$1.[8$ pts$]$ Given: You have a signal described as the following:

vin$($t$)=1+4$ cos$(300$t$)+2$ cos$(800$t$)+3$ cos$(1,700$t$)+5$ cos$(2,100$t$)$ mV

The above signal is input into the following ideal filters:

Filter Type Cut$-$Off Freqs in rad$/$sec Passband Gain

LPF c $=6003$

HPF c $=1,6002$

BPF c$1=700$ c$2=1,2004$

BRF c$1=200$ c$2=2,0005$

Find: Determine the output signal, vo$($t$),$ from each filter.

Solution:

voutLPF $=$

voutHPF $=$

voutBPF $=$

voutBRF $=$