one-order system realization

[vacant]

Hi!

I want to realize the following simple one-order system

x->(+)-> [D]-------->y
............^ ................|
............|----a----------

here, (+) is an adder, [D] is D-flip-flop, a is the feedback coefficient.

so the system equation is

x +ay=y(n+1)

if the a is chose to be 1, the system would be unstable, right? (since the pole=1 ,is at the unit circle); so if a is 1/2 or 1/4, it would be fine, but how to realize /2 or /4 in digital circuit ??
I don't want to use shift register since there would be extra delay, any other method? (like shifter without a period clock delay)

Thanks a lot.

 

[vacant]

any suggestions?
I would like to know how to realize this simple digital LPF ? thanks

 

[eruisi]

I don't know why you would need a shifter?
just choose y[n:1] out of y[n:0], you got /2, y[n:2] is /4
if you need sign extension, then {y[n],y[n:1]}, etc.