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Pulse integration in Matlab

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I am trying to extract a signal out of noise by integrating return echo pulses in MATLAB. i am using 'awgn' function to introduce noise. but the noise power increases as i integrate. shouldnt the sum of random nos. approach zero?
 

Re: PULSE INTEGRATION

Guess you integrate by addition.
perhaps you have forgotten to divide by number of samples after you add up the noise+signal samples?
-b
 

Re: PULSE INTEGRATION

thnx 4 the reply.
my point is that the signal of interest is deterministic while noise is random. random samples should add up to give approximately zero while the sinosoid of interest shud add up. dividing by no. of samples would also decrease the signal power.[/b]
 

Re: PULSE INTEGRATION

actually it is good question. To answer it accurately, you need to find what is the value of an accumulated gaussian randon variable, given the mean and variance of the distribution. I think the answer is that the accumulated sum is also gaussian.

In the context of your problem, you cannot assume that the noise accumulates to zero, only the average wil be nearly zero. The sum is still a gaussian random variable.

Of course, if your signal is also zero mean and periodic (as a sine is) it will also accumulate to zero, determinstically. In short, averaging is not a good idea in this context. correlation would be much better.
-b
 

PULSE INTEGRATION

what sort of correlation will it be? auto or cross-correlation?
which MATLAB function shud i use. there are quite a few.
 

PULSE INTEGRATION

Hi
assume that your deterministic signal say X(t) has a period of T.
and assume that each time you repeat X(t) ,an additive noise is added to X(t) ,say Ni(t) and you will have Yi(t); where i is the index of the corresponding interval and

Yi(t)=X(t)+Ni(t) ;X:deterministic;Yi & Ni random.

noise is gaussian with variance=var{N}

if you repeat X for M times and AVERAGE the result ,youwill have:

Y(t)=X(t)+N(t)
where
Y(t)=avg{Yi(t)}
N(t)=avg{Ni(t)}
((averaging is over # of experiments or repeats))

it's easily shown that:
var{Y(t)}=var{N(t)}=var{N}/M

so intuitively ,for enough large M: Y(t)-->X(t)

Armin


var{avg{Y}}
 

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