Signals and Systems
Figure 1 · section 4.6
A square wave is a sum of sine waves. Scroll, and its odd harmonics are added one at a time.
A low-pass system rounds its corners. The output is the input convolved with the impulse response.
In frequency the same system only scales each harmonic by |H(jω)|. Convolution became multiplication.
The course
The first half describes signals and systems in time. The second half moves the same questions into frequency, where convolution becomes multiplication.
What the course asks, and where its answers are used.
Energy and power, operations on the time axis, the impulse and the step, complex exponentials.
The six properties, and how to test a given system for each one.
The impulse response, and convolution as a sum and as an integral.
A periodic signal as a sum of harmonics, and what an LTI system does to each one.
The standard pairs, the properties, and systems described by a differential equation.
The same questions for sequences, and systems described by a difference equation.
The sampling theorem, reconstruction, and aliasing where it happens in practice.
On paper
Typeset from the same sources as the course, as PDFs.
The eight chapters written out as a book, with worked examples in Given, Find, Method, Solution, Check form.
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The 210 practice questions on their own, set out in the form the examination papers use.
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Both transform pairs, every property table the course establishes, and a definition for every symbol it uses.
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