Pattern: Shape Generator

Introduced in version 3.8.0

When shape selection is Expression with 5 parameters, the pulse shape will be generated from the provided expression.

Variables and functions are complex. Calculations are performed with time resolution provided by AWG. IMPORTANT: Trigonometric functions are defined in fractions of 2*pi, not radians, e.g. sin(0.25) = 1. Hyperbolic functions have standard definitions.

Built-in variables

t — absolute time within pulse sequence (vector)
t0 — time from the beginning of the pulse (vector)
tp — pulse length (scalar)
j — complex unit (0 + 1j, scalar)
par1 … par5 — parameters specified in PPL (scalars)

Built-in functions

cos(x) — cos(2*pi*x) cosine
sin(x) — sin(2*pi*x) sine
tan(x) — tan(2*pi*x) tangent
sec(x) — sec(2*pi*x) secant
exp(x) — exp(2*pi*x) complex exponent (use exp(j*t*f) syntax for IQ)
cosh(x) — cosh(x) hyperbolic cosine
sinh(x) — sinh(x) hyperbolic sine
tanh(x) — tanh(x) hyperbolic tan
sech(x) — sech(x) hyperbolic sec
exph(x) — exp(x) complex exponent (2*pi factor is not used)
gaussian(x,x0,w) — Gaussian with width w centered at x0
sinc(x,x0,tp) — sinc with first lobe at 2/tp centered at x0
chirp(x,fw,tp) — linear frequency sweep of width fw spread over tp, no carrier
chirp(x,f0,fw,tp) — the same sweep around carrier frequency f0
wurst(x,fw,tp,n) — WURST: the same sweep with the smoothly truncated WURST envelope of power n, no carrier
wurst(x,f0,fw,tp,n) — the same pulse around carrier frequency f0

Introduced in version 3.8.7

chirp sweeps the instantaneous frequency from -fw/2 at x = 0 to +fw/2 at x = tp, which is the phase of the built-in Chirp shape. Keep the carrier out of it (3 arguments) and write it as exp(j*par1*t) when the pulse has to stay phase coherent with the rest of the sequence — the sweep itself is referenced to the pulse start, t0, while the carrier is referenced to t.

wurst is that sweep multiplied by the WURST amplitude 1-|cos(pi*x/tp)|^n, reproducing the built-in WURST shape. The envelope is zero at both pulse edges and flattens near the top as n grows; n is limited to the 1…100 range of the built-in shape. Carrier handling is the same as for chirp. Setting fw to 0 removes the sweep and leaves the bare envelope, which is useful as a soft-edged replacement for a square pulse.

Example:

exp(j*par1*t) * sin(0.5*t0/tp) - IQ RF pulse sin(par1*t) * gaussian(t0, 0.5*tp, 0.1*tp) - Gaussian RF pulse exp(j*par1*t) * sinc(t0, tp/2, tp) - Sinc RF pulse exp(j*par1*t) * chirp(t0, par2, tp) - chirp, par1 carrier, par2 sweep width chirp(t0, par1, par2, tp) - chirp, phase referenced to the pulse gaussian(t0, tp/2, tp/6) * exp(j*par1*t) * chirp(t0, par2, tp) - apodized chirp exp(j*par1*t) * wurst(t0, par2, tp, 20) - WURST, par1 carrier, par2 sweep width wurst(t0, par1, par2, tp, 20) - WURST, phase referenced to the pulse exp(j*par1*t) * wurst(t0, 0, tp, 20) - WURST envelope only, no sweep