Applications of Hadamard Transform to Gas
Chromatography/Mass Spectrometry and Liquid
Cheng-Huang Lin,*,†Takashi Kaneta,‡Hung-Ming Chen,†Wen-Xiong Chen,†Hung-Wei Chang,†
and Ju-Tsung Liu§
Department of Chemistry, National Taiwan Normal University, 88 Section 4, Tingchow Road, Taipei, Taiwan,
Department of Applied Chemistry, Graduate School of Engineering, and Division of Translational Research, Center for
Future Chemistry, Kyushu University, Motooka, Fukuoka 819-0395, Japan, and Forensic Science Center, Military
Police Command, Department of Defense, Taipei, Taiwan
Successful application of the Hadamard transform (HT)
technique to gas chromatography/mass spectrometry
(GC/MS) and liquid chromatography/mass spectrometry
(LC/MS) is described. Novel sample injection devices
were developed to achieve multiple sample injections in
both GC and LC instruments. Air pressure was controlled
by an electromagnetic valve in GC, while a syringe pump
and Tee connector were employed for the injection device
in LC. Two well-known, abused drugs, 3,4-methylene-
dioxy-N-methylamphetamine (MDMA) and N,N-dimeth-
yltryptamine (DMT), were employed as model samples.
Both of the injection devices permitted precise successive
injections, resulting in clearly modulated chromatograms
encoded by Hadamard matrices. After inverse Hadamard
transformation of the encoded chromatogram, the signal-
to-noise (S/N) ratios of the signals were substantially
improved compared with those expected from theoretical
values. The S/N ratios were enhanced ∼10-fold in HT-
GC/MS and 6.8 in HT-LC/MS, using the matrices of 1023
and 511, respectively. The HT-GC/MS was successfully
applied to the determination of MDMA in the urine sample
of a suspect.
In separation science, the limit of detection (LOD) for analytes
is an important issue. Thus, much research has focused on the
development of sensitive detectors and improvements in the
sensitivity of detectors for separation techniques such as gas
chromatography (GC), liquid chromatography (LC), and capillary
electrophoresis (CE). These studies have resulted in the develop-
ment of sophisticated detectors. Therefore, in some cases, further
improvement in LOD is physically limited by the detection
principle. The use of mathematical methods is one alternative for
the improvement of the LOD and resolution of analytical instru-
mentation. In chromatographic separations, correlation methods
have been employed for improving the LOD. In 1970, Smit
demonstrated correlation gas chromatography in which a sample
was injected into a column according to a pseudorandom binary
sequence (PRBS).1Correlation chromatography is a powerful
method for reduction of the LOD. Therefore, correlation chro-
matography has been applied to not only GC2–5but also to LC6–11
and to CE.12,13The Hadamard transform (HT) technique is a
technique that is analogous to the correlation method. The HT
technique has been applied in many fields, including time-of-flight
mass spectrometry,14–16Raman,17,18fluorescence imaging,19–21ion
mobility spectrometry,22,23and NMR.24,25In our previous
studies,26–29Hadamard transformation has been successfully
applied to capillary electrophoretic separations where the signal-
* Corresponding author. E-mail: firstname.lastname@example.org.
†National Taiwan Normal University.
§Forensic Science Center.
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10.1021/ac800201r CCC: $40.75 2008 American Chemical Society
Published on Web 06/21/2008
Analytical Chemistry, Vol. 80, No. 15, August 1, 2008