Real FID

Now we can construct a perfectly balanced real and imaginary FID from these signals by combining all the sine functions into a real FID and all the cosine functions into an imaginary FID ... 

The chemical-shift evolution during the FID is taken care of by the exponential term in 2b t2, with a positive exponential because it is the 1 that is evolving. In this complex arithmetic, the real part corresponds to the real FID in t2 (Mx component in the rotating frame) and the imaginary part is the imaginary FID in t2 (My component). We can substitute sines and cosines for the imaginary exponentials as... 

Now we have exactly the same kind of data we have with States mode acquisition cosine modulation in t for the real FID and sine modulation in ti for the imaginary FID. In I2 we can equate Mx with the real part and My with the imaginary part, so that in each case we have Mx = —sin(f2bD) and My = cost f2b/2). This represents a vector starting on the y axis at t2 = 0 and rotating counter clockwise (positive offset 2) at the rate of f2b rad s-1. Once these rearrangements have been made in the computer, the data is processed just like States data, with a complex Fourier transform in t. ... 

The first Fourier transformation of the FID yields a complex function of frequency with real (cosine) and imaginary (sine) coefficients. Each FID therefore has a real half and an imaginary half, and when subjected to the first Fourier transformation the resulting spectrum will also have real and imaginary data points. When these real and imaginary data points are arranged behind one another, vertical columns result. This transposed data... 

Figure 3.5 Schematic representation of data processing in a 2D experiment (one zero-filling in and two zero-fillings in F ). (a) A(, FIDs composed of Afj quadrature data points, which are acquired with alternate (sequential) sampling, (b) On a real...

At the end of the 2D experiment, we will have acquired a set of N FIDs composed of quadrature data points, with N /2 points from channel A and points from channel B, acquired with sequential (alternate) sampling. How the data are processed is critical for a successful outcome. The data processing involves (a) dc (direct current) correction (performed automatically by the instrument software), (b) apodization (window multiplication) of the <2 time-domain data, (c) Fourier transformation and phase correction, (d) window multiplication of the t domain data and phase correction (unless it is a magnitude or a power-mode spectrum, in which case phase correction is not required), (e) complex Fourier transformation in Fu (f) coaddition of real and imaginary data (if phase-sensitive representation is required) to give a magnitude (M) or a power-mode (P) spectrum. Additional steps may be tilting, symmetrization, and calculation of projections. A schematic representation of the steps involved is presented in Fig. 3.5. 

The second time variable, is the so called real-time variable, representing the time spent in data acquisition, while ti is the evolution interval between the two pulses during the experiment. The effect of can only be observed indirectly by noting its influence on It is therefore necessary to carry out F2 transformation first, in order to generate a series of spectra (rows of the matrix), which is then used as a pseudo-FID for F] transformation in the second step. 

The frequency-domain spectrum is computed by Fourier transformation of the FIDs. Real and imaginary components v(co) and ifi ct>) of the NMR spectrum are obtained as a result. Magnitude-mode or powermode spectra P o)) can be computed from the real and imaginary parts of the spectrum through application of the following equation ... 

Real and imaginary parts Two equal blocks of frequency that result from Fourier transformation of the FIDs. 

K X 512 real data points with zero-filling applied in the dimension to 2 K data points. For eaeh inerement 16 or 32 FID s were aeeumulated with a relaxation delay of 2 s. 

Real/Imag Toggles between display of the real and imaginary parts of the spectrum or FID. 

Load the ID H FID of peracetylated glucose D NMRDATA GLUCOSE 1D H GH 001001. FID, increase its vertical scale and inspect its last part on the screen. Notice the deviation of the mean FID from the zero horizontal line switch back and forth between the real and the imaginary part of the FID to recognize a DC offset between the two parts. From the Process pull-down menu choose the DC Correction option and apply a DC correction. Inspect the last part of the FID again. Fourier transform the FID with/without a DC... 

The real and imaginary spectra obtained by Fourier transformation of FID signals are usually mixtures of the absorption and dispersion modes as shown in Fig. 2.13 (a). These phase errors mainly arise from frequency-independent maladjustments of the phase sensitive detector and from frequency-dependent factors such as the finite length of rf pulses, delays in the start of data acquisition, and phase shifts induced by filtering frequencies outside the spectral width A. 

Figure 3. The acquired NMR signal (a), Free Induction Decay (FID) in the time domain response.Two transient signals each 90° out of phase comprise the real and imaginary part of the FID (b), its frequency domain response using Fburier transformation.

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