Signals, Control & Comms
Signals and systems, control theory, digital signal processing and communication engineering.
101 topics: 35 beginner, 33 intermediate, 33 advanced.
About this discipline
Signals, control and communications explain how information is represented, filtered, transmitted and used to control physical systems. The same mathematics appears in audio, radio, sensors, robots and industrial plants.
The course starts with signals and systems and the Fourier and Laplace transforms, moves to digital filters and sampling, then covers feedback control, state-space methods and modern communication systems, from modulation and coding to wireless networks.
Who it is for
Electronics, control and communications students, control and instrumentation engineers, and anyone who designs filters, feedback loops or wireless links.
How the levels build
Beginner topics cover signal types, systems, linearity, convolution and the basic transforms. Intermediate topics cover transfer functions, stability, root locus, Bode plots, PID and state-space design. Advanced topics cover modern control, communications, coding, OFDM, radar and estimation.
Use cases
- Designing a low-pass filter to remove noise from a sensor.
- Tuning a PID loop for a temperature or speed controller.
- Choosing a sampling rate for a vibration measurement system.
- Estimating the data rate and range of a wireless link with a link budget.
Beginner Signals, Control & Comms
Topic 1SignalsFunctions that carry information over time or space, such as voltage, sound or images.Topic 2Continuous and discrete signalsContinuous-time signals are defined for all t; discrete ones only at sample instants.Topic 3Periodic and aperiodic signalsPeriodic signals repeat after a period T; others do not.Topic 4Even and odd signalsSymmetry about the vertical axis or origin simplifies analysis.Topic 5Energy and power signalsClassified by whether total energy or average power is finite.Topic 6Basic signalsImpulse, step, ramp, exponential and sinusoid are the building blocks of analysis.Topic 7Signal operationsShifting, scaling and reversing transform signals.Topic 8SystemsEntities that map input signals to output signals.Topic 9Linearity and time invarianceLTI systems obey superposition and respond the same regardless of when input is applied.Topic 10Causality and stabilityCausal systems do not depend on future input; BIBO stable ones give bounded output for bounded input.Topic 11Impulse responseThe output for an impulse input characterises an LTI system.Topic 12ConvolutionThe output of an LTI system is the input convolved with its impulse response.Topic 13Differential equation modelsDynamic systems are modelled by ODEs linking input and output.Topic 14Fourier series of signalsPeriodic signals expressed as harmonics of the fundamental.Topic 15Fourier transform propertiesLinearity, shift, scaling and convolution-multiplication duality.Topic 16Spectrum and bandwidthFrequency content of a signal and range of significant frequencies.Topic 17Parseval's theoremEnergy in time domain equals energy in frequency domain.Topic 18Laplace transform in systemsPoles and zeros determine response.Topic 19Poles and zerosRoots of the denominator and numerator of a transfer function.Topic 20Block diagramsGraphical representation of interconnected subsystems.Topic 21Signal flow graphs and Mason's ruleCompute overall gain of complicated diagrams.Topic 22Filtering conceptSystems that modify frequency content.Topic 23SamplingConverting a continuous signal into discrete samples at fixed intervals.Topic 24AliasingFrequencies above half the sampling rate fold into lower frequencies.Topic 25QuantisationRounding samples to finite levels introduces quantisation noise.Topic 26Discrete-time Fourier transformFrequency analysis of discrete sequences.Topic 27Discrete Fourier transformFinite-length frequency analysis that computers calculate.Topic 28Fast Fourier transformAn O(N log N) algorithm to compute the DFT.Topic 29WindowingWindow functions reduce spectral leakage in FFT analysis.Topic 30Z-transformDiscrete counterpart of Laplace; poles inside the unit circle mean stability.Topic 31FIR filtersFinite impulse response filters are always stable and can have linear phase.Topic 32IIR filtersRecursive filters achieve sharp responses with fewer coefficients.Topic 33Filter design methodsWindowing, bilinear transform and optimisation produce coefficients.Topic 34Butterworth, Chebyshev and elliptic filtersClassic analogue prototypes with different ripple and roll-off.Topic 35Multirate processingDecimation and interpolation change the sampling rate.
