## Analog Passband Modulation

In most media for communication, only a fixed range of frequencies is
available for transmitting messages. One way to communicate a message whose
frequency spectrum does not fall within that fixed frequency range, or one
that is otherwise unsuitable for the channel, is to alter a carrier signal
according to the information in your message signal. This alteration is
called *modulation*. The transmitter sends the
modulated symbols. The receiver then recovers the original message symbols
through a process called *demodulation*.

### Modulation Methods

*Analog passband modulation* modulates analog
transmission signals into sinusoidal waveforms. Communications Toolbox™ software provides features to apply a variety of
analog passband modulation methods. The process by which a carrier
signal is altered according to information in a message signal
depends on the modulation method applied. The general form of the
carrier signal, *s*(*t*), is

*s*(*t*) =
*A*(*t*)cos[2π*f*_{0}*t*+ϕ(*t*)]

The information-carrying component is the amplitude
(*A*), frequency
(*f*_{0}), or phase (ϕ)
individually, or in combination. To satisfy the Nyquist criterion
when simulating analog modulation systems, the sample rate of the
system must be greater than twice the sum of the carrier frequency
and the signal bandwidth. For more information, see Baseband vs. Passband Simulation.

You can design your analog modulation system using these passband methods.

Functions | System objects | Blocks |
---|---|---|

None | Double-sideband AM (DSB AM) DSB AM Modulator Passband, DSB AM Demodulator Passband Double-sideband suppressed-carrier AM (DSB-SC AM) DSBSC AM Modulator Passband, DSBSC AM Demodulator Passband Single-sideband amplitude modulation (SSB AM) | |

### Filter Design Decisions

Unless otherwise indicated by filtering configuration controls, the
features for passband modulation and demodulation do not perform
pulse shaping or filtering. After demodulating a signal, you might
want to filter out the carrier signal. You can select a particular
filter, such as `butter`

, `cheby1`

, `cheby2`

, and
`ellip`

, on the
mask of the demodulator block. Different filtering methods have
different properties, and you might need to test your application
with several filters before deciding which is most suitable.

### DSB AM

Analog passband DSB AM modulates using double-sideband amplitude modulation. The output is a passband representation of the modulated signal. Both the input and output signals are real scalar signals.

For an input *u*(*t*) varying as a function of time *t*, then the output is

(*u*(*t*) +
*k*)cos(2π*f*_{c}*t* + θ)

where

*k*represents the input signal offset and is commonly set to the maximum absolute value of the negative part of the input signal*u*(*t*).*f*_{c}represents the carrier frequency.θ represents the initial phase.

Typically, an appropriate carrier frequency is much higher than the
highest frequency of the input signal. By the Nyquist sampling
theorem, 1 / *T*_{s}
>
*f*_{c}, where
*T*_{s} represents the
sample time of the input signal.

### DSB-SC AM

Analog passband DSB-SC AM modulates using double-sideband suppressed-carrier amplitude modulation. The output is a passband representation of the modulated signal. Both the input and output signals are real scalar signals.

For an input *u*(*t*) varying as a function of time *t*, then the output is

*u*(*t*)cos(2π*f*_{c}*t* + θ)

where

*f*_{c}represents the carrier frequency.θ represents the initial phase.

Typically, an appropriate carrier frequency is much higher than the
highest frequency of the input signal. By the Nyquist sampling
theorem, 1 / *T*_{s}
>
*f*_{c}, where
*T*_{s} represents the
sample time of the input signal.

### SSB AM

Analog passband SSB AM modulates using single-sideband amplitude modulation. The output is a passband representation of the modulated signal. Both the input and output signals are real scalar signals.

SSB AM transmits either the lower or upper sideband signal, but not both.

If the input is *u*(*t*) varying as a function of time
*t*, then the output
is

(*u*(*t*)cos(*f*_{c}*t* + θ) ±
*û*(*t*)sin(*f*_{c}*t* + θ)

where

*f*_{c}represents the carrier frequency.θ represents the initial phase.

*û*(*t*) represents the Hilbert transform of the input*u*(*t*).For ±, the minus sign indicates the upper sideband and the plus sign indicates the lower sideband.

### FM

Analog passband FM modulates using frequency modulation. The output is a passband representation of the modulated signal. The output signal's frequency varies with the input signal's amplitude. Both the input and output signals are real scalar signals.

If the input is *u*(*t*) varying as a function of time
*t*, then the output
is

$$\mathrm{cos}\left(2\pi {f}_{c}t+2\pi {K}_{c}{\displaystyle {\int}_{0}^{t}u(\tau )d\tau +\theta}\right)$$

where

*f*_{c}represents the carrier frequency.θ represents the initial phase.

*K*_{c}represents the frequency deviation.

Typically, an appropriate carrier frequency is much higher than the
highest frequency of the input signal. By the Nyquist sampling
theorem, 1 / *T*_{s}
>
*f*_{c}, where
*T*_{s} represents the
sample time of the input signal.

### PM

Analog passband PM modulates using phase modulation. The output is a passband representation of the modulated signal. The output signal's phase varies with the input signal's amplitude. Both the input and output signals are real scalar signals.

If the input is *u*(*t*) varying as a function of time
*t*, then the output
is

$$\mathrm{cos}(2\pi {f}_{c}t+{K}_{c}u(t)+\theta )$$

where

*f*_{c}represents the carrier frequency.θ represents the initial phase.

*K*_{c}represents the phase deviation.

*T*_{s}
>
*f*_{c}, where
*T*_{s} represents the
sample time of the input signal.

### Accessing Analog Passband Modulation Blocks

In Simulink^{®}, open the **Analog Passband
Modulation** sublibrary by double-clicking its icon
in the **Modulation** library. The **Analog
Passband Modulation** sublibrary contains
modulator-demodulator block pairs for these modulation
methods.

Block Pair | Modulation Methods |
---|---|

Double-sideband amplitude modulation | |

Double-sideband suppressed-carrier AM | |

Single-sideband AM | |

Frequency modulation | |

Phase modulation |

### References

[1] Peebles, Peyton Z, Jr. *Communication
System Principles*. Reading, MA: Addison-Wesley, 1976.