στο Αριστοτέλειο υλικού.

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1 Σήματα Συστήματα Εισαγωγικά Κωνσταντίνος Κοτρόπουλος Τμήμα Πληροφορικής Θεσσαλονίκη, Ιούνιος 2013

2 Άδειες Χρήσης Το παρόν εκπαιδευτικό υλικό υπόκειται σε άδειες χρήσης Creative Commons. Για εκπαιδευτικό υλικό, όπως εικόνες, που υπόκειται σε άλλου τύπου άδειας χρήσης, η άδεια χρήσης αναφέρεται ρητώς. Χρηματοδότηση Το παρόν εκπαιδευτικό υλικό έχει αναπτυχθεί στα πλαίσια του εκπαιδευτικού έργου του διδάσκοντα. Το έργο «Ανοικτά Ακαδημαϊκά Μαθήματα στο Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης»» έχει χρηματοδοτήσει μόνο τη αναδιαμόρφωση του εκπαιδευτικού υλικού. Το έργο υλοποιείται στο πλαίσιο του Επιχειρησιακού Προγράμματος «Εκπαίδευση και Δια Βίου Μάθηση»» και συγχρηματοδοτείται από την Ευρωπαϊκή Ένωση (Ευρωπαϊκό Κοινωνικό Ταμείο) και από εθνικούς πόρους. Θεσσαλονίκη, Ιούνιος 2013

3 Kef laio 1 Eisagwgik Prolegìmena Ac xekin soume to eisagwgikì m jhma prospaj ntac na oriojet soume tð eðnai s ma, gia na jemeli soume to epiqeðrhma ìti h spoud tou antikeimènou S mata-sust mata den apoteleð èna perifereiakì stìqo el ssonoc shmasðac enìc proptuqiakoô progr mmatoc sthn Plhroforik. Ja prostrèxoume sthn kajomiloumènh gia thn prìslhyh parast sewn sqetik n me thn ènnoia <<s ma>> ( shm di sth dhmotik ), anatrèqontac sta kajierwmèna lexik thc koin c neoellhnik c, ìpwc ta lexik tou Emmanou l Kriar [1], tou GewrgÐou Mpampini th [2] kai tou InstitoÔtou Neoellhnik n Spoud n ['Idruma Manìlh TriantafullÐdh] [3]: par stash pou apoteleð stoiqeðo gia thn anagn rish pro ìntoc orismènhc biomhqanðac (p.q. h fr sh <<s ma katatejèn>> sta mpouk lia thc Coca Cola paliìtera); diakritikì mel n swmateðou, sunedrðou (p.q. <<s mata podosfairik c om dac>>); diakritik shm dia pou fèroun oi axiwmatikoð sth stol touc, endeiktik tou ìplou s matoc sto opoðo an koun kai tou bajmoô touc; sunjhmatikì shm di me to opoðo dðnetai mia plhroforða diatag apì apìstash alli c sini lo: <<shmatodosða dia fan n kai shmai n>> gia thn kajod ghsh twn odhg n oqhm - twn sta Tejwrakismèna kat llhlh kðnhsh mikr n shmai n gia th sunennìhsh metaxô skaf n; 1

