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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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)

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1230

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302sin)(⎟⎟⎠

⎞⎜⎜⎝

⎛ −−

⎟⎟⎠

⎞⎜⎜⎝

⎛ −= T

t

eT

ttf π

2

28.1100

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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


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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


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


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

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


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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


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Circuiti elettronici analogici L-A

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