1 Circuiti Circuiti elettronici elettronici analogici analogici L L - - A A DEIS University of Bologna Italy Luca De Marchi Presentazione Temi per Tesi di TIROCINIO e LAUREA •Tirocinio: inserimento nel piano didattico, attività formative di tipologia F (9 crediti). •Date importanti: Domande di ammissione per la Commissione di Tirocinio del Corso di Studio 30 settembre (novembre) 20 dicembre (febbraio 2009)
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•Tirocinio: inserimento nel piano didattico, attività formative di tipologia F (9 crediti).
•Date importanti: Domande di ammissione perla Commissione di Tirocinio del Corso di Studio30 settembre (novembre)20 dicembre (febbraio 2009)
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OUTLINEOUTLINE
Time-Frequency AnalysisIntroduction on Wavelet Operators Examples of applications: Radar/SonarActivitiesConclusions
DEISUniversity of Bologna
Italy
3
FourierFourier AnalysisAnalysisDEIS
University of Bologna Italy
∫
∫∞
∞−
∞
∞−
−
Π=
=
ωω
ω
ω
ω
deFtf
dtetfF
tj
tj
)(21)(
)()(
• Fast Discrete Algorithm (FFT)• FFT: a rotation in function space• New basis functions sines and cosines• Not localized in time
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Signal Analysis Signal Analysis DEIS
University of BolognaItaly
f(t) = f1(t) + f2(t) + f3(t)
2
1230
11
302sin)(⎟⎟⎠
⎞⎜⎜⎝
⎛ −−
⎟⎟⎠
⎞⎜⎜⎝
⎛ −= T
t
eT
ttf π
2
28.1100
22
1002sin)(⎟⎟⎠
⎞⎜⎜⎝
⎛ −−
⎟⎟⎠
⎞⎜⎜⎝
⎛ −= T
t
eT
ttf π
2
32.3155
33
1552sin)(⎟⎟⎠
⎞⎜⎜⎝
⎛ −−
⎟⎟⎠
⎞⎜⎜⎝
⎛ −= T
t
eT
ttf π
T1=28
T2 = 14
T3 = 7
5
Fast Fast FourierFourier TransformTransformDEIS
University of Bologna Italy
6
Freq
Time
TimeTime--FrequencyFrequency AnalysisAnalysis::A A WellWell--KnownKnown ExampleExample
DEISUniversity of Bologna
Italy
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Wavelet TransformsWavelet Transforms
Continuous WT, ƒ(τ) finite energyc(a,b) is a resemblance index between ƒ(τ) and ψ(τ)located at a position b and scale a representing how closely correlated is the wavelet with a portion of the signalψ(τ) is localized in frequency and in time
( ) ( ) RbRadta
bttfa
bac ∈∈⎟⎠⎞
⎜⎝⎛ −
⋅= +∞+
∞−
∗∫ ,1, ψ
DEISUniversity of Bologna
Italy
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Wavelet Wavelet AnalysisAnalysis
DEISUniversity of Bologna
Italy
( ) ( )xeCxx
5cos2
2−
⋅=ψ
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CWT CWT AnalysisAnalysisDEIS
University of Bologna Italy
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FourierFourier AnalysisAnalysisDEIS
University of Bologna Italy
1 21 2 , ,( ) sin(2 ) sin(2 ) [ ]n n n nf n f n f nτ π τ π τ α δ δ= + + +
“ If you steal from one author it’s plagiarism, if you steal from many it’s research” W.Mizner
DEISUniversity of Bologna
Italy
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Data Data compressioncompression
•Fast Discrete algorithms
• WT renders sparse largeclasses of functionsi.e. few noticeable coefficientsmany negligible
• Ex. Standard JPEG 2000
DEISUniversity of Bologna
Italy
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Research topics: Research topics: Music Signal AnalysisMusic Signal Analysis
Definition of algorithmsHardware implementations on FPGA board, on DSP, or Full Custom Design. Applications: Music Information Retrieval, Sound Synthesis and Analysis…
“ La musique est une mathématique mystérieuse dontles élément partecipent de l’infini” C.Debussy
DEISUniversity of Bologna
Italy
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ConclusionsConclusions
Wavelet Transform: a tool for time -frequency analysis
Easy to implement: fast algorithms
Well suited for many applications: such as non-stationary analysis or data compression
DEISUniversity of Bologna
Italy
“Des chercheurs qui cherchent, on en trouve. Des chercheurs qui trouvent, on en cherche.”
de Gaulle
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Multiresolution Analysis and Simulation Multiresolution Analysis and Simulation GroupGroup
FPGA Implementation of QCWT Based Algorithm for filtering Low SNR Signals, A.Marcianesi, R.Padovani, N.Speciale, N.Testoni, G. Masetti, 2003. Wavelet-based Algorithms for Speckle Removal from B-Mode Images, S. Caporale, A. Palladini, L. De Marchi, N. Speciale, G. Masetti, 2004.Wavelet-based Deconvolution Algorithms Applied to Ultrasound Images, S. Maggio, N. Testoni, L. De Marchi, N. Speciale, G. Masetti, 2005.RLS Adaptive Filters for Ultrasonics SignalDeconvolution, M. Alessandrini, L. De Marchi, N. Speciale,2007