Modulator — Control Systems/Waveform Functions

Modulator

Control Systems / Waveform Functions

Puts a message signal onto a carrier, one sample at a time. The carrier phase is θ[k] = 2πF_c·k·T_s and f is the carrier function (cosine or sine); the method decides what is done with it:

• AM suppressed carrier – y = x·f(θ). The carrier disappears when the message does.
• AM transmitted carrier – y = (x − c)·f(θ), with c the Carrier Offset. Shifting the message so it never changes sign leaves a carrier present at all times, which is what an envelope detector needs.
• PM – y = f(θ + k_p·x). The message moves the phase; the amplitude never changes.

These are the three methods of MATLAB's modulate that produce one output sample per input sample. The rest are covered elsewhere or cannot stream – see Notes.

Ports

• x – the message, scalar. In the two AM methods it is the amplitude the carrier is multiplied by, so its units are the output's; in PM it is multiplied by the phase deviation and so is a phase in radians before it reaches the carrier. Any value is accepted.
• y – the modulated carrier, scalar. In PM it never leaves [−1, +1]; in the AM methods its size follows the message's.

Parameters

• Modulation – which of the three relations above is computed.
  • AM suppressed carrier – y = x·f(θ), the default. This is modulate's 'am' and its 'amdsb-sc': the two are one branch of the function and return identical values, so one setting covers both.
  • AM transmitted carrier – y = (x − c)·f(θ), 'amdsb-tc'. Reads Carrier Offset.
  • PM – y = f(θ + k_p·x), 'pm'. Reads Phase Deviation (rad).
• Carrier Frequency (Hz) – F_c. Any real value; a negative one runs the phase backwards. A frequency at or beyond half the block's sampling rate aliases, as any sampled oscillation does – MATLAB's function refuses that case outright and this block does not, because the rate is the model's rather than an argument.
• Carrier Function – cos (MATLAB's, and the default) or sin, the same carrier a quarter cycle later. It is a setting rather than a fixed cosine so that a quadrature pair can be built from two of these blocks – see Notes.
• Carrier Offset – c, subtracted from the message before it multiplies the carrier. Read by AM transmitted carrier only, and ignored by the other two. MATLAB's function defaults it to the smallest sample of the whole message; a block that sees one sample at a time cannot know that number, so it is entered here.
• Phase Deviation (rad) – k_p, radians of carrier phase per unit of message. Read by PM only, and ignored by the other two. MATLAB's function defaults it to π divided by the largest magnitude in the whole message – again a number a streaming block cannot have – so it is entered here.
• Sampling Time (s) – zero or less inherits the solver's rate; a positive value runs the block at that period.

Code export

All ten targets: Python, MATLAB, Java, Rust, C, C++, VHDL, Verilog, SystemVerilog and PLC Structured Text.

Everything except the message is structural and is inlined at export time: the carrier step folds the frequency together with the block's own period, and the offset, the deviation and the choice of method and carrier function all become part of the emitted arithmetic rather than tunable parameters. The period is inside the carrier step, so a core exported at one rate does not carry the frequency to another – re-export after changing either.

The three HDL targets are simulation-only, and only because of the trigonometric call: the phase, its wrap and the product all stay in the Q16.16 datapath and just the carrier value converts at the port boundary and evaluates in real. A synthesizable carrier is a phase accumulator driving a lookup table, which is a different block.

Simulink bridge

No equivalent (Support::None). modulate is a Signal Processing Toolbox function, and that toolbox ships no Simulink library at all. The modulator blocks in the installed libraries belong to Communications Toolbox and are different blocks – they carry symbol mapping, pulse shaping and a complex baseband convention that this block does not – so mapping onto one would misreport what crossed. The bridge reports this block instead, and it carries no parity testbench; code export verification covers it across all ten languages.

Notes

• Stateful (one phase register) and discrete by nature (setDiscreteOnlyBlock(true)): the carrier advances once per sample.
• The first output sits at θ = 0, as modulate's first sample sits at t = 0. The carrier step is added after the sample is produced, never before.
• The carrier is accumulated, not multiplied out. θ is a running sum wrapped into 0, 2π) rather than 2πF_ct computed from a growing t. The two agree to 2.2×10⁻¹⁶ over 8 samples and 2.9×10⁻¹⁴ over 500, measured at F_c = 3.4 Hz and T_s = 0.01 s; the accumulator is what keeps the argument inside the range the HDL cores carry.
• QAM is two of these blocks. modulate's 'qam' is x·cos(θ) + x₂·sin(θ) over two messages: one modulator with Carrier Function cos, one with sin, and a Sum. That is why the carrier function is a setting.
• FM is the Voltage Controlled Oscillator in this same family, which is modulate(…, 'fm') exactly – vco is implemented by calling it. Reach for that block rather than looking for an FM setting here.
• PWM is the PWM block under Discontinuities, which is that method with the duty arriving on a port and one output sample per input sample.
• Three methods are deliberately absent. 'amssb' needs the analytic signal of the whole message, which one sample cannot form; 'ptm' and 'ppm' emit F_s/F_c samples for every message sample, so they change the signal's rate where this block produces one output per input.
• Scalar only: one message, one carrier phase. Wire one block per channel, so that two channels cannot silently share a phase.
• No state space. The block multiplies its input by a time-varying quantity (and in PM is not even linear in it), so it carries none and model reduction correctly declines to merge it.