4 2 K. Kotrìpouloc: S mata-sust mata hqhtikì optikì shm di p.q. <<mou èkane s ma o troqonìmoc na proqwr sw>>; s mata odik c kukloforðac dhlad f ta pinakðdec topojethmèna stouc drìmouc gia th rôjmish thc kukloforðac oqhm twn kai pez n; (thlepikoinwnðec) k je metabol hlektromagnhtikoô pedðou pou metafèrei plhroforða thn opoða lamb nei èna kat llhlo ìrgano p.q. thlefwnikì s ma, s mata Mors, <ésteilan s ma se ìla ta peripolik thc AstunomÐac na ton katadi xoun>>, <<Den èqw s ma sto kinhtì>>; H etumologða thc lèxhc, an kai abèbaih, parapèmpei sth lèxh dhyāman sta sanskritik (dhlad, skèyh), pou tairi zei morfologik c par shmasiologik c. Ligìtero pijan eðnai h antistoiqða me to boreioarmenikì sāma, pou shmaðnei s ma shm di. Par gwga thc lèxhc s ma eðnai ta ex c: shmeðo, shmaðnw, shmaða. Stouc neìterouc qrìnouc eðnai genik paradektì ìti h lèxh s ma eðnai shmasiologikì antid neio apì th gallik gl ssa (signal). Lème ìti eðnai antid neio, giatð h lèxh s ma ( s ma sth dwrik di lekto) eðnai arqaða. L.q. apant ston 'Omhro. Pr gmati; sthn epifullðda tou <<Qrìnoc kai s mata>> [4] o Kajhght c D. N. MarwnÐthc analôei th fr sh <<lugr s mata gr yac>> (se met frash:... ègraye jan sima s mata) apì thn èkth raywdða thc Ili dac pou afor th q raxh se diplì ki diplwmèno pin kio shm twn fonik c entol c tou ProÐtou, basili thc EfÔrac, proc ton pejerì tou, basili thc LukÐac, me epðdoxo jôma to Bellerofìnth...>> Dhlad, h lèxh s mata ermhneôetai wc egq rakta shm dia se prìsforh epif neia. Diastèllontac to sqìlio tou MarwnÐth pou sundu zei th fr sh aut me thn aparq thc shmeiwtik c, m pwc aniqneôontai kai oi aparqèc thc kwdikopoðhshc thc plhroforðac, pou apoteleð organikì mèroc thc met doshc thc plhroforðac? H lèxh s ma me thn ermhneða << mnhmeðo>> apant kai ston Epit feio tou Periklèouc dia thc grafðdoc tou JoukudÐdh: <<(Perikl c)... proelj n apì tou s matoc...>> ( se met frash EleujerÐou Benizèlou:... eproq rhsen apì to mnhmeðo...). Gia na embajônoume sthn ermhneða thc lèxhc <<s ma>> mac bohj èna endiafèron dðpolo apì th GlwssologÐa pou apodðdetai ston F. de Saussure [5]: shmaðnon: gr mmata, fwn mata, sq mata, fwnologik morf, hqhtik morf me thn opoða dhl netai h plhroforða (sta gallik signifiant) shmainìmeno: shmasða lèxewn, ènnoia (sta gallik signifié).

