Nonlinear least-squares fitting frequency domain

Nonlinear least-squares fitting in the frequency domain... 

The procedure was tested on simulated time domain MRS data where the model data consisted of metabolite peaks at 3.2, 3.0 and 2.0 ppm representing choline, creatine and IV-acetylaspartate (NAA) respectively, with corresponding values of Ak of 1.0, 1.0 and 3.0 units.89 White noise of specified standard deviation, crt, was then added. The Levenberg-Marquardt method requires suitable initial values for each of the nine parameters being fitted. The initial values of the three frequencies were taken as their known values. An exponentially decaying curve with a constant offset parameter was fitted, using a nonlinear least-squares fit, to the envelope of the free induction decay, Mv(t), in order to obtain an initial value for T and for the amplitudes, each of which was taken to be one-third of the amplitude of the envelope. The constant offset was added to account for the presence of the noise. 

Varian VXR 500 NMR spectrometer operating at a proton frequency of 500 MHz. The spectral width was 6000 Hz with the carrier frequency at the HDO resonance. The solvent resonance was suppressed by presaturation. Each FID was composed of 16 k data points with 80 transients. The delay between successive transients was 2.8 s. The time domain data were processed by zero-filling to 32 k points, exponential multiplication (0.5 Hz) and Fourier transformation. Chemical shifts were referenced to internal sodium 3-(trimethylsilyl)-propionate-2,2,3,3-d4. The Kj values were obtained by nonlinear least square fit of the data to the equation... 

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