$(20$p$)$ Giri$$i $4]$ ve ba$$lang$$ ko$$ullar$0$ olan, $y[n]+0\mathrm{.}3y[n-1]=0\mathrm{.}2x[n-2]+0\mathrm{.}3x[n-1]+0\mathrm{.}5x[n]$ olarak tan$$mlanan bir sistemin $$k$$m$n=5e$ kadar bulun.

Find the output of a system $($up to $n=5)$ defined as $y[n]+0\mathrm{.}3y[n-1]=0\mathrm{.}2x[n-2]+0\mathrm{.}3x[n-1]+0\mathrm{.}5x[n]$ while the input is $x=\left[\begin{array}{ccc}2& 3& 1\\ 5& 4& ?\end{array}\right]$ and initial conditions are $0.$

$(20$p$)$ FIR ve IIR filtreleri nelerdir? Her ikisinin fark denklemlerine $$rnekler verin ve d$$rtu cevaplarim $h[n]$ hesaplaym.

What are FIR and IIR filters? Give examples of the difference equations of both and calculate their impulse response h$[$n$].$

$(30$p$)$ Yanda blok diyagram ile g$$sterilen sistem i$$in

a$)$ Fark denklemini yaz$$n$$z$.$

b$)$ Transfer fonksiyonu ve frekans cevab$$n$$ yaz$$n$$z$.$

b$)$ Genlik cevab$$n elde etmek i$$in gereken Matlab kodlar$$m yaz$$n$$z$,$ cevab$$iziniz$.$

For the system shown in the block diagram

a$)$ Write the difference equation.

b$)$ Write the transfer function and frequency response.

b$)$ Write the Matlab codes required to obtain the amplitude response and draw the response.

$(30p)z=0\mathrm{.}9$ konumuda kutbu ve

$z=-1$ konumunda s$$f$$r$$ olan bir sistem i$$in

a$)$ Kutup s$$fir grafigini $$iziniz ve transfer fonksiyonunu yaz$$nz$.$

b$)$ Fark denklemini elde ediniz.

c$)$ Genlik cevab$$n$$ elde etmek i$$in gereken Matlab kodlar$$n$$ yaz$$n$$z$,$ cevab$$iziniz$.$

For a system with a pole at $z=0\mathrm{.}9$ and a zero at $z=-1$

a$)$ Draw the pole zero graph and write the transfer function.

b$)$ Obtain the difference equation.

c$)$ Write the Matlab codes required to obtain the amplitude response and draw the response.