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Chapter 27

Modulation

Five lessons in Part X, Modulation, analytic signals and images. Read them in order, or start anywhere: a prerequisite is a link, never a gate.

Start with 27.1
0 of 5 read1 on the essential pathabout 94 minutes

Lessons in this chapter

One panel on time from 0 to 0.2 s, values from −3.5 to 3.5: the AM signal y[n], a thin solid trace of 50 carrier cycles; 1 + μx, dotted; and the envelope |1 + μx|, dashed, drawn over it. Index μ = 1.50: 1 + μx is lowest at −0.405. It is below zero at 240 of the 1600 samples, where the envelope folds up above the zero line.One panel on time from 0 to 0.2 s, values from −3.5 to 3.5: the AM signal y[n], a thin solid trace of 50 carrier cycles; 1 + μx, dotted; and the envelope |1 + μx|, dashed, drawn over it. Index μ = 1.50: 1 + μx is lowest at −0.405. It is below zero at 240 of the 1600 samples, where the envelope folds up above the zero line.

Lesson 1 Essential18 minYou are hereRead

Amplitude modulation

Multiply a slow message by a fast carrier and its spectrum moves up; an envelope or a second multiply brings it back; mixing tunes receivers.

Three stacked panels on n from 0 to 799. Panel received x[n], from −1.1 to 1.1: the passband signal as a thin solid line. Panels I branch and Q branch, from −1.7 to 1.7: the mixer output as a faint thin line (mixed), the filter output as a solid line (filtered) and the sent message as a dashed line (sent), shifted by the 9-sample delay. Mixer outputs: 2x[n] cos in the I branch and −2x[n] sin in the Q branch, each its message plus ripple at 0.2 cycles/sample. The filtered outputs lie on the sent messages: largest error from n = 18, I 0.002 and Q 0.008.Three stacked panels on n from 0 to 799. Panel received x[n], from −1.1 to 1.1: the passband signal as a thin solid line. Panels I branch and Q branch, from −1.7 to 1.7: the mixer output as a faint thin line (mixed), the filter output as a solid line (filtered) and the sent message as a dashed line (sent), shifted by the 9-sample delay. Mixer outputs: 2x[n] cos in the I branch and −2x[n] sin in the Q branch, each its message plus ripple at 0.2 cycles/sample. The filtered outputs lie on the sent messages: largest error from n = 18, I 0.002 and Q 0.008.

Lesson 320 minYou are hereRead

I/Q and complex baseband

One carrier can carry two messages, on its cosine and its sine. Two mixers separate them, and a carrier offset spins the constellation.

One panel: line height from 0 to 1.05 against frequency (Hz) from 750 to 3250. Twenty-five stems with round heads at 2000 + 100k Hz, k from −12 to 12; the carrier's stem, at 2000 Hz, has a square head. Carson's band is a light fill between two dashed edges. Modulation index β = 5.000. Carrier 0.178, first pair of sidebands 0.328; 17 lines above 0.01. Carson's band from 1400 to 2600 Hz (1200 Hz) holds 99.4 % of the power.One panel: line height from 0 to 1.05 against frequency (Hz) from 750 to 3250. Twenty-five stems with round heads at 2000 + 100k Hz, k from −12 to 12; the carrier's stem, at 2000 Hz, has a square head. Carson's band is a light fill between two dashed edges. Modulation index β = 5.000. Carrier 0.178, first pair of sidebands 0.328; 17 lines above 0.01. Carson's band from 1400 to 2600 Hz (1200 Hz) holds 99.4 % of the power.

Lesson 418 minYou are hereRead

Frequency and phase modulation

The message turns the carrier's angle: the phase in PM, its slope in FM. A tone makes Bessel sidebands, and Carson's rule gives the band.

Raised-cosine pulses on a time axis in symbols, from −4 to 16, with heights from −4.5 to 4.5. 12 of the 12 pulses drawn dashed, each centred on its symbol time with its symbol's height. Their sum, the solid curve, runs from −3.15 to 3.97. Filled circles at the 12 symbol times sit on the sum at the symbols 1, −3, 3, 3, 3, 3, 1, 1, 3, 3, −1 and −3; the largest miss is below 10 to the power −15.Raised-cosine pulses on a time axis in symbols, from −4 to 16, with heights from −4.5 to 4.5. 12 of the 12 pulses drawn dashed, each centred on its symbol time with its symbol's height. Their sum, the solid curve, runs from −3.15 to 3.97. Filled circles at the 12 symbol times sit on the sum at the symbols 1, −3, 3, 3, 3, 3, 1, 1, 3, 3, −1 and −3; the largest miss is below 10 to the power −15.

Lesson 518 minYou are hereRead

Digital modulation and OFDM

Raised-cosine pulses send symbols that leave each other's symbol times alone; with OFDM and a cyclic prefix, a channel becomes one gain per subcarrier.

After this chapter

Where to go next.

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

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