5 K. Kotrìpouloc: S mata-sust mata 3 Skopìc thc spoud c mac eðnai akrib c h exagwg tou no matoc apì èna forèa ( alli c fèron stic thlepikoinwnðec), dhlad mia morf epifaneðac. Gia par deigma, s> èna s ma o- milðac, dhlad, th metabol akoustik c pðeshc ìpwc sullamb netai apì èna mikrìfwno kai upob lletai se deigmatolhyða sthn k rta qou tou upologist, p c mporeð na apofasisteð an up rqei hqhtik drasthriìthta sig, an mil ndrac gunaðka, tð lèei (anagn rish omilðac), poiìc mil (anagn rish omilht ), poi h sunaisjhmatik tou kat stash (euqaristhmènoc, qaroômenoc, luphmènoc, orgismènoc, k.t.ì.). Mia eikìna, dhlad disdi stath qwrik katanom twn fwteinot twn twn eikonostoiqeðwn (pixels), p c mporeð na katatmhjeð se perioqèc, p.q. prosk nio upìbajro. Epiprosjètwc analôontac mia eikìna mia eikonoseir (dhlad, bðnteo) p c mporoôn na aniqneutoôn prìswpa, na anagnwristoôn, k.t.ì. Apì th suqnìthta emf nishc lèxewn se keðmena p c mporeð na aniqneuteð h jematik tou keimènou, na omadopoihjoôn keðmena, k.t.ì. Ta proanaferjènta probl mata ja antimetwpistoôn se pio proqwrhmèna maj mata thc kateôjunshc <<Yhfiak n Mèswn>>, ìpwc thn Yhfiak EpexergasÐa Eikìnac Yhfiak EpexergasÐa OmilÐac. Sto parìn m jhma shmaðnon ja eðnai mia sun rthsh miac (anex rththc) metablht c pou upodhloð qrìno, x(t), en shmainìmeno ja eðnai to suqnotikì perieqìmeno tou s matoc f sma (spectrum, apì to latinikì specter) pou eðnai lanj non (latent) se k je s ma, dhlad enup rqei s> autì. To f sma ja sumbolðzetai wc X(ω), ìpou ω =2πf h kuklik suqnìthta pou metriètai se rad/sec kai f h suqnìthta pou metriètai se Hz. H prohgoômenh ermhneða sumfwneð me thn an lush tou Jose M. F. Moura [6]: << Poll qrìnia prin, o ìroc s ma anaferìtan se k poia fusik ekd lwsh thc plhroforðac pou metaballìtan wc proc to qrìno kai/ to q ro. Molonìti h prosèggish aut exakoloujeð na eðnai se isqô, wc s mata mporoôn na eklhfjoôn kai llec sumbolikèc afhrhmènec anaparast seic thc plhroforðac, ìpwc makrièc akoloujðec twn tess rwn sumbìlwn tou genetikoô k dika (tic b seic tou DNAA,C,G,T) pou dieujetoôntai p.q. se gonðdia. Wc s mata eklamb nontai o qoc, oi eikonoseirèc (bðnteo), o proforikìc kai graptìc lìgoc (dhlad, omilða kai keðmena), oi eikìnec, ta polumèsa, h mousik, ta hqoentopistik s mata (sonar), ta radioentopistik s mata (radar), oi katagrafèc twn aisjht rwn stic thlepikoinwnðec, gewfusik, qhmeða, moriak biologða, genetik, iatrik k.o.k. H epexergasða shm twn sugkroteðtai apì ìlec tic leitourgðec anapar stashc, kwdikopoðhshc, met doshc, ektðmhshc, anðqneushc,

6 4 K. Kotrìpouloc: S mata-sust mata sunagwg c, anak luyhc, anagn rishc, sônjeshc, katagraf c anaparagwg c shm twn me yhfiakèc analogikèc diat xeic, teqnikèc algorðjmouc se morf logismikoô, ulikoô, e- xeidikeumènou logismikoô suskeu n (firmware). Epomènwc, anakefalai nontac mporoôme na isquristoôme ìti epexergasða s matoc eðnai h teqnologða pou agkali zei th jemeli dh jewrða, tic efarmogèc, touc algorðjmouc kai tic ulopoi seic epexergasðac met doshc thc plhroforðac pou emperièqetai se polloôc diaforetikoôc fusikoôc, sumbolikoôc afhrhmènouc tôpouc (format), pou apokaloôntai swrreutik c s mata. H teqnologða aut qrhsimopoieð majhmatikèc, statistikèc, upologistikèc, eurhmatikèc eðte glwssologikèc anaparast seic (p.q. peperasmèna autìmata) kai teqnikèc montelopoðhshc, an lushc, sônjeshc, anak luyhc, apok luyhc, aðsjhshc, katagraf c, exagwg c, m jhshc prostasðac (p.q. asf leiac). Sto Ðdio pneôma o Li Deng aparijmeð tic ereunhtikèc perioqèc an mèso [7] ston PÐnaka 1.1. Oi ereunhtikèc perioqèc den eðnai kat> an gkh anex rthtec. Antijètwc, ìpwc prolègei o tðtloc tou rjrou, diapist nontai gonimopoi seic metaxô touc. Upì to prðsma twn apìyewn pou paratèjhkan, h kateôjunsh twn <<Yhfiak n Mèswn>> epiqeireð na apant sei sto ex c er thma: S> ènan kìsmo pou kataklôzetai apì dwre n yhfiakì perieqìmeno (bðnteo, eikìnec, mousik, grafik, k.o.k.) 2D, 3D, HD kai ufaðnetai p nw sfl ènan istì (Facebook, Twitter, YouTube, Last.fm) pou orðzei k poio plaðsio sumfrazomènwn (koinwnik n eðte shmasiologik n), p c ja anaptôxoume no monec algorðjmouc se di forec efarmogèc (p.q. an kthsh, katanìhsh) eðte ja sunjèsoume eikonikoôc kìsmouc pou ja euqarist soun to qr sth-katanalwt? Isqurizìmaste ìti isqôei h exðswsh: Yhfiak Mèsa = Perieqìmeno + Eufuòa pou anafèretai stic treic apì tic èxi èdrec tou plhroforiakoô kôbou tou Sq matoc 1.1 pou anafèrontai sto perieqìmeno, ta sumfrazìmena kai ton katanalwt. Oi ajèatec èdrec tou kôbou aforoôn rimec teqnologðec (p.q. sumpðesh) eðte uponooômenec diergasðec pou gðnontai oôtwc llwc (p.q. upologismoð) ereunhtikèc perioqèc stic opoðec den drasthriopoioômaste proc to parìn (p.q. epikoinwnðec). Sth sunodeutik parousðash gðnetai mia ekten c parousðash thc kateôjunshc aut c.

