circuiti elettronici analogici l-a
TRANSCRIPT
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CircuitiCircuiti elettronicielettronici analogicianalogici LL--AA
DEISUniversity 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 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
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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
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Fast Fast FourierFourier TransformTransformDEIS
University of Bologna Italy
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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= + + +
f1= 500Hzf2=1 KHzτ=1/8000 sα=1.5n1=250n2=282
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Wavelet Wavelet AnalysisAnalysisDEIS
University of Bologna Italy
2 2 22 4( )
ti tt Ce e e
π απαψ− −⎛ ⎞= −⎜ ⎟
⎝ ⎠
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Radar/Sonar Radar/Sonar AppplicationsAppplications
DEISUniversity of Bologna
Italy
Radar Signal: fc=64Mhz, Tr=50us, τ=6us, fcarrier=1Mhz
Tx Tx
Tr
τ τ
Rx
sτ
T
APPLICATIONS: airport Radar, metal detector, medical application (tissue imaging, velocity blood measurements)
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DENOISINGDENOISING
DEISUniversity of Bologna
Italy
Problem: Radar/Sonar pulses detection and filtering in presence of strong noise and jamming signals
Solution: using a thresholding procedure performed on coefficients resulting from a Wavelet Transform analysis
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Denoising images (1)se
nsor
s
samples100 200 300 400 500 600 700 800 900 1000
5
10
15
20
25
30
sens
ors
samples100 200 300 400 500 600 700 800 900 1000 1100
5
10
15
20
25
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• Algorithm Performance on a echografic image
DEISUniversity of Bologna
Italy
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Denoising Images (2)
Enhancement of attenuation effects
DEISUniversity of Bologna
Italy
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Attività di ricerca: segnale ecografico
DEISUniversity of Bologna
Italy
• Elaborazione del segnale ecografico• Rimozione del rumore• Algoritmi di deconvoluzione
• Estrazione del contenuto informativo• Analisi di parametri frequenziali• Analisi di caratteristiche tessiturali
• Classificazione del tessuto• Feature extraction e feature selection• Classificatori statistici lineari / non lineari
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Analisi di segnale
Un segnale non stazionario contiene informazione:
• Strumenti intelligenti di analisi di segnale
• Tecniche mirate per estrarre l’informazione
• Algoritmi per classificazione e decisione
•Necessario studiare il modello di segnale• Statistico / Deterministico• Identificazione componenti
Analisi
Estrazione
Classificazione
Segnale
Componenti
Features
DEISUniversity of Bologna
Italy
Estrazione del contenuto informativo
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Analisi di caratteristiche tessiturali
• Diversità nei pattern tessiturali identificabile tramite analisi statistica
DEISUniversity of Bologna
Italy
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Classificatori statistici lineari / non lineari
• Separazione di gruppi di regioni sane e malate nello spazio dei parametri
DEISUniversity of Bologna
Italy
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Research topics: Research topics: UltrasoundsUltrasounds
Definition of algorithms
Applications: Biomedical Imaging Enhancement, Tissues properties investigation…
“ 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
Professors: Guido Masetti, Nicolò Speciale. (Sistemi Integrati per l’Analisi Spettrale LS)
Post Doc: Luca De Marchi, Marco Messina
PhD Students: Martino Alessandrini, EmanueleBaravelli, Salvatore Caporale, Simona Maggio, Alessandro Palladini, Nicola Testoni.
Contact: [email protected]
DEISUniversity of Bologna
Italy
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Students PublicationsStudents Publications
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
DEISUniversity of Bologna
Italy