What the syllabus asks you to cover
Signal definition, Impulse response and convolution, Fourier series, Fourier Transform, Unit step, Delta, Sinc & Signum function, Hilbert transform, LTI system Continuous time Fourier series representation, Properties of continuous time Fourier Series. Discrete time Fourier series representation, Properties of discrete time Fourier series , Continuous time Fourier transform representation, Properties. Energy spectral densities, power spectral density, discrete time Fourier transform representation and Properties.
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.
Classify before calculating
Identify whether a signal is continuous-time or discrete-time, periodic or aperiodic, deterministic or random, and an energy or power signal. Be explicit about the variable and units. A discrete-time signal is not necessarily quantized in amplitude.
Use the basic building blocks
The unit step describes switching; an impulse is a mathematical building block for system responses. A continuous-time impulse is a distribution with unit area, while the discrete-time unit impulse is an ordinary sequence. Fourier-series coefficients describe periodic signals; Fourier transforms and spectral densities answer related but different questions.
Try it
The sequence has values 1 at zero, 2 at one, and zero elsewhere. Its energy is .
Check your understanding
Why is an ideal nonzero sinusoid usually treated as a power signal? How do time shifting and time scaling affect a signal? Continue with the Hilbert transform, Fourier properties and energy/power spectral densities in the reference course.
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.