7 PÐnakac 1.1: Org nwsh twn ereunhtik n perioq n thc epexergasðac s matoc an mèso (media signal processing). Mèso/Efarmogèc 'Hqoc/Mousik OmilÐa (Proforikìc KwdikopoÐhsh, SumpÐesh BeltÐwsh, An lush Exom lunsh jorôbou, lìgoc) Diaqwrismìc hqhtik c phg c, entopismìc hqhtik c phg c me sustoiqða mikrof nwn, qwrikìc qoc Anagn rish, Epal jeush SÔnjesh Mousik Upologist n An lush hqhtik n skhn n, Akoustik antðlhyh upologist n (p.q. anðqneush omilðac, melwdðac, a- nagn rish tautìthtac tragoudist ) BeltÐwsh omilðac, a- n lush omilðac, proepexergasða BeltÐwsh eikìnac/bðnteo, diaqwrismìc upob jrou, kat tmhsh, exagwg qarakthristik n, upologistik fwtografða, trisdi stath anakataskeu apì pollaplèc ìyeic, trisdi - stath epðdeixh Eikìnec/Grafik Eikonoseirèc (BÐnteo) KeÐmena (Graptìc lìgoc) KwdikopoÐhsh qou KwdikopoÐhsh omilðac KwdikopoÐhsh eikìnac KwdikopoÐhsh bðnteo KwdikopoÐhsh kai perðlhyh keimènwn 'Elegqoc grammatik c, an lush keimènou Anagn rish omilðac/ omilht n An kthsh, Exìruxh An kthsh mousik c, Efarmogèc se koinwnik mèsa anaz thsh qwn Katanìhsh Katanìhsh proforikoô lìgou An kthsh proforik n keimènwn, anaz thsh sth fwn Anagn rish eikìnwn (p.q. anagn rish optik n qarakt rwn, anagn rish daktulik n apotupwm twn) 'Orash upologist n (p.q. anagn rish trisdi statwn antikeimènwn, anagn rish pros pou) An kthsh eikìnwn me b sh to perieqìmeno An lush skhn n Katanìhsh gegonìtwn/ drasthriot twn, existìrhsh apì bðnteo Anaz thsh bðnteo me b sh to perieqìmeno SÔnjesh OmilÐac Grafik upologist n KinoÔmena grafik Gènesh fusik c gl ssac KathgoriopoÐhsh keimènou, mhqanik met - frash Katanìhsh fusik n glwss n An kthsh keimènwn (an kthsh plhroforðac), exìruxh keimènou K. Kotrìpouloc: S mata-sust mata 5 Hqografhmènec ekpompèc Itunes (podcasts), YouTube 3D Second Life blogs, Wiki, Twitter Diamoirasmìc eikìnwn Diamoirasmìc bðnteo Diepafèc Polutropik allhlepðdrash anjr pou upologist, di logoi Asf leia, EgklhmatologÐa Udatogr fhsh polumèswn, kruptogr fhsh

