Magnitude spectra

The sine-bell, sine-bell squared, phase-shifted sine-bell, and phase-shifted sine-bell squared window functions are generally used in 2D NMR spectroscopy. Each of these has a different effect on the appearance of the peak shape. For all these functions, a certain price may have to be paid in terms of the signal-to-noise ratio, since they remove the dispersive components of the magnitude spectrum. This is illustrated in the following COSY spectra ... 

Magnitude spectrum PoSKer spectrum Baseline correction... 

Note If the FT in ti has been applied with PHmod for Fl accidentally set to no, choose the Magnitude spectrum submenu from the Process pull-down menu and select the command of Fl columns [xfim] for a subsequent magnitude calculation. 

If the real part v(a>) of the NMR spectrum is computed in the absorption (r) mode, the imaginary part is usually displayed in the dispersion (h) mode. The magnitude spectrum is therefore related to the t and u modes as indicated in eq. (1.37). 

Due to the quadratic form of eq. (1.37), the magnitude spectrum is phase independent, and a manipulated signal noise improvement relative to the pure u and v modes is attained (Fig. 2.14). If only magnitude information is desired, phase correction is not necessary, and P(v) can be computed immediately after Fourier transformation. 

The magnitude and phase of the incoming signal are computed on a block-by-block basis using the FFT. The noise magnitude spectrum is calculated as a running average... 

A variant on spectral subtraction is the INTEL technique [Weiss et al., 1975], in which the square root of the magnitude spectrum is computed and the rooted spectrum is then further transformed via a second FFT. Processing similar to that described above is then performed in this pseudo-cepstral domain. The estimate of the speech amplitude function in this domain is transformed back to the magnitude spectral domain and squared to remove the effect of rooting the spectrum. 

First, it is important to appreciate that the detected ion cyclotron signal magnitude is (to a good approximation) directly proportional to the excitation magnitude, as we have previously demonstrated experimentally (13,14). Thus, in contrast to sector or quadrupole mass spectrometers, it is not necessary to compute the detailed trajectories of the ions in order to determine the effect of those trajectories upon the detector. In other words, we need only characterize the excitation magnitude spectrum (i.e., how much power reaches ions at each ICR frequency) in order to know how much signal to expect at the receiver (for a given number of ions at that cyclotron frequency). 

Unfortunately, the result shown in Figure 2 corresponds to time-shared (i.e., essentially simultaneous) excitation/detectlon, so that the (discrete) frequencies sampled by the detector are the same as those initially specified in synthesis of the time-domain transmitter signal. However, FT/ICR is more easily conducted with temporally separated excitation and detection periods. In practical terms, the result is that for FT/ICR, we need to know the excitation magnitude spectrum at all frequencies, not just those (equally-spaced) discrete frequencies that defined the desired excitation spectrum. 

The result for one such apodization function is shown in the right-hand column of Figure 3. The final frequency-domain excitation magnitude spectrum is considerably smoother than without apodization. 

Figure 4. Comparison of a theoretical magnitude-mode excitation spectrum (top) with those detected (on one pair of cell transverse plates) during transmission (on the other pair of cell transverse plates) of a frequency-sweep (middle) or SWIFT (bottom) waveform. The time-domain signals were zero-filled once before Fourier transformation to reveal the full shape of the excitation magnitude spectrum. Note the much improved uniformity and selectivity for SWIFT compared to frequency-sweep excitation.

An alternative is to take die absolute value, or magnitude, spectrum, which is defined by... 

E2.5 Assign as far as possible the COSY spectrum of the aliphatic region of this tripeptide analogue (over the page). Conditions 400 MHz, D2O, magnitude spectrum with coarse digital resolution. 

Alternatively, the magnitude spectrum A(uj) - -iZ>(ft)) can be displayed. Here, however, the linewidth at half height is broader by a factor of 3, so that the spectral resolution is... 

In Check its 2.33.7 and 2.3.3.8 a phase-cycled COSY magnitude spectrum is converted into a gradient selected COSY spectrum. The Check its also show how the choice of either the n- or p-type CT pathways influences the frequency display in the fl dimension. 

Deconvolution of response to frequency-sweep excitation, (a) Cosine Fourier transform of linearly increasing frequency sweep time-domain waveform, (b) Magnitude spectrum of excitation, (c) Cosine Fourier transform of time-domain response to excitation, (d) Magnitude spectrum of response, (e) = (c)/(a). (f) Magnitude spectrum... 

To this stage, we have considered only continuous waveforms and their various Fourier transform spectra. Experimentally, however, it is now usual to obtain a desired point-by-point discrete spectrum by suitable transformation of the point-by-point sampled output of a output of a detector. In this section, we will examine various recipes for relating a discretely sampled response to the desired absorption or magnitude spectrum. 

Figure 7.6 The log magnitude spectrum shows the pattern of harmonics as a series of evenly spaced...

At first sight, this may seem strange as the Fourier Transform for a shifted impulse seems very different for a normal impulse which simply had a Fourier Transform of 1. Recall however, that the magnitude of will be 1, and so the magnitude spectrum will be the same as the delta... 

Figure 10.20, shows the time domain, z-domain pole zero plot and frequency domain magnitude spectrum for this filter with bo = I and a varying over 0.8,0.7,0.6,0.4. Figure 10.20d shows a 3-d z-domain magnitude plot for a single value, oi = 0.7. 

Figure 10.26 Operation of simulated /ih/ vowel filter on square wave. Figure (b) shows the time domain output for the square wave input (a). While the shape of the output is different, it has exactly the same period as the input. Figure (d) is the magnitude spectrum of the square wave. Figure (e) is the magnitude spectrum of the output, calculated by DFT. The harmonics are at the same intervals as the input spectrum, but each has had its amplitude changed. Figure (e) demonstrates that the effect of the filter is to multiply the input spectrum by the frequency response, Figure (c).

Spectra are complex, and are usually represented by the magnitude spectrum and phase... 

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