Gaussian RF Pulse — Control Systems/Waveform Functions

Gaussian RF Pulse

Control Systems / Waveform Functions

A Gaussian envelope carrying a sinusoid of centre frequency fc, evaluated entry by entry and emitted as all three of its parts:

• envelope e = exp(−x² / (2·tv))
• in phase I = e·cos(2π·fc·x)
• quadrature Q = e·sin(2π·fc·x)

The time-domain variance tv is not set directly: it is derived from the frequency-domain specification the parameters state – a fractional bandwidth bw measured at a reference level bwr dB below the peak of the spectrum – as r = 10^bwr/20, fv = −(bw·fc)² / (8·ln r), tv = 1 / (4π²·fv).

Ports

• Input – the argument x of the relations above, of any size [m,n], applied entry by entry. It is a time, in the unit the centre frequency is the reciprocal of.
• Output I – the in-phase pulse I, of the SAME size [m,n]. This is the value MATLAB's gauspuls returns when asked for one output.
• Output Q – the quadrature pulse Q, of the SAME size [m,n]: the same envelope on a carrier a quarter turn behind.
• Output env – the envelope e alone, of the SAME size [m,n], in (0,1]. It is the modulus of the other two taken together.

The block never reshapes a signal: all three outputs carry the input's size.

Parameters

• Center Frequency (Hz) – the carrier frequency fc, a non-negative scalar. Default 1 – MATLAB's gauspuls defaults to 1000 instead, so set 1000 to reproduce a script exactly; at 1 kHz the whole pulse is about a millisecond wide and reads as flat zero at any ordinary step size.
• Fractional Bandwidth – the bandwidth bw as a fraction of the centre frequency, a strictly positive scalar. Default 0.5.
• Bandwidth Reference Level (dB) – the level bwr at which that bandwidth is measured, a strictly NEGATIVE scalar, in dB relative to the peak of the spectrum. Default −6. Zero is rejected: at 0 dB the reference level is the peak itself, ln r is zero, and the bandwidth stops naming a width.
• 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.

All three parameters are structural: twice the time-domain variance and the carrier's angular frequency are folded once at export time and written into the body as decimal literals, so the generated core carries no tunable parameter and never re-derives the variance from the bandwidth. Re-export after changing any of the three.

The three HDL targets are simulation-only. The Q16.16 datapath carries neither an exponential nor a sine, and the squared argument inside the envelope spans a range sixteen fractional bits cannot hold, so the generated cores convert at the port boundary and evaluate in real arithmetic – correct in simulation, but not offered as synthesizable.

Simulink bridge

None. The Simulink standard library has no Gaussian RF pulse block: MathWorks offers it as the Signal Processing Toolbox function gauspuls, which is not a block and has no library path a diagram could name. A model carrying this block is reported rather than silently dropped when it crosses, and none of its configuration crosses either – "Center Frequency (Hz)", "Fractional Bandwidth", "Bandwidth Reference Level (dB)" and "Sampling Time (s)" have no counterparts to be written to.

Notes

• Algebraic, with no state: the outputs depend only on the current input.
• Not linear, so the block deliberately carries no state space and model reduction reports it as unmergeable.
• Three outputs rather than three blocks. The envelope is common to all three parts, and splitting them would evaluate the same exponential more than once – agreeing to within the last bit rather than exactly.
• The envelope never reaches zero: it decays without bound but stays strictly positive, so a pulse "ends" only at the precision of the arithmetic.