EC-7.2 Systems, and the Properties Worth Testing For
You can test a system for linearity, time invariance, causality, stability, memory and invertibility, and say what each property buys you or costs you.
Before:EC-4. Transforms, Complex Variables and Numerical MethodsUnlocks:S4-1. Analog CircuitsS4-3. Control SystemsS4-5. Probability Theory & Stochastic ProcessesS5-3. Digital Signal ProcessingPE2-3. Biomedical Instrumentation and Signal ProcessingEC-9. Microcontrollers and Embedded Systems
This is the topic that decides whether the rest of the subject applies. Every method taught afterwards — the impulse response, the frequency response, the transfer function, the pole diagram — is a method for one particular kind of system, and applying any of them to a system that fails the two conditions gives an answer that looks right and is not. Learning to run the tests before reaching for the tools is the whole point.
Work through these
A system as a rule that turns one signal into another
A system is not a box of components here but a rule taking an input signal to an output signal. That definition is deliberately wide, so the same results apply to a circuit, a program, a mechanical linkage and a population model.
NPTEL: Signals and Systems (IIT Kanpur) · CourseLinearity, and the two conditions it actually asks for
Linearity asks that scaling the input scales the output, and that the response to a sum is the sum of the responses. Both have to hold, and a system with a constant offset at its output fails the first while looking harmless.
NPTEL: Principles of Signals and Systems · CourseTime invariance, and how to test for it without hand-waving
A time-invariant system responds to a delayed input with the same output, delayed by the same amount. The test is to delay the input and to delay the output, then to check the two expressions agree for every delay rather than for one.
Causality, and why it is a constraint on what can be built
A causal system's output at any instant depends only on the input up to that instant. Anything that needs a future value cannot run in real time, which is why some ideal filters are describable and not buildable.
MIT RES.6-007: Signals and Systems · CourseStability in the bounded-input bounded-output sense
A stable system answers every bounded input with a bounded output. This is the definition used throughout the module, and it is worth separating from the looser everyday sense of a system that does not misbehave.
Memory, invertibility, and why linear plus time invariant is the pair worth having
A system with memory uses past values, and an invertible one lets the input be recovered from the output. Linearity and time invariance together are what make the impulse response and every transform method in this module legitimate.
NPTEL: Signals and Systems (IISER Bhopal) · Course
Sign in to keep your progress.
Free resources
We haven't checked most of these for screen reader use yet.
Links last checked 3 Sept 2026.
Stuck here?
Ask a mentor. A real person answers, and they can see exactly which topic you're on. Usually within a couple of working days.
Checking your session…
Topics shown in module order.