Fig. 2

In vitro proton MRS and dMRS for samples of human biofluids: malignant ovarian cyst (serous cystadenocarcinoma) from a patient. The input time signal is the average of 128 FID transients encoded at a Bruker 600 MHz (\(\approx 14.1\)T) spectrometer [30]. In a narrow band with the choline compounds as recognized cancer biomarkers for the ovary, the focus is on the derivative fast Fourier transform, the dFFT: optimized versus unoptimized. Unnormalized nonderivative FFT (\(m=0\)) using (7) as: (a) Real part mode and (b) magnitude mode. Panels (c-h): normalized derivative spectra (\(m=1-5\)) in the magnitude mode. Optimized dFFT using (1) for the APEF (2) with \(\alpha =3\) in (3): \(m=1\) (c), \(m=2\) (d), \(m=3\) (e), \(m=4\) (f) and \(m=5\) (g). Unoptimized dFFT using (7): \(m=5\) (h). The spectral intensities on the ordinates are in arbitrary units (au). Resonance frequencies (chemical shifts) on the abscissae are dimensionless units, parts per million (ppm). For details, see the text (color online)