Modulation is a process that alters the characteristics of a carrier wave according to information in the message signal to generate and transmit a modulated wave. There are several different types of modulation.

Unmodulated Carrier Signal

The unmodulated carrier is represented by the following equation:

v ( t ) = A c cos ( 2 π f t + φ )

Amplitude-Modulated Carrier Signal

The amplitude-modulated carrier signal is represented by the following equation:

v ( t ) = ( m ( t ) + A c ) cos ( 2 π f t + φ )

Frequency-Modulated Carrier Signal

The frequency-modulated carrier signal is represented by the following equation:

v ( t ) = A c ( ( m ( t ) + 2 π f ) t + φ )

This yields the following equation:

A c cos ( 2 π f t + φ + ∫ m ( t ) ⅆ t )

Phase-Modulated Carrier Signal

The phase-modulated carrier signal is represented by the following equation:

v ( t ) = A c cos ( 2 π f t + φ + m ( t ) )

where

  • m(t) is the time-varying modulation
  • Ac is the amplitude of the carrier wave
  • f is the frequency of the carrier wave