you own.
Your progress
8 lessons
The big ideas
Signals are functions; systems transform them
A signal is a varying quantity — a function of time. A system eats signals and produces signals. Two familiar math objects, given jobs.
LTI: one experiment reveals everything
For linear, time-invariant systems, the response to a single kick (the impulse response) determines the response to any input — via convolution.
Complex numbers are rotation bookkeeping
e^{iωt} is a spinning arrow whose shadow is a wave. Amplitude, frequency, and phase live in one object, and wave arithmetic becomes arrow arithmetic.
Frequency is the natural lens
Sinusoids pass through LTI systems unbent — only scaled and shifted. Describing systems by what they do to each frequency (the frequency response) is the field's master move.
The course — start at lesson one
- 01What is a signal?Continuous vs discrete; the cast of recurring characters.Hard
- 02Systems & the LTI ideaLinearity and time-invariance: the master key.Hard
- 03ConvolutionFlip, slide, multiply, sum — the one operation.Hard
- 04Complex numbers, rehabilitatedi as a quarter-turn; polar form as amplitude-and-phase.Hard
- 05Euler's formula & phasorsWaves as rotating arrows; trig agony becomes arrow addition.Hard
- 06Oscillation, decay & resonanceThe damped oscillator: every system's personality.Hard
- 07Difference equationsDigital dynamics, feedback, and the unit-circle stability law.Hard
- 08Filters & frequency responseSculpting signals; why averaging is low-pass.Hard
Out in the world
Audio effects & EQs
Reverb is convolution; tone controls are frequency responses; echo pedals are difference equations with feedback.
Noise-cancelling & comms
Phase manipulation cancels noise; phasor constellations carry your Wi-Fi and 5G data.
Suspension to spacecraft
Damping ratios and resonance — the oscillator equation — tune car rides, buildings, and control loops.
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