Accurate Quantification of 1H Spectra: From Finite Impulse Response Filter Design for Solvent Suppression to Parameter Estimation

MR spectroscopy quantitation: a review of time‐domain methods

“…This issue was pursued in Craven and Waltho et al 73 where the FIR filter ability to suppress entire peaks including their frequency domain 'tails' was pointed out using relations in the frequency domain. The same point was made for the time domain in Sundin et al 72 where the derivations show that the FIR filters have the ability to completely remove spectral lines in the stop band while not altering the magnitude of the spectral lines in the passband. Note that suppressing entire peaks including their large frequency domain 'tails' is something that cannot be done by simple operations in the frequency domain.…”

“…Finally the extrapolation of the data (using linear extrapolation or linear prediction methods) introduces distortions in the first and last (M À 1)/2 samples. In Sundin et al 72 a scheme to handle the above problems was proposed. The filters used are in this case high-pass filters designed to suppress the water signal as opposed to the low-pass filters in Marion et al 70 designed to suppress the high frequency metabolite peaks.…”

“…The h T b k scalar is a function of the filter coefficients, the damping and the frequency of the individual sinusoids. The derived model allows one to correct the final parameter estimates or alternatively, as proposed in Sundin et al, 72 to use the altered model function in combination with an iterative time-domain quantitation algorithm (based on the numerical solver used in the AMARES algorithm). This improves the accuracy of the final parameter estimates and ensures the correct incorporation of prior knowledge in the estimation procedure.…”

“…The filter methods need to be modified primarily in the filter design step to allow more flexibility in the design of the filter. The maximum phase filter proposed in Sundin et al 72 to suppress the water resonance is generalized in Vanhamme et al 80 to suppress any region in the spectrum. For the model based methods such as HSVD it is only necessary to redefine the frequency regions containing the nuisance peaks.…”

“…The starting time and zero order phase are estimated. The signal is filtered with a maximum-phase FIR filter 72 and the filter effect is included in the formulation of the NLLS problem. The resulting fit is shown in Fig.…”