PULSED NMR Acquire F.I.D.

Free Induction DecayNMR detection soon after a strong pulse: precessing nuclear magnetization induces a signal in coil when it is free of the perturbing EM radiation

F.I.D.DIGITIZE

Analogue to Digital Converter

A.D.C.

Address Contents

1 0000

15

1111

2 0001

14

1110

3 0010

13

1101

4 0011

11

1011

5 0100

8

1000

6 0101

4

0100

7

0110

1

0001

8

0111

0

0000

--------- ---------

Computer memory

Time domain

15

0

11

FFT from FID

Computer input

Frequency Domain Spectrum

Computer output

This one-dimensional FT NMR spectrum is the same information as the C.W. NMR spectrum

Acquisition is automatically in the digitized form

Next Slide

dimension A(50),B(50),Y(50),X(50) K=32 open (unit=1, file="output") Print 10,K DO 11 N=1,K X(N)=(N-1)*3.5/K X(N)=EXP(-1.0*X(N)) Y(N)=X(N)*(COS(2*3.14*(N-1)*10.0/K)+ 1 COS(2*3.14*(N-1)*4.0/K)) 11 write (1,20) N,Y(N) DO 12 M=1,K A(M)=0 B(M)=0 DO 13 N=1,K-1 A(M)=A(M)+Y(N)*COS(2*3.14*(M-1)*(N-1)/K) 13 B(M)=B(M)+Y(N)*SIN(2*3.14*(M-1)*(N-1)/K) A(M)=A(M)/K B(M)=B(M)/K M2=M/2 12 write (1,30) M2,A(M2),B(M2) 10 FORMAT(1x,I2) 20 FORMAT(1x,I2,2x,F10.5) 30 FORMAT(1x,I2,2x,F10.5,2x,F10.5) close (unit=1) STOP

END

A program in

Fortran for “Fast Fourier Transform”

Digitized FID Signal

Digital Computer

---------------------------------------------------------------------- ---------------------- ------------ -

FFT Program run

OUTPUT

Time domain FID data: 32 points

Real Imaginary 16 data 16data points points

Frequency domain spectrum

cosine Sine arbitrary phae sinuous

COS Real Imaginary

F.T

RealImaginaryF.T

SIN

Real Imaginary

F.T

Arbitrary Phase

Provision is made in the data processing system, for routinely applying phase corrections

t=0

+1

0

Value between +1 & 0

fc cos(2πνt) + fs sin (2πνt)

with fc2 +fs

2 =1