Hello,I need help with my matlab assignment. I will attach a copy of the assignment. I also have an online access to matlab, and if you need it, then let me know, and i'll provide my password.if you have any question, let me know, thank you. ECE 220: Continuous-Time Signals and Systems Spring 2020 Lab 2 Due Date Refer to the ECE 220 Laboratory Schedule for your section to determine the report due date. Submit via Blackboard. Description The purpose of this project is to learn how to use Matlab to implement the convolution integral numerically. You will gain more practice with

Hello,I need help with my matlab assignment. I will attach a copy of the assignment. I also have an online access to matlab, and if you need it, then let me know, and i'll provide my password.if you have any question, let me know, thank you. ECE 220: Continuous-Time Signals and Systems Spring 2020 Lab 2 Due Date Refer to the ECE 220 Laboratory Schedule for your section to determine the report due date. Submit via Blackboard. Description The purpose of this project is to learn how to use Matlab to implement the convolution integral numerically. You will gain more practice with convolution, and see an application of convolution in implementing an acoustic model of a room or other performance space. 1 Prelab Before starting on the lab exercises below, review section 2.2.1 in the Signals and Systems text by Oppenheim/Willsky/Nawab. Also prior to beginning the lab, determine and sketch the convolution y(t) = x(t) _ h(t) when h(t) and x(t) are as defined below: h(t) = u(t) x(t) = e _tu(t). 2 Numerical Approximation to Convolution The continuous-time convolution integral is defined as follows: y(t) = Z +_ __ x(_ )h(t _ _ )d_. (1) In order to use Matlab to implement the convolution integral, it is helpful to model the signals x(t) and h(t) as piecewise-constant functions. Following section 2.2.1 of the Oppenheim/Willsky/Nawab textbook, the signal x(t) can be approximated by x(t): x(t) = + X_ k=__ x(k_)__(t _ k_), (2) where the short rectangular pulse __(t) is defined as follows __(t) = ( 1 __/2 _ t < _/2="" 0="" otherwise="" (3)="" note="" that="" the="" definition="" of="" __(t)="" in="" equation="" 3="" differs="" slightly="" from="" that="" of="" the="" textbook,="" but="" the="" basic="" idea="" is="" the="" same.="" the="" signal="" h(t)="" can="" be="" approximated="" in="" a="" similar="" manner,="" i.e.,="" h(t)="+" x_="" k="__" h(k_)__(t="" _="" k_),="" (4)="" in="" other="" words,="" x(t)="" and="" h(t)="" are="" approximated="" as="" a="" series="" of="" narrow="" rectangular="" pulses="" with="" heights="" determined="" by="" the="" values="" of="" the="" functions="" sampled="" at="" the="" center="" of="" each="" rectangular="" pulse.="" figure="" 1="" shows="" x(t)="" and="" h(t)="" 0="" 0.5="" 1="" 1.5="" 2="" 2.5="" 3="" 3.5="" 4="" 4.5="" 5="" 0="" 0.5="" 1="" 1.5="" 2="" t="" x(t)="" 0="" 0.5="" 1="" 1.5="" 2="" 2.5="" 3="" 3.5="" 4="" 4.5="" 5="" 0="" 0.5="" 1="" 1.5="" 2="" t="" h(t)="" figure="" 1:="" piecewise-constant="" approximations="" to="" the="" signals="" x(t)="" and="" h(t).="" these="" approximations="" were="" computed="" with="" _="0.25." computed="" using="" _="0.25," thus="" there="" is="" a="" short="" pulse="" located="" every="" 0.25="" seconds.="" obviously="" the="" approximations="" will="" improve="" as="" _="" is="" reduced.="" the="" goal="" of="" this="" section="" is="" to="" compute="" the="" convolution="" of="" these="" piecewise-constant="" signals,="" i.e.,="" to="" compute="" y(t)="" defined="" as="" y(t)="Z" +_="" __="" x(_="" )h(t="" _="" _="" )d_.="" (5)="" matlab="" cant="" compute="" a="" continuous="" function,="" but="" it="" can="" compute="" samples="" of="" a="" function.="" fortunately,="" if="" we="" choose="" to="" compute="" the="" samples="" of="" y(t)="" located="" _="" seconds="" apart,="" the="" calculations="" will="" be="" simplified="" substantially.="" in="" other="" words,="" well="" focus="" on="" computing="" the="" samples="" y(n_)="" for="" n="0," 1,="" 2,="" .="" .="" .="" consider="" the="" equation="" for="" y(1_):="" y(1_)="Z" +_="" __="" x(_="" )h(1="" _="" _="" )d_.="" (6)="" to="" compute="" this="" integral,="" we="" need="" h(1="" _="" _="" ),="" which="" is="" shown="" in="" figure="" 2.