Proceedings of: 18th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Amsterdam, 31 Oct. - 03 Nov. 1996.This paper presents the use of undersampling
in an NMR prototype equipment. The results show that
undersampling is a convenient tool to be used in the
processing of these signals. It allows to easily transform
bandpass Free Induction Decay (FID) signals, centered at
high frequencies, into lowpass signals or bandpass signals
at much lower frequencies. Main advantages of using this
technique are improved signal to noise ratio and analog
electronic stages suppression.Publicad

Pozo, Francisco del

Pérez, Pablo

Rivera, Manuel

Santos, Andrés

Vaquero López, Juan José

Proceedings of: 18th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Amsterdam, 31 Oct. - 03 Nov. 1996.This paper presents the use of undersampling
in an NMR prototype equipment. The results show that
undersampling is a convenient tool to be used in the
processing of these signals. It allows to easily transform
bandpass Free Induction Decay (FID) signals, centered at
high frequencies, into lowpass signals or bandpass signals
at much lower frequencies. Main advantages of using this
technique are improved signal to noise ratio and analog
electronic stages suppression.Publicad

Vaquero, Juan José

Name not available

Applying undersampling to the nuclear magnetic resonance signal

Universidad Carlos III de Madrid e-Archivo

  © 1996 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. APPLYING UNDERSAMPLING TO THE NUCLEAR MAGNETIC RESONANCE SIGNAL Pablo Perez, Juan Jos6 Vaquero, AndrCs Santos, Manuel Rivera, Francisco dei Pozo Grupo de Bioingenieria y Telemedicina, E.T.S.I. Telecomunicacih (U.P.M.) 28040 Madrid, Spain. E-mail: andres @ teb.upm.es Abstract - This paper presents the use of undersampling in an NMR prototype equipment. The results show that undersampling is a convenient tool to be used in the processing of these signals. It allows to easily transform bandpass Free Induction Decay (FID) signals, centered at high frequencies, into lowpass signals or bandpass signals at much lower frequencies. Main advantages of using this technique are improved signal to noise ratio and analog electronic stages suppression. I. INTRODUCTION In ii typical Nuclear Magnetic Resonance imaging system, the signal obtained in the receiver coil is amplified using tuned amplifiers, processed with demodulators and intermediate frequency amplifiers (IF), and finally by ;1 quadrature phase sensitive detector. The last step produces two FID (Free Induction Decay) signals, which must be filtered to remove high-frequency components [ I ] .  Among other problems of this classic architecture, the analog mixer required is i t  component that generates a relatively large noise These analog sections can be replaced by using digital techniques, which reduce the noise level and the phase distortion, and therefore increase the quality of the final images. One of these digital techniques is oversampling, but then the high conversion rate needed implies the use of fast electronic circuits and large storage capacities. Another alternative is the use of undersampling techniques or passband sampling. which have been successfully applied in the radiocominunications field, in what is called software radio. In software radio an analog to digital converter takes the IF signal and samples it at a rate below the Nyquist frequency. This sampling process causes the replication of the IF signal spectrum at the baseband, i.e. undersampling moves the spectrum to a lower frequency. functioning like a mixer 131. The original information could be completely recovered from these sampled values if we ensure that the signal has no frequency components above a frequency f l l  or below a frequency ,fl and (,f;, - J; ) 5 f, . Passband signal must also satisfy 14.51 power 121. where is an integer that fulfills Basically, the NMR signal is a passband signal with a center frequency which can take values from a few megahertz to a few hundred megahertz, depending on the main magnetic field used. In this work we show the use of bandpass sampling in the processing of signals coming from an NMR equipment and the advantages of this method. Undersampling directly applied to the amplified resonance signal allows to reduce the speed and storage requirements, and therefore the costs of implementation. The sample and hold circuit is the only component that must keep the same characteristics when oversampling or undersampling is used, with the purpose that it could manage all the frequency components contained in the original signal. 