Spectral baseline distortion simulation - Bruker smile

Question

I work with Magnetic Resonance Spectroscopy data. Data (complex signals) obtained from Bruker scanners (one of the biggest manufacturers of MRS scanners) start with an important group delay - around 60-80 points (in the time domain) - probably due to the fact that they use a long FIR filter.

The effect of this group delay cumulated with some other (unfortunately unknown) problems results in a baseline distortion called Bruker smile/frown. (in the frequency domain, after FFT)

I would like to simulate this kind of distortion (smile or frown). I tried with a bandpass FIR of several taps (80- 140) and I cannot reach this effect. Could you recommend me any way of getting this distortion? Thank you in advance.

Answer 1

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)) +
     rnorm(length(t_index),0, 0.1)

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.