Consider a binary communication system. The pulse p(t) and the pulse q(t) are defined by 0 st y or

Suppose a6=6, a7=7, a8 = 8, a9 = 9

y or < y="" the="" impulse="" response="" of="" the="" lti="" filter="" h(t)="" is="" given="" by="" 0sts1,="" else.="" sketch="" the="" signals="" p(t)="" and="" q(t).="" s1,="" h(t)="{" а.="" b.="" suppose="" that="" “1"="" is="" sent.="" determine,="" in="" terms="" of="" no,="" the="" probability="" of="" error="" if="" y="ag" –="" 2.="" c.="" suppose="" that="" you="" can="" change="" the="" lti="" filter="" and="" the="" threshold="" at="" the="" receiver.="" sketch="" the="" impulse="" response="" of="" the="" optimal="" filter.="" determine="" the="" minimax="" threshold="" with="" the="" optimal="" filter.="" determine="" the="" probability="" of="" error="" with="" the="" optimal="" filter="" and="" the="" i.="" ii.="" iii.="" associated="" minimax="" threshold.="" "/="">
Extracted text: Consider a binary communication system. The pulse p(t) and the pulse q(t) are defined by 0 st<1,><>< 2,="" 2=""><>< 3,="" else,="" ´a6="" +="" 1,="" az="" +="" ag,="" p(t)="ag," 0,="" and=""><1,><>< 2,="" 2="">< 3,="" else.="" ag="" –="" 5,="" -а,="" —="" 2,="" 0,="" to="" send="" "l",="" p(t)="" is="" transmitted.="" to="" send="" “0",="" q(t)="" is="" transmitted.="" the="" channel="" is="" contaminated="" by="" awgn="" with="" two-sided="" power="" spectral="" density="" of="" no/2.="" the="" following="" receiver="" is="" used="" for="" detection.="" the="" receiver="" decides="" "i"="" if="" the="" output="" of="" the="" sampler="" is="" q(t)="bigger" than="" y,="" and="" “0"="" otherwise.="" @t,="2" h(t)=""> y or < y="" the="" impulse="" response="" of="" the="" lti="" filter="" h(t)="" is="" given="" by="" 0sts1,="" else.="" sketch="" the="" signals="" p(t)="" and="" q(t).="" s1,="" h(t)="{" а.="" b.="" suppose="" that="" “1"="" is="" sent.="" determine,="" in="" terms="" of="" no,="" the="" probability="" of="" error="" if="" y="ag" –="" 2.="" c.="" suppose="" that="" you="" can="" change="" the="" lti="" filter="" and="" the="" threshold="" at="" the="" receiver.="" sketch="" the="" impulse="" response="" of="" the="" optimal="" filter.="" determine="" the="" minimax="" threshold="" with="" the="" optimal="" filter.="" determine="" the="" probability="" of="" error="" with="" the="" optimal="" filter="" and="" the="" i.="" ii.="" iii.="" associated="" minimax="">