11. METHOD In order to evaluate if undersampling is a viable alternative to detect and process the NMR signal, we have performed some tests using a prototype of nuclear magnetic resonance equipment, which operates at 5.017 MHz. This equipment was completely developed with analog circuitry. During this evaluation the NMR signals were sampled, quantized and processed using a digital oscilloscope (Tektronix TDS-524A with GPIB interface). This oscilloscope can manage up to 500 MHz signals and different sampling rates can be used. It allows to acquire the signals with undersampling and oversampling techniques. The FID signal has been sampled at two different points of the NMR system: - After the tuned filters that receive the signal from the coil: in this point the signal is a passband signal and has a carrier frequency equal to the Larmor frequency (5.0 17 MHz) - The equipment output, where the signal i s  in  baseband after the detection, filtering and amplifying stages. Signals in both points were acquired with a sampling rate of 50 Ksamples/s and their spectra were obtained. 111. RESULTS As shown in Fig. I ,  the resonance information is completely recovered in  a lower frequency, just by undersampling according to the specified conditions. The 1? ? ? ? ? ? ? ??? ????????????????? ??? ?????????????? ???? ?? ???????????????? ? ? ? ? ? ???? ??? ???? ??????????? ???????? ???? ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? ???? ???? ???????? ?????????? ? ? ? ? ? ? ???? ??? ???????? ????????????? ????????? ????? ?????? ???????? ????????? ????????????? ????????? ????? ??????? ???? ????? ?????? ????? ???? ?????????? ???????????? ??????????????? ??? ?????????? ??? ????????????????? ???? ???????????? ???????? ?????? ????? ??? ????? ????? ? ? ?????????????????????????????????????????????????????? ???????????????? ???????????????????????????????????????????????????????????????????????????????????????????????? ? ? ? ????????? ???????????????????? ? ???????? ? ? ? ??? ?????????? ?? ? ? ?? ??? ?????? ???? ? ? ? ? ? ??????????? ? ????? ?????????????? ? ? ? ?????? ???????????????????????????? ????????????????????????????????????????????????? ?????????????????? ?????????????????????????? ?? ????????? ??????????? ?????????? ?????????????????????????????? ?????????????????????????????? ?????????????? ????????????? ?? ????????????????????????????????? ????????? ???????????????????????? ??? ???????????? ?? ? ???????????? ?????? ???? ??????? ???????????? ???????????? ?????????? ???????????????????????????????? ???????????????????????????????????????? ??????????? ?????? ?????????? ?? ??????????? ????????????????????? ????? ????????? ???? ???????? ?????? ?????????? ????????????????? ?????????? ??????????????? ??????????????????????? ? ? ? ? ?? ??????? ??????????????????? ??? ????? ????? ??? ???? ???? ??????? ??? ????????? ???????? ???? ????????????? ?????????? ???????? ???????? ???? ??????????? ????????????????????????????????? ???? ??????? ???? ????? ??????????????????????????????? ????????????????????????????????????????????????????????????????? ??????????? ???? ????????? ???? ?????????????? ??????????????????????????? ????? ?????????? ???? ??? ????? ??????? ????????????????????????????????????????????????????????????????????????????? ??????????? ?????????? ?????????? ????? ????? ???? ?????????????? ??????????? ??????????? ????????? ??? ?????? ??????? ?????????? ???? ???????? ????????????? ???? ????? ???????? ???????????????????? ?????????????????????????????????????????????????????? ???????????????? ???? ??? ????? ???????? ??? ?????????????????????????????????????? ??????????? ??????????? ?????????????? ???????????????????????????????????????????????????????????????????? ???? ????? ???? ??????? ?????? ?????????? ???????? ??????????????????????? ???????????????????????????? ? ? ? ????? ????? ???? ??? ??? ??????? ??????????? ?????????????????????????????????? ???????????? ????????????? ???????????????????????????????????? ?????????????????????????? ?????????????????????? ????? ? ????? ??? ?????????? ???????????? ???????????? ?????????????????????????????????? ? ?????????????????????????????? ??? ????????????? ???? ? ? ? ? ???????? ?????????? ???? ? ??????????????????? ?????????????? ??????? ? ? ? ??? ???????????? ??????????????????? ??????????? ???? ??????????????????? ??? ?????? ???????????? ????? ??????????????????????????????????????? ??? ??????????? ??????????????? ?????????????? ??? ??? ????????????2

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Applying undersampling to the nuclear magnetic resonance signal

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