8 6 K. Kotrìpouloc: S mata-sust mata Sq ma 1.1: Plhroforiakìc kôboc. Di rjrwsh tou ekpaideutikoô ulikoô To perieqìmeno tou maj matoc eðnai dunamikì kai ìqi statikì: p.q. h je rhsh sust matoc mporeð na axiopoihjeð sth sônjesh kai an lush sônjetwn diergasi n ( l.q. qrhmatist rio). EÐnai shmantikì na eðnai kaneðc exðsou exoikeiwmènoc me thn an lush kai sônjesh twn susthm twn suneqoôc qrìnou, all kai twn diakrit n susthm twn. Ja paratejoôn diadoqik ta analutik ergaleða gia tic dôo kathgorðec susthm twn. 'Emfash apodðdetai sthn an deixh twn omoiot twn an mesa stic mejìdouc suneqoôc kai diakritoô qrìnou, entopismì kai katanìhsh twn diafor n metaxô twn proseggðsewn. H spoud apoblèpei sth qr sh twn basik n analutik n mejìdwn se praktik probl mata, ìpwc ta fðltra epilog c suqnot twn, deigmatolhyða. H katanìhsh twn analutik n mejìdwn eðnai proapaitoômeno gia th sqedðash yhfiak n fðltrwn pou melet ntai leptomer c sthn Yhfiak EpexergasÐa S matoc. sthn ektðmhsh tou eôrouc efarmog n kai sth q raxh kateujônsewn peraitèrw melèthc. H mejodologða pou prokrðnetai sundu zei thn katanìhsh thc jewrðac, thn paradeigmatik epðlush frontisthriak n ask sewn kaj c kai th di jesh seir n lutwn ask sewn gia ex skhsh twn foitht n. Bohj thn kalôterh katanìhsh thc didaskìmenhc Ôlhc kal gn sh Grammik c 'Algebrac kai stoiqei dhc gn sh Migadik c An lushc kai Diaforik n Exis sewn. Proslamb nousec parast seic apì th basik jewrða kuklwm twn se epðpedo Fusik c

9 K. Kotrìpouloc: S mata-sust mata 7 LukeÐou bohjoôn sthn katanìhsh twn ennoi n. Se k je perðptwsh, h jewrða anaptôssetai autodônama. AkoloÔjwc perigr fetai qondrik h logik di rjrwsh thc Ôlhc apodðdontac èmfash stic basikèc ènnoiec pou melet ntai. H qronik èkjesh sthn Ôlh tou maj matoc upodhl netai me thn arðjmhsh twn enot twn. Enìthta 1 Eisagwgik - GiatÐ to m jhma eðnai anagkaðo? Poi eðnai ta kðnhtra gia th melèth twn shm twn kai susthm twn? Enìthta 2 Majhmatik anapar stash shm twn kai susthm twn MetasqhmatismoÐ anex rththc metablht c. Qronik olðsjhsh (metatìpish) Klim kwsh. Basik s mata suneqoôc & diakritoô qrìnou Pragmatik, fantastik, kai migadik ekjetik Bhmatik sun rthsh (step function) Sun rthsh monadiaðac shc kroustikìc palmìc (delta function, impulse) Basikèc ènnoiec sta sust mata Block di gramma susthm twn Basikèc idiìthtec susthm twn: Me/qwrÐc mn mh Aitiatìthta Grammikìthta Qronik ametablhtìthta Eust jeia Enìthta 3 Grammik Qronoamet blhta Sust mata (G.Q.A.) Olokl rwma thc sunèlixhc gia sust mata suneqoôc qrìnou 'Ajroisma thc sunèlixhc gia sust mata diakritoô qrìnou Grammik diaforik exðswsh (G.D.E.) me stajeroôc suntelestèc - Grammik exðswsh diafor n me stajeroôc suntelestèc

