If an LTI system is described by the difference equation y(n)=ay(n-1)+bx(n), 0<a<1, then what is the output of the system when input x(n)= (5+12sin frac{ }{2}n-20cos( n+ frac{ }{4}) )?(Given a=0.9 and b=0.1)

(5+0.888sin( frac{ }{2}n+420)-1.06cos( n+ frac{ }{4}) )

(5+0.888sin( frac{ }{2}n-420)-1.06cos( n- frac{ }{4}) )

(5+0.888sin( frac{ }{2}n-420)+1.06cos( n+ frac{ }{4}) )

(5+0.888sin( frac{ }{2}n-420)-1.06cos( n+ frac{ }{4}) )

(5+0.888sin( frac{ }{2}n+420)-1.06cos( n+ frac{ }{4}) )

If an LTI system is described by the difference equation y(n)=ay(n-1)+

1.	If an LTI system is described by the difference equation y(n)=ay(n-1)+bx(n), 0<a<1, then what is the output of the system when input x(n)= (5+12sin frac{ }{2}n-20cos( n+ frac{ }{4}) )?(Given a=0.9 and b=0.1)
A.	(5+0.888sin( frac{ }{2}n-420)-1.06cos( n- frac{ }{4}) )
B.	(5+0.888sin( frac{ }{2}n-420)+1.06cos( n+ frac{ }{4}) )
C.	(5+0.888sin( frac{ }{2}n-420)-1.06cos( n+ frac{ }{4}) )
D.	(5+0.888sin( frac{ }{2}n+420)-1.06cos( n+ frac{ }{4}) )
Answer» D. (5+0.888sin( frac{ }{2}n+420)-1.06cos( n+ frac{ }{4}) )