Analog Amplitude Modulator/Demodulator (ampmodem)

The ampmodem object implements an analog amplitude modulation (AM) modulator/demodulator pair. Two basic transmission schemes are available: single side-band (SSB), and double side-band (DSB). For an input message signal \(-1 \le s(t) \le 1\) , the double side-band transmitted signal is

$$ x_{DSB}(t) = \begin{cases} s(t)e^{j 2 \pi f_c t} & \text{suppressed carrier} \\ \frac{1}{2}\bigl(1+ks(t)\bigr)e^{j 2 \pi f_c t} & \text{unsuppressed carrier} \end{cases} $$

where \(f_c\) is the carrier frequency, and \(k\) is the modulation index. For single side-band, only the upper (USB) or lower half (LSB) of the spectrum is transmitted. The opposing half of the spectrum is rejected using a Hilbert transform (see [ref:section-filter-firhilb] ). Let \(\dot{s}(t)\) represent the Hilbert transform of the message signal\(s(t)\) such that its Fourier transform is non-zero only for positive frequency components, viz

$$ \dot{S}(\omega) = F\left\{ \dot{s}(t) \right\} = \begin{cases} S(\omega) = F\left\{ s(t) \right\} & \omega \gt 0 \\ 0 & \omega \leq 0 \end{cases} $$

Consequently the transmitted upper side-band signal is

$$ x_{USB}(t) = \begin{cases} \dot{s}(t)e^{j 2 \pi f_c t} & \text{suppressed carrier} \\ \frac{1}{2}\bigl(1+k\dot{s}(t)\bigr)e^{j 2 \pi f_c t} & \text{unsuppressed carrier} \end{cases} $$

For lower single side-band, \(\dot{s}(t)\) is simply conjugated. For suppressed carrier modulation the receiver uses a phase-locked loop for carrier frequency and phase tracking. When the carrier is not suppressed the receiver demodulates using a simple peak detector and IIR bias removal filter. An example of the freqmodem interface is listed below.

#include <liquid/liquid.h>

int main() {
    // options
    float mod_index  = 0.1f;                // modulation index (bandwidth)
    int   type       = LIQUID_AMPMODEM_USB; // AM type
    int   suppressed = 0;                   // suppressed carrier?

    // create mod/demod objects
    ampmodem mod   = ampmodem_create(mod_index, type, suppressed);
    ampmodem demod = ampmodem_create(mod_index, type, suppressed);

    float         x;    // original
    float complex y;    // modulated
    float         z;    // demodulated

    // repeat as necessary
    {
        // modulate sample
        ampmodem_modulate(mod, x, &y);

        // demodulate sample
        ampmodem_demodulate(demod, y, &z);
    }

    // destroy objects
    ampmodem_destroy(mod);
    ampmodem_destroy(demod);

    return 0;
}

A more detailed example can be found in examples/ampmodem_example.c located under the main liquid project source directory. Listed below is the full interface to the ampmodem object for analog frequency modulation/demodulation.

• ampmodem_create(k,fc,type,suppressed_carrier) creates and returns an ampmodem object with a modulation index \(k\) , a carrier \(f_c\) , a modulation scheme defined by type , and a binary flag specifying whether the carrier should be suppressed. The modulation type can either be LIQUID_AMPMODEM_DSB (double side-band), LIQUID_AMPMODEM_USB (single upper side-band), or LIQUID_AMPMODEM_LSB (single lower side-band). method.
• ampmodem_destroy(q) destroys an ampmodem object, freeing all internally-allocated memory.
• ampmodem_reset(q) resets the state of the ampmodem object.
• ampmodem_print(q) prints the internal state of the ampmodem object.
• ampmodem_modulate(q,x,*y) modulates the input sample \(x\) storing the output to \(y\) .
• ampmodem_demodulate(q,y,*x) demodulates the input sample \(y\) storing the output to \(x\) .

An example of the ampmodem can be found in[ref:fig-modem-ampmodem]

#include <liquid/liquid.h>

int main() {
    // options
    float mod_index  = 0.1f;                // modulation index (bandwidth)
    int   type       = LIQUID_AMPMODEM_USB; // AM type
    int   suppressed = 0;                   // suppressed carrier?

    // create mod/demod objects
    ampmodem mod   = ampmodem_create(mod_index, type, suppressed);
    ampmodem demod = ampmodem_create(mod_index, type, suppressed);

    float         x;    // original
    float complex y;    // modulated
    float         z;    // demodulated

    // repeat as necessary
    {
        // modulate sample
        ampmodem_modulate(mod, x, &y);

        // demodulate sample
        ampmodem_demodulate(demod, y, &z);
    }

    // destroy objects
    ampmodem_destroy(mod);
    ampmodem_destroy(demod);

    return 0;
}