10 8 K. Kotrìpouloc: S mata-sust mata ApeujeÐac lôsh Mèjodoi metasqhmatismoô Domik stoiqeða ulopoi sewn susthm twn SuneqoÔc qrìnou: ajroistèc, pollaplasiastèc, oloklhrwtèc. DiakritoÔ qrìnou: ajroistèc, pollaplasiastèc, diat xeic kajustèrhshc. Ulopoi seic: seiriak, par llhlh. Enìthta 4 An lush Fourier gia s mata kai sust mata suneqoôc qrìnou - Periodik s mata (Seir Fourier) Enìthta 5 An lush Fourier gia s mata kai sust mata suneqoôc qrìnou - Metasqhmatismìc Fourier Enìthta 7 An lush Fourier gia s mata kai sust mata diakritoô qrìnou Mia eureða kathgorða shm twn mporoôn na anaparastajoôn wc ajroðsmata oloklhr mata migadik n ekjetik n me suntelestèc. H apìkrish twn G.Q.A. susthm twn se eðsodo pou eðnai migadikì ekjetikì eðnai apl c to Ðdio ekjetikì pollaplasiasmèno m> èna migadikì arijmì (qarakthristikì) tou sust matoc. Lème ìti ta migadik ekjetik eðnai idiosunart seic twn G.Q.A. susthm twn. Seir Fourier periodikoô s matoc Metasqhmatismìc Fourier mh-periodikoô s matoc orismènoc wc to ìrio thc seir c gia peirh perðodo Idiìthtec AnalogÐec kai epèktash sthn an lush shm twn kai susthm twn diakritoô qrìnou: diakrit seir Fourier, metasqhmatismìc Fourier diakritoô qrìnou, diakritìc metasqhmatismìc Fourier. Enìthta 6 Metasqhmatismìc Laplace Qr sh: EpÐlush G.D.E. me stajeroôc suntelestèc Sqèsh me to metasqhmatismì Fourier Rhtèc sunart seic sust matoc: pìloi/mhdenik.

11 K. Kotrìpouloc: S mata-sust mata 9 Enìthta 8 Metasqhmatismìc Z Sten sundedemènoc me to metasqhmatismì Laplace, all gia sust mata diakritoô qrìnou. Enìthta 9 DeigmatolhyÐa Anapar stash shm twn suneqoôc qrìnou me ìrouc deigm twn. Anakataskeu s matoc apì ta deðgmata me parembol (Je rhma Shannon). Melèth tou fainomènou sto pedðo thc suqnìthtac. To prìblhma thc epik luyhc. To ekpaideutikì ulikì (shmei seic, dialèxeic, frontist ria) èqei deqjeð èntonec epirroèc apì ta suggr mmata twn Oppenheim, Schafer kai Nawab [8], tou dask lou mou S. Pan [25, 26]. Wstìso fèrei thn proswpik sfragðda tou dhmiourgoô tou apì th makroqrìnia trib me th didaskalða tou antikeimènou anadeiknôontac th sun fei tou me plei da llwn majhm twn. Sumb llei ètsi sto na katadeiqjeð h sunoq thc epist mhc uperbaðnontac touc teqnhtoôc katakermatismoôc thc. Sto suqwremèno NÐko M rgarh ofeðlontai oi èxoqec apodìseic sthn ellhnik twn ìrwn explicit kai implicit wc prìdhlwn kai dhlwn (pìlwn eðte mhdenik n), antistoðqwc. 'Opwc ja diapist sei o anagn sthc, prosfèretai ploôsia bibliografða ìqi mìno sthn Agglik, all kai sthn Ellhnik, tìso se epðpedo jewrðac, all kai upologistik n epideðxewn se MATLAB. Se qrhstikì epðpedo gia k je enìthta X, ìpou X=1,2,...,9 prosfèrontai binteoskophmènec dialèxeic jewrðac kai frontisthriak n ask sewn pou brðskontai ston kat logo Unit X videolectures. diadrastikèc parousi seic se pdf ston kat logo Unit X slides. To kôrio arqeðo fèrei to ìnoma UnitX Slides.pdf kai endeqomènwc kaleð epideðxeic pðnakec se pdf, pou paratðjentai wc xeqwrist arqeða ston proanaferjènta kat logo. An shmeiwjoôn probl mata sto noigm touc mèsa apì to kôrio arqeðo pdf, diorj ste ta.bat arqeða parajètontac to pl rec monop ti proc to sugkekrimèno exwterikì arqeðo. Sun jwc den sunant ntai probl mata ston Acrobat Professional pou sunist tai. An qrhsimopoihjeð o Acrobat Reader, oi epideðxeic autèc mporoôn na klhjoôn xeqwrist.

