## Amplitude Modulation

Amplitude modulation (AM) is a linear baseband modulation technique in which the message modulates the amplitude of a constant frequency signal.

Communications Toolbox™ software includes these modulation and demodulation functions, System objects, and blocks to model pulse amplitude modulation (PAM) and quadrature amplitude modulation (QAM).

FunctionsSystem objectsBlocks

### PAM

In digital PAM, quantized pulses modulate a carrier signal. A pulse train is the carrier signal for digital data. As described in Proakis ([2]), the signal waveforms may be expressed as

sm(t) = Am p(t), 1 ≤ m ≤ M

where:

• p(t) is a pulse of duration T.

• {Am, 1 ≤ m ≤ M} denotes the set of M possible amplitudes corresponding to M = 2b possible b-bit blocks of symbols.

### QAM

In digital QAM, two carrier signals of the same frequency are out of phase with each other by 90°, a condition known as orthogonality or quadrature. The transmitted signal is created by adding the two carrier signals together. At the receiver, the two signals can be coherently separated (demodulated) because of their orthogonality property.

The QAM signal waveforms may be viewed as combined amplitude (rm) and phase (ϕm) modulation. As described in Proakis ([2]), the signal waveforms may be expressed as

sm(t) = Re[rmejϕmejfct] = rmcos(2πfctm)

• ${r}_{m}=\sqrt{{A}_{mi}^{2}+{A}_{mq}^{2}}$

• ϕm = tan-1(Amq/Ami)