My guess is that somewhere in the processing you are using an AR (or ARMA) model that is being over / under fitted and that is what is causing the issue.
If I make a fake signal like this in R:
group_delay <- 84
T <- 350
omega <- 2*pi*0.252352890
tau <- 0.005
phi <- 2*pi*0.0989038
t <- 1:T
bruker_signal <- rep(0,T)
t_index <- seq(group_delay, T)
bruker_signal[t_index] <- exp(-(t_index-group_delay)*tau)*(
sin(omega*t_index) + sin(1.5*omega*t_index + phi)) +
i.e. it's a noisy, delayed, damped sum of two sinusoids and then do AR modelling of the spectrum with different orders, then I get something like the smiles / frowns you are seeing.
An earlier attempt I made used a low-pass filtered version of the signal added to the same thing, modulated to $f_s/2$.
smile_filter <- butter(3,0.1)
smile_signal <- filter(smile_filter, bruker_signal)
plot(abs(fft(bruker_signal+2*smile_signal + 2*smile_signal*rep(c(1,-1), lenght.out=T)))[1:175], type='l')
title('Attempt at Smile Spectrum ')
but that seemed way noisier than what you're after.