Circuiti elettronici analogici L-A
Transcript of Circuiti elettronici analogici L-A
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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
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Italy
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FourierFourier AnalysisAnalysisDEIS
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∫
∫∞
∞−
∞
∞−
−
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
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f(t) = f1(t) + f2(t) + f3(t)
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1230
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302sin)(⎟⎟⎠
⎞⎜⎜⎝
⎛ −−
⎟⎟⎠
⎞⎜⎜⎝
⎛ −= T
t
eT
ttf π
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28.1100
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1002sin)(⎟⎟⎠
⎞⎜⎜⎝
⎛ −−
⎟⎟⎠
⎞⎜⎜⎝
⎛ −= T
t
eT
ttf π
2
32.3155
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1552sin)(⎟⎟⎠
⎞⎜⎜⎝
⎛ −−
⎟⎟⎠
⎞⎜⎜⎝
⎛ −= T
t
eT
ttf π
T1=28
T2 = 14
T3 = 7
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Fast Fast FourierFourier TransformTransformDEIS
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Freq
Time
TimeTime--FrequencyFrequency AnalysisAnalysis::A A WellWell--KnownKnown ExampleExample
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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
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Wavelet Wavelet AnalysisAnalysis
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( ) ( )xeCxx
5cos2
2−
⋅=ψ
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CWT CWT AnalysisAnalysisDEIS
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FourierFourier AnalysisAnalysisDEIS
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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
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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
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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
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samples100 200 300 400 500 600 700 800 900 1000
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sens
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samples100 200 300 400 500 600 700 800 900 1000 1100
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• Algorithm Performance on a echografic image
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Denoising Images (2)
Enhancement of attenuation effects
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Attività di ricerca: segnale ecografico
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• 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
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Estrazione del contenuto informativo
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Analisi di caratteristiche tessiturali
• Diversità nei pattern tessiturali identificabile tramite analisi statistica
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Classificatori statistici lineari / non lineari
• Separazione di gruppi di regioni sane e malate nello spazio dei parametri
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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
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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
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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
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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
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“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]
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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