# How Does Finite Acquisition Time Affect NMR Signal Spectrum?

• johnq2k7
In summary, the Free Induction Decay signal (FID) is a type of NMR signal observed in MRI and MRS. The spectrum of the signal is represented by G(w) and is calculated assuming that the signal is acquired for an infinite period of time. However, in reality, the signal is acquired over a finite time denoted as T. The shape of the spectrum is then obtained by assuming that S(t)=0 for t>T, leading to G(w)= S(0){(T2* + i*(w-w_0)(T2*)^2 / (1 + [(w-w_0)T2*]^2} (1- X). The magnitude of X is equal to 1 when T
johnq2k7
The "Free Induction Decay signal" (FID) is a particular type of NMR signal observed in both MRI and MRS. An idealized representation of the signal S(t) is given by:

S(t)= S(0)exp (i*w_0*t)exp(-t/T2*), t>=0
S(t)=0 , t<0

You showed the spectrum G(w) corresponding signal is given by:

G(w)= S(0) {((T2* + (w-w_0)(T2*)^2))/ (1+[(w-w_0)T2*]^2}

However, the exact form of the spectrum above is obtained assuming that the signal is acquired for an infinite period of time. In reality the signal is acquired over a finite time that will be denoted here as T. In that case the shape of the spectrum is obtained by assuming that S(t)=0, for t>T and that leads to the following spectrum:

G(w)= S(0){(T2* + i*(w-w_0)(T2*)^2 / (1 + [(w-w_0)T2*]^2} (1- X)

where X is a complex parameter that depends on T,T2*,w, and w_0

a.) Determine the value of the magnitude of X for the case where T=T2*

b.) if T=a*T2*, determin the min. value of the parameter 'a' such that |X|<0.01
(|X| rep. the magnitude of 'X')

. Thank you!a.) In the case where T=T2*, the magnitude of X is equal to 1. b.) For the case where T=a*T2*, the minimum value of 'a' such that |X|<0.01 is equal to a=1.01.

## 1. What is a Fourier Transform NMR Physics?

A Fourier Transform NMR Physics is a technique used in nuclear magnetic resonance (NMR) spectroscopy to analyze the frequencies of signals emitted by atomic nuclei in a sample. It allows for the identification of different compounds and their relative concentrations in a sample.

## 2. How does a Fourier Transform NMR Physics work?

A Fourier Transform NMR Physics works by applying a radio frequency pulse to a sample, causing the atomic nuclei to emit a signal. This signal is then detected and converted into a time domain signal. The Fourier transform is then used to convert this signal into a frequency domain, allowing for the analysis of the different frequencies present in the sample.

## 3. What are the advantages of using a Fourier Transform NMR Physics?

The main advantage of using a Fourier Transform NMR Physics is that it allows for the analysis of multiple frequencies within a sample, providing a more detailed and accurate spectrum. It also has a high sensitivity and can be used to analyze small sample sizes.

## 4. What types of samples can be analyzed using a Fourier Transform NMR Physics?

A Fourier Transform NMR Physics can be used to analyze a wide range of samples, including liquids, solids, and gases. It is commonly used in chemistry, biochemistry, and material science to study the structure and composition of different compounds.

## 5. Are there any limitations to using a Fourier Transform NMR Physics?

While a Fourier Transform NMR Physics is a powerful analytical tool, it does have some limitations. It requires a strong magnetic field and can only analyze samples that contain atoms with a magnetic moment. It also cannot provide information on the spatial arrangement of atoms in a molecule.

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