12 10 K. Kotrìpouloc: S mata-sust mata shmei seic jewrðac, lumènwn frontisthriak n ask sewn kai seirèc lutwn ask sewn pou paratðjentai ston kat logo Unit X hands on me ta akìlouja onìmata: UnitX Notes.pdf, UnitX Tutorials.pdf kai UnitX Problems.pdf, antistoðqwc.

13 BibliografÐa [1] E. Kriar c, Nèo Ellhnikì Lexikì thc SÔgqronhc Dhmotik c Gl ssac. Aj na: Ekdotik Ajhn n, [2] G. D. Mpampini thc, Lexikì thc Nèac Ellhnik c Gl ssac. Aj na: Kèntro LexikologÐac, [3] Lexikì thc Koin c Neoellhnik c. JessalonÐkh: Aristotèleio Panepist mio JessalonÐkhc, InstitoÔto Neoellhnik n Spoud n ['Idruma Manìlh TriantafullÐdh], Diajèsimo: triantafyllides/ [4] D. N. MarwnÐthc, <<Qrìnoc kai s mata>>, TO BHMA, sel. A56, 7 AugoÔstou [5] E. Filipp kh-warburton, Eisagwg sth Jewrhtik GlwssologÐa. Aj na: Nefèlh, [6] J. M. F. Moura, What is signal processing? President s Message, IEEE Signal Processing Magazine, vol. 26, no. 6, p. 6, November [7] L. Deng, Cross-pollination in signal processing technical areas, IEEE Signal Processing Magazine, vol. 26, no. 6, pp. 2-3, November [8] A. V. Oppenheim, A. S. Willsky, and S. H. Nawab, Signals and Systems, 2/e. Upper Saddle River, NJ: Prentice Hall International, (Met frash Tzwrtzìpouloc, Mam c, k.., S mata kai Sust mata. Aj na: Ekdìseic Fount c, 2011). [9] J. McClellan, R. W. Schafer, and M. Yoder, DSP First: A Multimedia Approach, 1/e. Upper Saddle River, NJ: Prentice Hall, 1998). [10] J. McClellan, R. W. Schafer, and M. A. Yoder, Signal Processing First. Upper Saddle River, NJ: Pearson Education Prentice Hall, (Met frash-episthmonik epimèleia 11

