SSB AM Modulator Passband

Modulate using single-sideband amplitude modulation

• 

Libraries:
Communications Toolbox / Modulation / Analog Passband Modulation

Description

The SSB AM Modulator Passband block modulates a signal using single-sideband amplitude modulation with a Hilbert transform filter. Both the input and output signals are real scalar signals.

Examples

SSB-Modulate and -Demodulate Passband Signal in Simulink

Sample a 100 Hz input signal at 8000 samples per second. Modulate the input signal using the single-sideband amplitude modulation method with a Hilbert transform filter of order 100. Demodulate the signal. Plot the input signal, the modulated signal, and the demodulated signal.

The ssb_response model modulates a signal using single-sideband amplitude modulation with a Hilbert transform filter and a carrier frequency of 2000 Hz and then demodulates the signal. When the model runs, it plots the signals. The model samples a 100 Hz linear frequency sweep chirp with a 400 Hz target frequency at 8000 samples per second. This configuration ensures the Hilbert transform filter operates in the flat section of the magnitude response and that the modulated signal has the desired magnitude and form.

Run the model with the SSB AM Modulator Passband block configured to modulate the upper sideband. Plot the input signal, the modulated upper sideband, and the demodulated signal by using a spectrum analyzer.

Reconfigure the SSB AM Modulator Passband block to modulate the lower sideband and plot the signals again.

Limitations

• This block does not work inside a triggered subsystem.

Ports

Input

In — Input signal

scalar

Input signal, specified as a scalar.

This port is unnamed on the block.

Data Types: double

Output

Out — Output signal

scalar

Output signal, returned as a scalar. The output is a passband representation of the modulated signal.

This port is unnamed on the block.

Data Types: double

Parameters

To edit block parameters interactively, use the Property Inspector. From the Simulink^® Toolstrip, on the Simulation tab, in the Prepare gallery, select Property Inspector.

Carrier frequency (Hz) — Carrier frequency in Hz

300 (default) | positive scalar

Carrier frequency in Hz, specified as a positive scalar.

Due to the implementation of the Hilbert transform by means of a filter, for best results, choose a carrier frequency, f_c, that exceeds the sample rate of the input signal by at least 10%. For more information, see Hilbert Transform Filter.

Typically, an appropriate carrier frequency is a much higher than the highest frequency of the input signal. By the Nyquist sampling theorem, 1 / T_s > (2 × f_c), where T_s represents the sample time of the input signal. For more information, see Baseband vs. Passband Simulation.

Initial phase (rad) — Initial phase offset in radians

0 (default) | scalar

Initial phase offset of the modulated signal in radians, specified as a scalar.

Sideband to modulate — Sideband to modulate

Upper (default) | Lower

Sideband to modulate, specified as Upper or Lower.

Hilbert Transform filter order (must be even) — Hilbert transform filter order

100 (default) | positive scalar

Hilbert transform filter order, specified as an even, positive scalar with a value greater than 2. This parameter value defines the length of the FIR filter used to compute the Hilbert transform.

Block Characteristics

Data Types	double
Multidimensional Signals	no
Variable-Size Signals	no

Algorithms

The SSB AM Modulator Passband block transmits either the lower or upper sideband signal, but not both. To control which sideband it transmits, use the Sideband to modulate parameter.

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

$$u(t)\cos (f_{c}t+\theta )\mp \widehat{u}(t)\sin (f_{c}t+\theta )$$

where:

• f_c represents the Carrier frequency (Hz) parameter.

• θ represents the Initial phase (rad) parameter.

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

• The minus sign indicates the upper sideband and the plus sign indicates the lower sideband.

Hilbert Transform Filter

To design the Hilbert transform filter, this block uses the Analytic Signal block, which computes the complex analytic signal corresponding to each channel of the real M-by-N input, u

$$y=u+j{\rm H}\left\{u\right\}$$

where $$j=\sqrt{-1}$$ and $${\rm H}\left\{\right\}$$ denotes the Hilbert transform. The real part of the output in each channel is a replica of the real input in that channel. The imaginary part is the Hilbert transform of the input. In the frequency domain, the analytic signal retains the positive frequency content of the original signal while zeroing-out negative frequencies and doubling the DC component.

The block computes the Hilbert transform using an equiripple FIR filter with the order that you specify using the Hilbert Transform filter order (must be even) parameter, n. This linear phase filter uses the Remez exchange algorithm and imposes a delay of n/2 on the input samples.

Because the block uses this filter, it requires a carrier frequency that exceeds the sample rate of the input signal by at least 10%.

For example, this plot shows the response for a 10 Hz input signal at 8000 samples per second passed through a Hilbert transform filter of order 100.

A carrier frequency that is 10% to 90% higher than the sample rate of the input signal, ensures that the Hilbert transform filter operates in the flat section of its magnitude response (shown in blue) and that the modulated signal has the desired magnitude and form.

References

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

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced before R2006a