Instrumentation & Measurement Magazine 24-4 - 17

Francesco Bonavolontà is a Research Fellow in the Department
of Electrical and Information Technologies at University
of Naples Federico II, Italy. Dr. Bonovolontà's research activity
is centered in the area of Instrumentation and Measurement
and is mainly focused on developing of innovative DAS
systems based on compressive sampling techniques, also including
Internet of Things devices for smart applications.
Mauro D'Arco (mauro.darco@unina.it) (M'16-SM'19) is currently
an Associate Professor with the University of Naples
Federico II, Italy. He received the Ph.D. degree in electrotechnical
engineering in 2003 and the Electronic Engineering
degree in 1999. He was the coordinator of a task force at DESTI-ECE,
CERN, where he spent a period as Unpaid Associate
in 2010/2011 and was Visiting Scientist at TE-MSC-MM, CERN
in 2014. His current research interests include: definition of descriptive
models for digital-to-analog converters (D/A), use
of arbitrary waveform generators to play critical waveforms,
and investigation of innovative acquisition modes to improve
high-speed digitizers performance.
Egidio De Benedetto, (M'14-SM'16) is an Associate Professor
with the University of Naples Federico II, Italy. He received the
Ph.D. degree in information engineering from the University
of Salento, Lecce, Italy in 2010. His current research interests
include the characterization of devices and materials through
reflectometric methods, the metrological characterization of
augmented reality system, and the development of microwave-reflectometry
systems for monitoring applications.
Dominique Dallet is Full Professor in the field of digital electronic
design with the Engineer School Bordeaux INP, France
and currently, he is the Head of the Electronic Design Group
at the IMS Laboratory, University of Bordeaux. His research
interests include data converter (A/D-D/A) modelling and
testing, parameter estimation, digital signal processing implementation,
and electronic design for the digital enhancement
of analog and mixed electronic circuits (ADC, DAC, power
amplifiers).
Annarita Tedesco is pursuing her Ph.D. degree in physical
sciences and engineering at the University of Bordeaux,
France. Her research interests focus on industrial measurement,
monitoring systems, AR-based measurement systems,
measurements for Industry 4.0, sensor networks, human computer
interaction, and brain computer interface. She received
the M.S. degree in telecommunication engineering in 2002. For
many years she was involved in R&D divisions of world wide
technology companies, promoting strong cooperation with
the academic world.
Appendix 1
The most common example utilized to illustrate GSE concerns
the reconstruction of a signal u(t) bandlimited to (-B, B) from
its samples and those of its time derivative. In this case M = 2,
H1
(f) = 1 (identity filter), H2
(f) = j2πf (time derivative filter), fs
= B, and the reconstruction filters can be obtained summing a
term related to the interval (-B, 0), labelled with a subscript L,
to that related to (0, B), labelled with a subscript U. In particular
for the lower term holds that:



jf Yf B
12
12j fB Yf1L
2L
 f
B, 0
 

tion filters Y1L(f) and Y2L
inverting (1.1):
 f BB 0
1
  
1
 
22
Yf1
L
2L
 

Yf B



B, 0
jj
BB

The representation of the frequency responses in the interval
(0, B), are obtained using the shortcut highlighted in the
discussion of the GSE, that, in this case, requires translating by
B the functions in the matrix in (1.2) and selecting the first column.
One can thus conclude that the reconstruction filters are
given by:
Yf Y f Y f
11 1
 LU

  

Yf Y f Y f
jj
22 2
   

 LU
22


22, 0
BB

    

 ff
B B BB
11
11
 ff  0,

 

 
BB, 0
 ff0,BB 
As shown by (1.3) the reconstruction filter Y1(f) has a frequency
response characterized by a triangular shape in (-B,
B) and is zero outside, whereas Y2
y t sinc Bt
y t
1
2


2


1
B
 
sinc Bt sin Bt
  
(f) consists in a biphasic impulse
in (-B, B) and is zero outside; their time-domain images
are the interpolation functions:
(1.4)


1


ff
(1.2)
1
 f δ2
B, 0

(1.1)
where  is the characteristic function of the interval (-B,
0), and δ2 = [0, 1]T
. The frequency responses of the reconstruc(f),
are straightforwardly obtained
(1.3)
June 2021
IEEE Instrumentation & Measurement Magazine
17

Instrumentation & Measurement Magazine 24-4

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