14 12 K. Kotrìpouloc: S mata-sust mata E. Z. Yarr khc, Jemeli deic 'Ennoiec thc EpexergasÐac Shm twn. P tra: Ekdìseic Filom jeia, 2006.) [11] H. P. Hsu, Signals and Systems. New York, NY: Schaum s Outlines, McGraw-Hill,1995. [12] E. A. Lee and P. Varaiya, Structure and Interpretation of Signals and Systems. Boston, MA: Addison Wesley, [13] C. L. Phillips, J. M. Parr, and E. A. Riskin, Signals, Systems, and Transforms, 4/e. Upper Saddle River, NJ: Pearson Education, [14] E. Kudeki and D. C. Munson, Jr., Analog Signals and Systems. Upper Saddle River, NJ: Pearson Education, [15] J. Proakis and D. Manolakis, Digital Signal Processing, 4/e. Upper Saddle River, NJ: Prentice Hall, 1996, [16] S. K. Mitra, Digital Signal Processing. A Computer-based Approach, 2/e. Boston, MA: McGraw-Hill International, [17] U. Karrenberg, An Interactive Multimedia Introduction to Signal Processing (& CDROM), Springer Verlag, April [18] The student edition of MATLAB, Version 5: For Windows 95 and Windows NT. The Mathworks. [19] C. S. Burrus, J. H. McClellan, A. V. Oppenheim, T. W. Parks, R. W. Schafer, and H. W. Schuessler, Computer-Based Exercises for Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, [20] E. W. Kamen and B. S. Heck, Fundamentals of Signals and Systems Using MATLAB, 1/e. Upper Saddle River, NJ: Prentice Hall, [21] J. R. Buck, M. M. Daniel, and A. C. Singer, Computer Explorations in Signals and Systems Using MATLAB. Upper Saddle River, NJ: Pearson Education, [22] J. G. Proakis and V. K. Ingle, Digital Signal Processing. Upper Saddle River, NJ: Pearson Education, 2004.

15 K. Kotrìpouloc: S mata-sust mata 13 [23] J. D. Sherrick, Concepts in Systems and Signals, 2/e. Upper Saddle River, NJ: Pearson Education Prentice Hall, [24] T. Dutoit and F. Marques, Applied Signal Processing. A MATLAB-Based Proof of Concept. New York, NY: Springer, [25] S. Pan c, EpexergasÐa AnalogikoÔ S matoc. JessalonÐkh: University Studio Press, [26] S. Pan c, Yhfiak EpexergasÐa S matoc. JessalonÐkh: University Studio Press, [27] N. KalouptsÐdhc, S mata, Sust mata kai Algìrijmoi. Aj na: DÐauloc, [28] S. JeodwrÐdhc, K. MpermperÐdhc kai L. KofÐdhc, Eisagwg sth JewrÐa Shm twn & Susthm twn. Aj na: Tupwj tw-ekdìseic Gi rgou DardanoÔ, [29] M. H. Hayes, Yhfiak EpexergasÐa S matoc, Seir Shaum. JessalonÐkh: Ekdìseic Tziìla, [30] G. Karagi nnhc kai K. Tzitzir qoc, Eisagwg sta S mata-sust mata, Aj na: PapaswthrÐou, [31] G. Gewrganìpouloc, Eisagwg sth JewrÐa kai EpexergasÐa twn Yhfiak n kai Analogik n Shm twn. JessalonÐkh: KuriakÐdhc, [32] G. MoustakÐdhc, Basikèc Teqnikèc Yhfiak c EpexergasÐac Shm twn. JessalonÐkh: Ekdìseic Tziìla, [33] P. Fwtìpouloc kai A. Bel nh, S mata kai Sust mata gia Teqnolìgouc. Aj na: SÔgqronh Ekdotik, [34] A. PalamÐdhc kai A. Bel nh, S mata kai Sust mata me MATLAB. Aj na: SÔgqronh Ekdotik, [35] A. Antoniou, Yhfiak EpexergasÐa S matoc. S mata, Sust mata kai FÐltra. JessalonÐkh: Ekdìseic Tziìla, 2009.

16 14 K. Kotrìpouloc: S mata-sust mata [36] A. I. M rgarhc, S mata kai Sust mata SuneqoÔc & DiakritoÔ Qrìnou. JessalonÐkh: Ekdìseic Tziìla, 2012.