Probability

x[n] is a zero-mean white Gaussian random process with variance of 1 and
y[n] is the output when x[n] is filtered using a two-tap FIR filter with
coefficients of [1 1]. What's the probability of the event {y[n+1]>1}
given that y[n]=1?

ngeva0 wrote:
> x[n] is a zero-mean white Gaussian random process with variance of 1 and
> y[n] is the output when x[n] is filtered using a two-tap FIR filter with
> coefficients of [1 1]. What's the probability of the event {y[n+1]>1}
> given that y[n]=1?

Is the noise bandlimited before filtering? What is the effect of your 
filter on any signal? (Given y[n] = a and y[n+1] = b, what will the 
filter output be?)

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

ngeva0 wrote:
> x[n] is a zero-mean white Gaussian random process with variance of 1 and
> y[n] is the output when x[n] is filtered using a two-tap FIR filter with
> coefficients of [1 1]. What's the probability of the event {y[n+1]>1}
> given that y[n]=1?
> 
Technically the probability that y(n)=1, is zero for a continuous 
density. In practice it isn't. If y(n) is governed by a discrete 
probability density, the question makes some more sense.

Stan Pawlukiewicz wrote:
> ngeva0 wrote:
> 
>> x[n] is a zero-mean white Gaussian random process with variance of 1 and
>> y[n] is the output when x[n] is filtered using a two-tap FIR filter with
>> coefficients of [1 1]. What's the probability of the event {y[n+1]>1}
>> given that y[n]=1?
>>
> Technically the probability that y(n)=1, is zero for a continuous 
> density. In practice it isn't. If y(n) is governed by a discrete 
> probability density, the question makes some more sense.


Btw, I know that finals are happening all over the place.  I wouldn't 
normally answer this sort of question at this time of year, but I have a 
thing about a professors that ask trick questions.  IMHO they are chixen 
fhit pricks.

>ngeva0 wrote:
>> x[n] is a zero-mean white Gaussian random process with variance of 1
and
>> y[n] is the output when x[n] is filtered using a two-tap FIR filter
with
>> coefficients of [1 1]. What's the probability of the event {y[n+1]>1}
>> given that y[n]=1?
>
>Is the noise bandlimited before filtering? What is the effect of your 
>filter on any signal? (Given y[n] = a and y[n+1] = b, what will the 
>filter output be?)
>
>Jerry
>-- 
>Engineering is the art of making what you want from things you can get.
>�����������������������������������������������������������������������
>

the output y[n]=x[n]+x[n-1] after filtering. therefore, y[n+1]=x[n+1]+x[n]

Got some karma on this one, do you Stan??? :)

--RY

Randy Yates wrote:
> Got some karma on this one, do you Stan??? :)
> 
> --RY
> 
All I can say is that it's good that I went to college before I learned 
to use C4 in the Army.

Yup, I agreee....this a  tricky problem in Random processes....related
to linear systems, characteristic funtions. This particular operation
would correlate the uncorrelated input signal. So, to find the pdf of
the output is your problem...It has been a long time for me dealing
with this stuff....but I hope my 'clues' are correct

Nithin

nithin.pal@gmail.com wrote:
> Yup, I agreee....this a  tricky problem in Random processes....related
> to linear systems, characteristic funtions. This particular operation
> would correlate the uncorrelated input signal. So, to find the pdf of
> the output is your problem...It has been a long time for me dealing
> with this stuff....but I hope my 'clues' are correct
> 
> Nithin
> 


P( y(n)=1 ) = 0 , characteristic functions don't change that. Either it 
is a typo, or a trick question.

ngeva0 wrote:
>>ngeva0 wrote:
>>
>>>x[n] is a zero-mean white Gaussian random process with variance of 1
> 
> and
> 
>>>y[n] is the output when x[n] is filtered using a two-tap FIR filter
> 
> with
> 
>>>coefficients of [1 1]. What's the probability of the event {y[n+1]>1}
>>>given that y[n]=1?
>>
>>Is the noise bandlimited before filtering? What is the effect of your 
>>filter on any signal? (Given y[n] = a and y[n+1] = b, what will the 
>>filter output be?)
>>
>>Jerry
>>-- 
>>Engineering is the art of making what you want from things you can get.
>>�����������������������������������������������������������������������
>>
> 
> 
> the output y[n]=x[n]+x[n-1] after filtering. therefore, y[n+1]=x[n+1]+x[n]

Since the input to the filter isn't bandlimited, there will be aliasing 
at any sample rate, so beware of intuitive results. Nevertheless, if 
y[n] = 1, then x[n] + x[n-1] = n. You need to calculate the probability 
that x[n+1] will exceed x[n-1]. That's not trivial, but at least it's 
not a conditional probability. Pick a (Gaussian) number. Pick another. 
What is the probability that the second is more positive than the first?

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������