="" from="" figures="" 1="" and="" 2="" we="" can="" see="" that="" the="" piecewise-constant="" sections="" of="" x(_="" )="" and="" h(1__="" )="" are="" perfectly="" aligned.="" multiplication="" of="" x(_="" )="" and="" h(1__="" )="" yields="" another="" piecewise-constant="" function,="" and="" computing="" the="" integral="" is="" very="" easy="" to="" do.="" (remember="" that="" an="" integral="" corresponds="" to="" the="" area="" under="" a="" function,="" and="" it="" is="" easy="" to="" compute="" areas="" of="" rectangles.)="" whenever="" t="" is="" equal="" to="" a="" multiple="" of="" _="" (i.e.,="" t="n_)" the="" functions="" will="" be="" aligned="" and="" the="" integral="" will="" be="" easy="" to="" compute.="" 1.="" starting="" from="" the="" convolution="" sum,="" show="" how="" that="" the="" desired="" samples="" of="" y(t)="" can="" be="" computed="" as="" follows="" y(n_)="_" +="" x_="" k="__" x(k_)h((n="" _="" k)_).="" (7)="" note="" that="" this="" equation="" should="" be="" familiar="" from="" your="" work="" in="" ece="" 201.="" it="" is="" the="" discrete="" convolution="" sum!="" matlab="" provides="" a="" function="" called="" conv="" that="" computes="" discrete="" convolution="" sums.="" type="" help="" conv="" to="" read="" more="" about="" this="" function.="" 0="" 0.5="" 1="" 1.5="" 2="" 2.5="" 3="" 3.5="" 4="" 4.5="" 5="" 0="" 0.5="" 1="" 1.5="" 2="" _="" h(1__)="" figure="" 2:="" piecewise-constant="" approximation="" to="" the="" signal="" h(1__="" ).="" the="" approximation="" was="" computed="" assuming="" _="0.25." 2.="" define="" the="" vector="" x1="" to="" be="" samples="" of="" the="" signal="" x(t)="" defined="" in="" the="" prelab="" for="" 0="" _="" t="" _="" 10.="" similarly="" define="" the="" vector="" h1="" to="" be="" samples="" of="" the="" signal="" h(t)="" for="" 0="" _="" t="" _="" 10.="" (remember="" that="" matlab="" indexes="" its="" vectors="" starting="" at="" 1,="" so="" the="" n="0" sample="" will="" be="" x1(1)).="" use="" the="" conv="" function="" to="" compute="" y1="" defined="" by="" the="" convolution="" given="" in="" equation="" 7.="" note="" that="" because="" x1="" and="" h1="" are="" finite-length="" segments="" of="" infinite="" length="" signals,="" only="" a="" finite-length="" segment="" of="" y1="" will="" be="" valid.="" for="" what="" values="" of="" t="" does="" y1="" represent="" a="" good="" approximation="" to="" the="" y(t)="" you="" found="" in="" the="" prelab?="" 3.="" re-do="" the="" calculations="" in="" part="" b="" for="" several="" values="" of="" _:="" _="0.25," 0.1,="" and="" 0.01.="" plot="" your="" results="" on="" a="" single="" graph,="" along="" with="" the="" exact="" results="" you="" found="" in="" the="" prelab.="" comment="" on="" how="" well="" the="" approximations="" work="" for="" different="" values="" of="" _.="" 4.="" for="" x(t)="t(u(t)" _="" u(t="" _="" 8))="" and="" h(t)="u(t)" _="" u(t="" _="" 12),="" determine="" the="" convolution="" analytically.="" find="" the="" convolution="" by="" representing="" the="" signals="" as="" piece-wise="" continuous="" functions="" as="" above.="" does="" it="" match="" with="" your="" analytical="" prediction?="" what="" value="" of="" _="" did="" you="" choose?="" 3="" using="" convolution="" to="" model="" an="" acoustic="" system="" in="" this="" part="" of="" the="" lab="" you="" will="" use="" convolution="" to="" simulate="" what="" you="" would="" hear="" when="" someone="" speaks="" or="" sings="" in="" particular="" room="" (or="" other="" acoustic="" environment).="" what="" you="" hear="" includes="" the="" sound="" produced="" by="" the="" person="" and="" the="" sum="" of="" all="" the="" reflections="" of="" that="" sound="" off="" the="" walls="" and="" other="" objects="" in="" the="" room.="" reverberation="" is="" the="" term="" used="" to="" describe="" the="" sum="" of="" the="" reflected="" sound.="" in="" this="" lab="" you="" will="" model="" the="" reverberation="" effects="" of="" a="" room="" as="" a="" linear="" time-invariant="" system="" (lti)="" that="" is="" characterized="" by="" its="" impulse="" response.="" you="" will="" use="" convolution="" to="" implement="" the="" lti="" system="" and="" compute="" the="" output="" for="" a="" given="" acoustical="" input="" signal.