Intermediate Signals, Control & Comms
Topic 36Adaptive filtersCoefficients update to track changing signals, as in echo cancellation.Topic 37Spectral estimationPeriodogram and parametric methods estimate power spectra.Topic 38WaveletsTime-frequency analysis with scalable localised basis functions.Topic 39Image processing basicsFiltering, enhancement and edge detection of 2D signals.Topic 40Audio and speech processingCompression, recognition and synthesis of sound.Topic 41Random signals and noiseStochastic processes characterised by autocorrelation and power spectral density.Topic 42Wiener and Kalman filtersOptimal estimators that combine models with noisy measurements.Topic 43Introduction to control systemsUse feedback to make a system behave as desired.Topic 44Open-loop vs closed-loopClosed-loop systems use measured output to correct error.Topic 45Plant, sensor, controller, actuatorThe main blocks in a feedback loop.Topic 46Modelling mechanical and electrical systemsDerive transfer functions from physical laws.Topic 47First-order system responseCharacterised by time constant; reaches 63% in one τ.Topic 48Second-order system responseDefined by natural frequency and damping ratio.Topic 49Time-domain specificationsRise time, peak time, overshoot and settling time.Topic 50Steady-state errorFinal error depends on system type and input; integrators remove it.Topic 51Stability and Routh-HurwitzA criterion to check root locations without solving polynomials.Topic 52Root locusPlot of closed-loop pole paths as gain varies.Topic 53Frequency response methodsBode and Nyquist plots analyse stability and margins.Topic 54Gain and phase marginMeasures of how far a system is from instability.Topic 55Nyquist stability criterionUses the open-loop frequency response to determine closed-loop stability.Topic 56PID controlProportional, integral and derivative terms combine to reduce error and improve response.Topic 57PID tuningZiegler-Nichols and other methods set gains.Topic 58Lead and lag compensatorsShape frequency response to improve speed or accuracy.Topic 59State-space modelsDescribe systems with first-order equations x'=Ax+Bu.Topic 60Controllability and observabilityWhether states can be driven and inferred from outputs.Topic 61State feedback and pole placementChoose gains to place closed-loop poles.Topic 62ObserversEstimate unmeasured states from inputs and outputs.Topic 63LQROptimal control that minimises a quadratic cost.Topic 64Digital controlControllers implemented in discrete time on microprocessors.Topic 65Discretisation methodsConvert continuous controllers to discrete equivalents.Topic 66Nonlinear systemsDo not obey superposition; show limit cycles and multiple equilibria.Topic 67LinearisationApproximating a nonlinear system near an operating point.Topic 68Lyapunov stabilityUses energy-like functions to prove stability without solving equations.
Advanced Signals, Control & Comms
Topic 69Model predictive controlOptimises predicted future behaviour subject to constraints.Topic 70Robust controlMaintains performance despite uncertainty in the model.Topic 71Adaptive controlController parameters adjust online.Topic 72Feedforward and cascade controlAdd anticipatory action or nested loops to improve rejection.Topic 73PLC and industrial controlProgrammable logic controllers automate machines with ladder logic.Topic 74SCADA and DCSSupervisory and distributed systems monitor and control plants.Topic 75Communication systems overviewTransmitter, channel and receiver convey information.Topic 76Analog modulationAM, FM and PM impose messages on carriers.Topic 77Bandwidth and noise in commsSignal-to-noise ratio limits quality.Topic 78Shannon capacityC=B log2(1+SNR) is the maximum error-free data rate.Topic 79Sampling and PCMPulse code modulation converts analog to digital.Topic 80Digital modulationASK, FSK, PSK and QAM map bits to carrier changes.Topic 81Constellation diagramsPlot of symbol points showing modulation and noise effects.Topic 82Bit error rateProbability of bit errors as a function of SNR.Topic 83Source codingCompression using Huffman and arithmetic codes.Topic 84Channel codingError-correcting codes add redundancy to fix errors.Topic 85Block and convolutional codesHamming, Reed-Solomon and Viterbi decoding.Topic 86Modern codesTurbo, LDPC and polar codes approach Shannon limit.Topic 87MultiplexingTDM, FDM and CDMA share channels among users.Topic 88OFDMSplits data over many orthogonal subcarriers to fight multipath.Topic 89Spread spectrumSpreads a signal over wide bandwidth for robustness and security.Topic 90Antennas and propagationRadiation patterns, gain and path loss describe wireless links.Topic 91Link budgetAccount of gains and losses from transmitter to receiver.Topic 92Fading and multipathSignal strength varies due to reflections and movement.Topic 93MIMOMultiple antennas increase capacity and reliability.Topic 94Cellular systemsFrequency reuse and handover enable mobile coverage from 2G to 5G.Topic 95Satellite communicationLinks via geostationary or low-orbit satellites.Topic 96Optical fibre communicationLight in glass carries high-capacity data with low loss.Topic 97Radar basicsRadio waves reflect from targets to measure range and speed.Topic 98Software-defined radioRadios implemented mostly in software for flexibility.Topic 99Network information theory and 6GFuture networks integrate sensing, AI and ultra-reliable low latency.Topic 100Compressed sensingRecovers sparse signals from far fewer samples than Nyquist suggests.Topic 101Extended Kalman filterApplies Kalman estimation to nonlinear systems by local linearisation.
Frequently asked questions
What is Signals, Control & Comms?
Signals and systems, control theory, digital signal processing and communication engineering.
How many topics are in Signals, Control & Comms?
101 topics, ordered from beginner to advanced: 35 beginner, 33 intermediate and 33 advanced.
Where should a beginner start in Signals, Control & Comms?
Start with "Signals" and work through the list in order. Each topic builds on the one before it.
Why are transforms used so widely?
They turn differential equations and convolution into algebra, which makes analysis, filter design and controller design much simpler.
What does a stable system mean in practice?
Its output stays bounded and returns to rest after a disturbance. Poles in the left half of the s-plane indicate stability for continuous systems.
How do I choose between an FIR and an IIR filter?
Use FIR when exact linear phase or guaranteed stability matters. Use IIR when a sharp response must be reached with few coefficients.
Why do control loops oscillate?
High gain, time delay and lag can reduce the phase margin. When the margin is too small, the loop overshoots and rings, so the gain is reduced or the loop is shaped.
What limits how fast data can be sent?
Bandwidth and signal-to-noise ratio set the Shannon capacity. Coding and modulation determine how close a real system gets to that limit.
Practise in the interactive course with quizzes, tests and labs.