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Chapter 5

LTI systems and convolution

Four lessons in Part II, Systems. Read them in order, or start anywhere: a prerequisite is a link, never a gate.

Start with 5.1
0 of 4 read4 on the essential pathabout 74 minutes

Lessons in this chapter

The system's reply to a single spike at n = 0: its impulse response h[n], for the echo.The system's reply to a single spike at n = 0: its impulse response h[n], for the echo.

Lesson 1 Essential18 minYou are hereRead

The impulse response

See why a linear, time-invariant system's reply to one spike is enough to predict its reply to anything.

Two launched copies of h and their sum, with the sum highlighted.Two launched copies of h and their sum, with the sum highlighted.

Lesson 2 Essential20 minYou are hereRead

Discrete convolution

Give the "add up shifted copies of h" trick from 5.1 a name, a flip-and-slide picture, and a sum.

A fixed pulse x(τ) and a sliding pulse h(t − τ) at position t = 0.60. Their overlap is shaded; its area is 0.60.A fixed pulse x(τ) and a sliding pulse h(t − τ) at position t = 0.60. Their overlap is shaded; its area is 0.60.

Lesson 3 Essential18 minYou are hereRead

Continuous-time convolution

Turn the last page's convolution sum into a sliding overlap area, then use it on a real RC circuit.

Output of the chain with the adder-pair first: 1, 2, 2, -2, -3; the other order gives the same values.Output of the chain with the adder-pair first: 1, 2, 2, -2, -3; the other order gives the same values.

Lesson 4 Essential18 minYou are hereRead

Properties of LTI systems

Reorder cascades and merge parallel systems with convolution's own algebra, read causality and stability off h, and see why a spinning signal passes through unchanged in rate.

After this chapter

Where to go next.

The chapters either side, and the rest of Part II in the library.

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