Free induction decay in NMR (as stated in Pavia)

There is a statement in a very popular textbook of spectroscopy by Pavia (Chapter 3, Intro. to Spectroscopy), it says "The observed FID is actually an interference signal between the radiofrequency source (300 MHz in this case) and the frequency emitted by the excited nucleus"

As per my understanding this statement is not fully correct, as the free induction decay signal is acquired after the excitation pulse is turned off. Does anyone know if there is a overlap in timings of pulse excitation and signal acquisition?

• AFAIK, the signal from the nuclei must be mixed with a signal at the reference frequency (300 MHz) before it can be digitised. So the FID no longer contains the frequency of the nucleus (300 MHz +/- a bit), but rather the offset frequency (0 +/- a bit). The reference frequency signal would come from the rf source. See eg Levitt Spin Dynamics 2ed §4.5. – orthocresol Apr 23 at 23:55
• Thanks for that book. Nobody ever talks in that level of detail. So I gather that is "down conversion" of raw data. The interference pattern has a fundamental original from the de-phasing of the precessing nuclei. Do you think this is correct? This down conversion protocol is a signal processing approach. Levitt writes "A similar procedure takes place in an ordinary radio receiver. In that case, the modulated r.f. waves, travelling through space, are detected and down- converted to the audible frequency range, where they are transformed into mechanical oscillations to generate sound. " – M. Farooq Apr 24 at 1:42
• As it is not really practicable to digitise 300MHz or higher frequencies as @orthocresol states the 300MHz is mixed with the signal from the experiment (which is at almost the same frequency) and the difference frequency, now in the KHz region, is digitised instead. – porphyrin Apr 24 at 7:21
• Thanks @porphyrin. It makes sense what Pavia is trying to say, but do you agree that FID is not an interference pattern formed by mixing this reference frequency and the frequency emitted by precessing nuclei? – M. Farooq Apr 24 at 12:14
• Not really interference as the two signals are multiplied together not added. For example if they are sine waves then the product is two cosine waves, one of the sum and one of difference frequency. The math identity is $2\sin(v_1)\sin(v_2)=\cos(v_1-v_2)-\cos(v_1+v_2)$. The high frequency is filtered out leaving low frequency which is easily digitised . Electrical/communication engineers call this heterodyning. – porphyrin Apr 24 at 14:17