What the syllabus asks you to cover
Ideal sampling, linear time invariant (LTI) system, properties of LTI system, frequency response of LTI system, Ideal low pass filter, impulse response and step response of ideal low pass filter. Frequency response of LTI system, Stability of LTI systems, Implementation of LTI system.
Start here for the core ideas. A dedicated GitBook topic page was not available; this original guide is introductory. Use the syllabus checklist and references below to study the remaining details.
Start with the impulse response
An LTI system is linear and time invariant. Convolving the input with its impulse response gives the zero-state output. In continuous time use a convolution integral; in discrete time use a sum. A system may be LTI without being causal or stable.
Test properties independently
A discrete-time LTI system is BIBO stable when its impulse response is absolutely summable. Causality requires the impulse response to vanish for negative indices. Frequency response describes the steady-state effect on complex exponentials. Ideal brick-wall low-pass filtering is a useful mathematical model but does not provide a finite, causal impulse response.
Try it
For and , the output is simply . This system is causal and stable because its two impulse-response coefficients are finite and absolutely summable.
Check your understanding
Explain why stability cannot be inferred from linearity. Distinguish sampling a signal from filtering it. Work through both graphical and algebraic convolution examples.
Pause and recall
Without looking back, explain the main idea, recall a key definition or formula, and describe when it applies. Include assumptions and units where relevant. Revisit any step you could not explain.