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.

Functions	System objects	Blocks
ammod, amdemod ssbmod, ssbdemod	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) SSB AM Modulator Passband, SSB AM Demodulator Passband
fmmod, fmdemod		FM Modulator Passband, FM Demodulator Passband
pmmod, pmdemod		PM Modulator Passband, PM Demodulator Passband

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(2πf_ct + 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(2πf_ct + 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_ct + θ) ± û(t)sin(f_ct + 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

$$\cos \left(2\pi f_{c}t+2\pi K_c{\displaystyle {\int }_0^{t}u(\tau )d\tau +\theta }\right)$$

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

$$\cos (2\pi f_{c}t+K_{c}u(t)+\theta )$$

where

• f_c represents the carrier frequency.

• θ represents the initial phase.

• K_c represents the phase deviation.

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.

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
DSB AM Modulator Passband, DSB AM Demodulator Passband	Double-sideband amplitude modulation
DSBSC AM Modulator Passband, DSBSC AM Demodulator Passband	Double-sideband suppressed-carrier AM
SSB AM Modulator Passband, SSB AM Demodulator Passband	Single-sideband AM
FM Modulator Passband, FM Demodulator Passband	Frequency modulation
PM Modulator Passband, PM Demodulator Passband	Phase modulation

References

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

Related Topics

• What Is Modulation?
• Analog Passband Modulation Examples
• Analog Baseband Modulation
• Digital Baseband Modulation