="" in="" audio="" engineering,="" this="" type="" of="" simulation="" is="" often="" referrred="" to="" as="" auralization.="" 1.="" visit="" the="" website="" to="" read="" more="" about="" auralization="" and="" to="" download="" impulse="" responses="" for="" two="" different="" environments="" that="" you="" would="" like="" to="" simulate.="" make="" plots="" of="" those="" impulse="" responses="" in="" matlab="" and="" comment="" on="" their="" features.="" based="" on="" the="" impulse="" response,="" say="" what="" you="" expect="" to="" hear="" if="" you="" sang/spoke="" in="" that="" environment.="" note="" that="" your="" plots="" should="" correctly="" show="" the="" time="" axis="" for="" the="" impulse="" response="" signals.="" pay="" careful="" attention="" to="" the="" sampling="" frequency="" that="" was="" used="" to="" obtain="" the="" data.="" 2.="" download="" the="" recording="" of="" the="" anechoic="" voice="" from="" the="" website.="" load="" it="" into="" matlab="" and="" plot="" and="" play="" the="" signal.="" you="" will="" use="" this="" voice="" in="" some="" of="" your="" simulations.="" 3.="" write="" a="" function="" to="" compute="" the="" output="" of="" your="" room="" simulation="" given="" an="" input="" signal="" and="" the="" impulse="" response="" signal.="" include="" a="" copy="" of="" your="" function="" in="" the="" report,="" along="" with="" a="" description="" of="" how="" you="" verified="" that="" it="" was="" working.="" 4.="" test="" your="" function="" with="" the="" anechoic="" voice="" sample="" and="" the="" impulse="" responses="" for="" the="" two="" rooms.="" play="" the="" outputs="" in="" matlab="" and="" plot="" the="" output="" signals.="" describe="" what="" you="" hear.="" does="" the="" output="" sound="" like="" you="" expected="" it="" to?="" 5.="" in="" this="" final="" part="" of="" the="" project="" you="" will="" record="" the="" impulse="" response="" for="" a="" room/environment="" of="" your="" choice.="" first="" brainstorm="" about="" how="" to="" create="" an="" impulse="" so="" that="" you="" can="" record="" it="" using="" the="" same="" software="" you="" used="" in="" lab="" 1.="" describe="" your="" approach="" to="" measuring="" the="" impulse="" response="" in="" the="" report.="" 6.="" record="" the="" impulse="" response="" for="" the="" environment="" you="" selected.="" include="" plots="" of="" the="" measured="" impulse="" response="" along="" with="" a="" description="" of="" the="" room="" and="" your="" test="" setup.="" please="" include="" a="" picture="" of="" the="" room="" in="" your="" report.="" 7.="" make="" a="" short="" recording="" of="" your="" own="" voice="" to="" use="" in="" simulations.="" you="" should="" use="" the="" recording="" software="" you="" used="" last="" time.="" include="" a="" plot="" of="" your="" voice="" in="" the="" report.="" 8.="" run="" your="" voice="" through="" the="" room="" simulator="" function="" using="" your="" measured="" input.="" does="" the="" output="" sound="" like="" what="" you="" expected?="" why="" or="" why="" not?="" 4="" acknowledgment="" the="" first="" part="" of="" this="" assignment="" was="" motivated="" by="" a="" similar="" project="" in="" the="" book="" computer="" explorations="" in="" signals="" and="" systems="" using="" matlab="" by="" john="" r.="" buck,="" michael="" m.="" daniel,="" and="" andrew="" c.="" singer.="" ece="" 220="" lab="" 2="" check-off="" sheet="" name:="" lab="" section:="" show="" the="" ta="" that="" your="" analytical="" predictions="" for="" the="" two="" convolution="" problems="" match="" the="" results="" you="" got="" numerically.="" run="" the="" anechoic="" voice="" and="" your="" own="" voice="" sample="" through="" the="" room="" simulator="" function="" (using="" impulse="" response="" downloaded="" from="" the="" website="" and="" the="" impulse="" response="" of="" a="" room="" recorded="" by="" you).="" play="" the="" outputs="" to="" your="" ta.="" what="" did="" you="" use="" as="" your="" impulse="" function="" to="" record="" the="" impulse="" response="" of="" the="" room?="" ta="" signature="" and="" date:="" ta="">

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