Pulse Train — Control Systems/Sources

Pulse Train

Control Systems / Sources

A sum of shaped pulses placed at listed offsets – MATLAB's pulstran:

y(t) = Σ a_i · p(t − d_i)

The offsets and their amplitudes are a list, not a period, which is what separates this block from Pulse Generator: the pulses may be irregularly spaced, differently weighted, and of a shape other than rectangular. The train is finite – after the last pulse the output returns to zero and stays there.

Ports

• y – the train, in the amplitudes' own units. Scalar. The block takes no input: it is a source and reads only its own clock.

Parameters

• Pulse Offsets – where the pulses are, in seconds. Either a vector of offsets, each pulse then having unit amplitude, or an N×2 matrix whose first column is the offset and whose second is the amplitude – the two shapes MATLAB's D argument accepts. [1 1; 2 −0.6; 3 0.8] by default: three pulses, the middle one inverted and the last one smaller.
• Pulse Shape – which pulse is placed at each offset:
  • Rectangular – rectpuls: 1 across the width, 0 outside it. ⚠ The leading edge is included and the trailing one is not, which is MATLAB's own asymmetry rather than a rounding here.
  • Triangular – tripuls: rises to 1 at the apex and falls back, the apex placed by Triangular Skew.
  • Gaussian RF – gauspuls: a cosine at Center Frequency (Hz) under a Gaussian envelope whose width follows from Fractional Bandwidth. Unlike the other two it has no edges, so it never reaches exactly zero.
• Pulse Width (s) – the full width of a Rectangular or Triangular pulse. 0.5 by default. Ignored by Gaussian RF, whose width comes from its bandwidth instead.
• Triangular Skew – where the apex sits, from −1 (at the leading edge) through 0 (centred) to +1 (at the trailing edge). 0 by default. Read only by Triangular.
• Center Frequency (Hz) – the cosine carried under the Gaussian envelope. 5 by default. Read only by Gaussian RF.
• Fractional Bandwidth – the envelope's width, as a fraction of the centre frequency, at the −6 dB reference MATLAB uses by default. 0.5 by default; larger is a shorter pulse. Read only by Gaussian RF.
• 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.

Every offset, amplitude and derived coefficient is structural and is inlined into the arithmetic at export time rather than exposed as a tunable parameter: they decide the shape of the signal rather than scaling it, and a core with a different offset list is a different signal. Re-export after changing any of them.

⚠ The three HDL targets are simulation-only, as every source in this library is: they read the testbench's own simulation time rather than counting their own samples, and carry the arithmetic in real, quantising only at the port boundary.

⚠ A pulse edge placed exactly on a sample can differ in the HDL targets. The rectangular pulse's edge test is exact, and the three HDL targets compute time as a real number supplied by the testbench rather than as an exact multiple of the period – so a sample sitting exactly on a leading edge may fall on the other side of it there. Place edges between samples if that matters; the default offsets do.

Simulink bridge

No equivalent (Support::None). Measured rather than assumed: a find_system sweep at depth 6 under masks over 22 DSP System Toolbox libraries plus simulink and simulink_extras on R2026a matches nothing for pulse train or pulstran. Simulink's own Pulse Generator is a different block and is already bridged by Control_Systems/Sources/Pulse_Generator: its pulses are rectangular, identical and periodic, so a mapping onto it would drop the offset list that makes this block what it is. The bridge reports this block rather than dropping it silently, and it therefore has no parity testbench. Code export verification still covers it across all ten languages.

Notes

• Stateless, and a pure function of time: the output at a sample depends on nothing but the clock, so the block carries no state in any of the ten targets and needs no initial condition.
• No state space. The block is not linear in an input – it has no input – so it carries none and model reduction correctly declines to merge it.
• Rectangular and Triangular are bit-exact against MATLAB R2026a and Gaussian RF agrees to one unit in the last place, measured over 60 samples of a four-pulse train. The last is a library difference in exp and cos rather than a difference in the formula.
• ⚠ The triangular apex is its own case, and it is reachable. With a skew of 0 the apex sits exactly at the offset, which every offset that is a whole number of sample periods hits – so the branch runs rather than sitting there for completeness.
• Pulses may overlap, and where they do the amplitudes add. Nothing clips.
• Compare with Pulse Generator for a regular rectangular train, and with Repeating Sequence Stair for an arbitrary waveform given sample by sample.