2016 RIMS Joint Research & CoopMath2016
Wavelet analysis and signal processing
Organizer: Ryuichi Ashino (Mathematics Sciences, Osaka Kyoiku University)
Period: Oct. 24, 2016 – Oct. 25, 2016
Location: Research Institute for Mathematical Sciences, Room 111
Kyoto University, Kyoto 606-8502, Japan

Program
October 24
12:50 – 13:00 Michio Yamada (RIMS, Kyoto University) Opening
13:00 – 14:00 Leon Cohen (Department of Physics & Astronomy, The City University of New York)The representation of functions in time-frequency and position-wavenumber
It has been recognized for over eighty years that transforming functions into the phasespace of two non-commuting variables offers considerable insight into the nature of
the function, and also has many practical applications. The two most common variable pairs are time/frequency and position/wavenumber. We will describe why sucha transformation is an elegant and challenging problem, the immense strides thathave recently been made, and how these methods impinge on issues in probability
theory, differential equations, approximation methods, and other aspects of analysis.
These methods have become standard, and are routinely applied in many areas, including acoustics, radar, biomedical signals, machine fault analysis, image processing,speech, among many others. By way of examples from many fields, we will show why
considerable insight is gained in analyzing these signals in phase space.
14:15 – 15:15 Takeshi Mandai (Faculty of Engineering, Osaka Electro-Communication University)
On Inequalities about Instantaneous Amplitudes
For a real signal (a real-valued function) f (t), we consider its analytic signal (Af )(t) =f (t) + i(Hf )(t), where (Hf )(t) is the Hilbert transform of f (t). Its absolute valueA(t) = |(Af )(t)|, which is called instantaneous amplitude, often represents a coarse
variation of f (t), and the graph of A(t) looks like an “envelope” of the graph of |f (t)|.
However, for some signals, A(t) changes rather rapidly, and it doesn’t look like an“envelope” of the graph of |f (t)|. We give mathematically rigorous inequalities about
A2 (ξ) which can be considered to explain this difference.
15:45 – 16:45 Toshio Irino (Faculty of Systems Engineering, Wakayama University)
Acoustic Scale Processing in the Auditory SystemThis is a joint work with Roy D. Patterson, Department of Physiology, Development
and Neuroscience, University of Cambridge.
When we hear a voice over the telephone, we can tell whether the speaker is an adultor a child. We can also extract the message of the communication without being
confused by the size information. This shows that auditory signal processing is scale
invariant, automatically segregating information about vocal tract shape from information about vocal tract length. Patterson and colleagues have performed a seriesof experiments to measure the characteristics of size/shape perception [e.g., Smith etal., J. Acoust. Soc. Am. 117(1), 305-318, 2005], and provided a mathematical basis
for auditory scale invariance in the form of the stabilized wavelet-Mellin transform(SWMT) [Irino and Patterson, Speech Commun., 36 (3-4), 181-203, 2002]. The mathematics of the SWMT dictates the optimal form of the auditory filter, insofar as it
must satisfy minimal uncertainty in a time-scale representation [Irino and Patterson,

J. Acoust. Soc. Am. 101 (1), 412-419, 1997]. The resulting gammachirp auditory
ﬁlter is an asymmetric extension of the earlier gammatone auditory ﬁlter? one which
can explain the level dependence of human masking data. Thus, although it is not immediately intuitive, speaker size perception and auditory ﬁlter shape are both aspectsof a larger, uniﬁed framework for scale processing in the auditory system.
18:00 – 20:00 Friendly meeting (dinner)
A friendly meeting will be held on the evening of October 24. The time and restaurant will be announced. The fee is about 6000JPY. Participants should contact withProfessor Keiko Fujita (Department of Mathematics, Toyama University) until September 30. Her mail address is
B keiko@sci.u-toyama.ac.jp
October 25
9:30 – 10:30 Leon Cohen (Department of Physics & Astronomy, The City University of New York)The transformation of deterministic and random diﬀerential equations into phasespace
We describe methods that allow one to transform diﬀerential equations into phasespace diﬀerential equations. The advantages are manyfold, providing insight into thenature of the diﬀerential equation and also in yielding new methods of solution andapproximation. For the case of stochastic processes governed by random diﬀerentialequations, the approach allows one to deal with nonstationary stochastic systems. As
an example, we show how the methods lead to the full solution of Brownian motion.
10:45 – 11:45 Kunio Yoshino (Faculty of Knowledge Engineering, Tokyo City University)
Eigenvalue problem of Anti-Wick(Toeplitz) Operator in Bargmann-Fock space andApplicationsFirst we recall the deﬁnition of Anti-Wick(Toeplitz) operator in Bargmann-Fockspace. And we will give a formula for the eigenvalues of Anti-Wick(Toeplitz) operator with polyradial symbol in Bargmann-Fock space. By using this formula, we canconstruct symbol function of Anti-Wick(Toeplitz) operator. Clarifying the relationship between Toeplitz operators in Bargmann-Fock space and Daubechies operatorsin L2 (Rn ), we will show a new proof of the formula of the eigenvalues of Daubechies
operators with polyradial symbols.
13:15 – 14:15 Kazushi Mimura (Faculty of Information Sciences, Hiroshima City University)
Recent progress in compressed sensing
In recent years there has been many works on compressed sensing that exploits sparsity. We provide an introduction to some typical examples such as spatial-coupling,robust reconstruction, and an application to error correcting codes.
14:30 – 15:30 Tamotsu Kinosita (Division of Mathematics, University of Tsukuba)
Wavelet Transforms on Gelfand-Shilov Spaces
We shall study the continuity properties of wavelet transforms in the Gelfand-Shilov
spaces with the use of a vanishing moment condition. Moreover, we also compute theFourier transforms and the wavelet transforms of concrete functions in the GelfandShilov spaces and show the optimality of our results.
For more information, visit our website at
B http://www.osaka-kyoiku.ac.jp/~ashino/rims2016/
Contact: Ryuichi Ashino

Tel: 072-978-3685

ashino@cc.osaka-kyoiku.ac.jp