( ) ( ) (a) w(x) = a v(x) + b. (b) w(x) = a v(x + b) w = the system IS linear. (1) output as the sum of the outputs from each signal individually
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1 Hrk Sltis. Th fllig ipttpt rltis dscri ssts ith ipt d tpt. Which ssts r lir? Which r spc-irit? [6 pts.] i. tst lirit tstig lir sprpsiti lt thr t ipt sigls d tpt s th s f th tpts fr ch sigl idiidll ' tpt s th s f th t ipts " Sic " ' th sst is NOT lir ii. tst shift iric shiftig th th tpt d ipt d s if th rslt is th s shift th tpt shift th ipt Sic th tpt sts th s i th css th sst IS shift irit i. tst lirit tstig lir sprpsiti lt thr t ipt sigls d tpt s th s f th tpts fr ch sigl idiidll ' tpt s th s f th t ipts " sic " ' th sst IS lir
2 Hrk Sltis ii. tst shift iric shiftig th th tpt d ipt d s if th rslt is th s shift th tpt shift th ipt Sic th tpt sts th s i th css th sst IS shift irit c si i. tst lirit tstig lir sprpsiti lt thr t ipt sigls d tpt s th s f th tpts fr ch sigl idiidll si si ' si si si tpt s th s f th t ipts " si ' sic " th sst IS lir ii. tst shift iric shiftig th th tpt d ipt d s if th rslt is th s shift th tpt si shift th ipt si Sic th tpts r diffrt i th t css th sst is NOT shift irit
3 Hrk Sltis.0 Gi ctis sigl f lt th fllig; [6 pts.] f f 00 f 0 thris f [ ξ η ] ξ η dξdη f c f 3 dd f 3 dd 9 dd 0 d f [ ξ η ] ξ η dξdη f 3
4 Hrk Sltis.3 id th rir trsfrs f th fllig ctis sigls [0 pts.] s [ ] [ ] [ ] I I I [ ] [ ] I s [ ] [ ] [ ] I I I [ ] [ ] I c si s [ ] I dd s si [ ] dd dd si [ ] [ ] dd dd [ ] Ctd [K]: Crrctd Asr
5 Hrk Sltis d cs c [ ] I dd c cs [ ] dd dd cs [ ] [ ] dd dd [ ] f dd d d t tht gi d d d d d d d d Ctd [K]: Crrctd Asr 5
6 Hrk Sltis. A igig sst ith hich r pritig hs istrpic prprtis. Y sr th ipls rsps fcti s h [6 pts] Sktch th ipls rsps Wht is th trsfr fcti H H h dd dd dd Ctd [K3]: Crrctd sr 6
7 Hrk Sltis.5. W t t spl th -D ctis sigl f s f rctglr splig sch t ti.5 spls pr illitr. Dtri th PS h f idl l-pss ti-lisig filtr ith th i pssil frqc ctt. Wht prctg f th spctr rg f f is prsrd this filtr? I prctic c spl f lis-fr itht sig ti-lisig filtr? [6 pts.] Th splig rt is gi s.5 spls pr illitr. Ass d r i its f illitrs. This ld T id lisig this s tht th i sptil frqc f th sigls r T sr thr is lisig ld d t iplt ti-lisig l-pss filtr ith th i sptil frqcis sh. si si h Wht prctg f th spctrl rg f f is prsrd this filtr E E ttl filtrd E E ttl filtrd dd dd dd E % prsrd 00 E dd dd filtrd ttl 00 dd dd dd dd 98.%
8 Hrk Sltis 6. Mtl ssigt Writ Mtl script fil tht ds th fllig: Lds i th ipt ig fd i hr.t fil th sit Cpt th D rir Trsfr sig th fft cd 3 Crt difid rsi f th rir Trsfr frcig cfficits ithi crti rgis dscrid i th figrs l t zr Clclt th rcstrctd ig sig th difid rir Trsfr d plt th rslt. I r hrk shld prid; ctd cp f r Mtl cd igig rslts fr th 3 ids sh th t pg. [6 pts] 8
9 Hrk Sltis Prl 6: 0.5 L Pss rqc Di L Pss iltr
10 Hrk Sltis 0.5 L Pss rqc Di L Pss iltr
11 Hrk Sltis High Pss rqc Di High Pss iltr
12 Hrk Sltis % This script fil is fr BMEGELEG Prl 6 % ld ig t dcps it ch f sptil frqcis % This fil hs 3 rils: X D tri tht hlds th ig % i D ctr f crdits i D ctr f crdits ld hr.t % dtri th distc t crdits di-i; % dtri th distc t crdits di-i; % plt th rigil ig X figr clrp'gr'; igscx % fid th rir cfficits f th ig X. W s th D T % fcti t d this clld fft. This fcti is th D rir % Trsfr f th rigil ig fftx; % This fcti s th frqcis rd s tht th r sir t % rk ith fftshift; % crt ctrs f sptil frqcis i th pl lispc-.5.5nd; lispc-.5.5nd; % plt th rir trsfr f th rigil ig figr clrp'gr'; igsclg0s ll''; ll''; titl'lgs' % Cp th T s c dif it fr th thr cditis fftlpss ; fftlpss ; ffthighpss ; % Lp thrgh th D trics f frqcis d r th dsird % frqc ctt fr i :lgth Vl i; fr :lgth Vl ; % 0 t ll high frq ls t k th.5.5 sqr if svl > 0.5 svl > 0.5
13 Hrk Sltis d fftlpss i 0; % 0 t ll high frq ls t k th.5.5 sqr if svl > svl > fftlpss i 0; d % 0 t ll l frq ls t r th.5.5 sqr if svl < 0.5 && s Vl < 0.5 ffthighpss i 0; d d d % Plt T fr th.5.5 sqr figr3 clrp'gr'; igsc lg0sfftlpss; titl '0.5 L Pss rqc Di' ll''; ll''; % Plt rcstrctd ig ftr rig frqcis figr clrp'gr'; % ifftshift ds fftshift igscifftifftshiftfftlpss titl '0.5 L Pss iltr' % Plt T fr th.5.5 sqr figr5 clrp'gr'; igsc lg0sfftlpss; titl '0.5 L Pss rqc Di' ll''; ll''; % Plt rcstrctd ig ftr rig frqcis figr6 clrp'gr'; % ifftshift ds fftshift igscifftifftshiftfftlpss titl '0.5 L Pss iltr' % Plt th T fr th th high pss filtr figr7 clrp'gr'; igsc lg0sffthighpss; titl 'High Pss rqc Di' ll''; ll''; % Plt rcstrctd ig ftr rig frqcis 3
14 Hrk Sltis figr8 clrp'gr'; % ifftshift ds fftshift igscifftifftshiftffthighpss titl 'High Pss iltr'
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