# Free Induction Decay

When you open an experimental spectrum, not yet processed, you see a characteristic shape that soon becomes familiar: the Free Induction Decay (FID). It is a sum of audio-wave signals that contain all the information in an NMR spectrum. There is a strict analogy between NMR and radio broadcasting: music and speech travel as radio-waves, but what we are interested into is the sound (audio-waves). In NMR we perform a further step: we visualize the sound as a plot of intensity vs. frequency. The reason is that we sort, in this way, peaks according to their frequency and our mind has a simpler job to do. The correct terminology is: “passing from time domain into frequency domain”. The operation to pass from one domain into the other is called “Fourier Transform”, opportunely abbreviated as FT.

Even if you never observe the FID directly, there is one thing you better know about it. It is not merely a drawing, but a sequence of numbers. The drawing is merely a graphical summary. Because these numbers originate from a digital device (the analog-to-digital converter) they are, de facto, integer numbers, but they are never considered as such. Both the FT and another important operation, called “Phase Correction”, operate on Complex Numbers. This is why you and your software must conceptualize the FID as a sequence of complex numbers. Otherwise the software can't do nothing and you can't understand what it's doing.

The complex numbers contains two components, arbitrarily called the real and imaginary component. Don't let those terms mislead you. In the case of the FID, both components are experimental data of the same importance. iNMR always shows the real part only, but you can swap the two components. The old imaginary part becomes real and thus becomes visible. This is an example of phase correction. In general, changing the phase consists in mixing the two components in given proportions.

The same information contained into the two components can be recombined differently, using the so called Magnitude Representation, in which the two components are appropriately called module (or absolute value) and phase. The module is the intensity of a signal, while the phase indicates its relation with the rest of the spectrum. In our lives we go through up and downs. The same happens with audio-waves like NMR signals, but in a much more predictable fashion. The spectroscopist can tolerate these ups and downs, as long as all the signals go simultaneously up and simultaneously down. This ideal situation is called “being in phase”. When a spectrum is impossible to phase, you can turn to magnitude representation. The iNMR command to do this is ‘Process/Magnitude’ and it is reversible (just select it again). When in this representation, peaks acquire a less elegant shape, with larger tails. In today's practice only the COSY and some hetero-2D experiments need magnitude representation. To compensate for the bad shapes, they prefer a sine bell apodization.

After you have completed FT and Phase Correction, you don't need complex numbers anymore. Normally you store into the real component the well-shaped symmetric component of the spectrum. It is called the absorption signal (opposed to the dispersion signal, anti-symmetric). The imaginary part is either deleted (to recycle computer memory) or just forgotten.

## Close Inspection

Advanced users may want to examine the FID in detail, both its real and imaginary part. Apparently iNMR only allows the panoramic view of the real part, yet there is a back-door. The FT dialog contains the command “Fake”. After it, iNMR skips the FT but pretends it has been performed. The user can zoom in, pan and even phase correct the FID data points, using the same commands normally available for the frequency domain spectrum.