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[2πf0t+ϕ(t)]

The information-carrying component is the amplitude (A), frequency (f0), 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.

FunctionsSystem objectsBlocks

None

Double-sideband AM (DSB AM)

Double-sideband suppressed-carrier AM (DSB-SC AM)

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(2πfct + 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).

• fc 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 / Ts > fc, where Ts 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(2πfct + θ)

where

• fc 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 / Ts > fc, where Ts 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(fct + θ) ± û(t)sin(fct + θ)

where

• fc represents the carrier frequency.

• θ represents the initial phase.

• û(t) represents the Hilbert transform of the input u(t).

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

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

where

• fc represents the carrier frequency.

• θ represents the initial phase.

• Kc 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 / Ts > fc, where Ts 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

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

where

• fc represents the carrier frequency.

• θ represents the initial phase.

• Kc represents the phase deviation.

Typically, an appropriate carrier frequency is much higher than the highest frequency of the input signal. By the Nyquist sampling theorem, 1 / Ts > fc, where Ts 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 PairModulation 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, Mass.: Addison-Wesley, 1976.