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recursive and non recursive system

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tralne

tralne

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can some one explain what exactly is a recursive and non recursive system is?
 

A recursive system is a system in which current output depends on previous output(s) and input(s) but in non-recursive system current output does not depend on previous output(s).
 
Recursive is when a software function or procedure calls itself
 

MHanif said:
A recursive system is a system in which current output depends on previous output(s) and input(s) but in non-recursive system current output does not depend on previous output(s).
Click to expand...

like a system with memory element and without memory, right?

---------- Post added at 12:28 ---------- Previous post was at 12:21 ----------
klystron said:
Recursive is when a software function or procedure calls itself
Click to expand...

ya ,i ve learned that in programing.. :)
that word have lot of meaning i think..

i would like to know,how its related to a FIR filter..:-?

thanks
 

tralne said:
like a system with memory element and without memory, right?
Click to expand...

The system with memory is not necessarily a recursive system. For example in FIR systems for input x[n] and output y[n] if we have
y[n] = 0.5(x[n]+x[n-1]) then the current output does not depend on previous output but depends on current input and previous input. But for IIR case like an accumulator
y[n] = y[n-1]+x[n], current output is depended on previous output as well as on current input ( generally current and previous inputs). So accumulator is a recursive system.
 

first example , is system without memory and second one is with memory..
and both your example is a recursive system..

did i get you correctly?:-?
 

First example is a system with memory as we have x[n-1] with x[n] i-e we have stored x[n-1] and used that to compute y[n] but it is non-recursive as y[n] does not depend on y[n-1] or y[n-2] etc. Second one is recursive because y[n] depends on y[n-1].
 

MHanif said:
First example is a system with memory as we have x[n-1] with x[n] i-e we have stored x[n-1] and used that to compute y[n] but it is non-recursive as y[n] does not depend on y[n-1] or y[n-2] etc. Second one is recursive because y[n] depends on y[n-1].
Click to expand...

um..

so both have memory
first one is not recursive and second one is recursive

---------- Post added at 17:57 ---------- Previous post was at 17:53 ----------

and ,can FIR filter realize both recursive and non recursive system??
 

FIR filters can have recursive implementations. the most obvious is the simple moving sum (or moving average):
y[n] = x[n] + x[n-1] + x[n-2] + ... + x[n-511]
y[n] = y[n-1] + x[n] - x[n-512]
the first method is the direct method, the second works because y[n] and y[n-1] share many common terms.

IIR filters are always recursive.
 

tralne said:
and ,can FIR filter realize both recursive and non recursive system??
Click to expand...
FIR = Finite Impulse Response
and recursive systems have generally infinite impulse response. So, they cannot be implemented as FIR. Only systems having Finite Impulse response can be implemented using FIR filters.
 

FIR filters can have utilize recursion within the implementation. I show the most common example of this in my previous post. For the specific case of the moving average (or moving accumulation), each input is multiplied by 1, then summed. thus for a 4 tap filter h = [1 1 1 1]:
y[10] = x[10] + x[9] + x[8] + x[7]
y[11] = x[11] + x[10] + x[9] + x[8]
are two samples from the sequence. notice that:
y[11] = y[10] + x[11] - x[7]
or "the next value is the current value, plus the new input, minus the oldest input"

IIR filters must be recursive, and furthermore, the impulse response is infinitely long. while IIR filters are often strongly associated with recursive systems, it is actually the impulse response that gives them the name. As shown above, there are recursive systems that have finite impulse responses.

All IIR filters are recursive
not all recursive systems are IIR

So if you know a system is IIR, you know it has recursion. If you only know that a system is recursive, you must do further analysis to determine FIR/IIR.
 
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    tralne

    tralne

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IIR filter has recursion

and ,FIR filter can have recursion too.. so filter which realizes non recursive system is FIR filter itself?

and in practical life,why should we look if a system is recursive or not?what s its importance?
 

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