Many ways exist to modulate a message signal m(t) to produce a modulated (transmitted) signal x(t). For amplitude, frequency, and phase modulation, modulated signals can be expressed in the same form as
where A(t) is a real-valued amplitude function (a.k.a. the envelope),
is the carrier frequency, and
is the real-valued phase function.
Using this framework, several common modulation schemes are described below:
h(t) is the impulse response of a bandpass filter or phase
shifter to effect a cancellation of one pair of redundant sidebands.
For ideal filters and phase shifters, the modulation is amplitude modulation
because the phase would not carry any information about m(t).
Note that there is one more variant of amplitude modulation known
as vestigal sideband modulation in which the upper sideband is kept
and a fraction of the lower sideband is kept or vice-versa.
Each TV channel is allocated a bandwidth of 6 MHz. The picture intensity and color information are transmitted using vestigal sideband modulation. The audio portion is frequency modulated.
The quantity
is known as the complex envelope, where
is called the in-phase component and
is called the quadrature component.
Both and are lowpass signals, and hence,
the complex envelope 
is a lowpass signal.
An alterative representation for the modulated signal x(t) is
