Determining the parameters of a uniform distribution from its autocorrelation function
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I have a noise process v(t) which is wide sense stationary (WSS) and uniformly distributed with autocorrelation $R_{vv}(tau)=c^2e^{-betamidtaumid}$ where c =0.1.
How would I find $E[v(t)]$, the expected value of v(t)?
I think the way to solve is to take the Fouier transform ($FT$) of $R_{vv}$ and evaluate the function at 0, the DC value. I.e. $S_{vv}(omega)=FT{R_{vv}}$, $E[v(t)] = S_{vv}(0)$
Next, I want to determine the amplitude range of v(t). I believe this is equivalent to finding the bounds of the uniform distribution. I am unsure how to proceed with finding this. Here is what I have tried:
I would think the autocorrelation function would help because $R_{vv}=E[v(t)v(t+tau)]$ but I don't see how to derive PDF properties from this.
The power spectral density (PSD) contains the same information as $R_{vv}$ so if 1 can't help me, this can't either.
Any ideas?
2.
stochastic-processes random-variables stationary-processes
asked Dec 21 '18 at 1:27
AvedisAvedis
667
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add a comment |
$begingroup$
I have a noise process v(t) which is wide sense stationary (WSS) and uniformly distributed with autocorrelation $R_{vv}(tau)=c^2e^{-betamidtaumid}$ where c =0.1.
How would I find $E[v(t)]$, the expected value of v(t)?
I think the way to solve is to take the Fouier transform ($FT$) of $R_{vv}$ and evaluate the function at 0, the DC value. I.e. $S_{vv}(omega)=FT{R_{vv}}$, $E[v(t)] = S_{vv}(0)$
Next, I want to determine the amplitude range of v(t). I believe this is equivalent to finding the bounds of the uniform distribution. I am unsure how to proceed with finding this. Here is what I have tried:
I would think the autocorrelation function would help because $R_{vv}=E[v(t)v(t+tau)]$ but I don't see how to derive PDF properties from this.
The power spectral density (PSD) contains the same information as $R_{vv}$ so if 1 can't help me, this can't either.
Any ideas?
2.
stochastic-processes random-variables stationary-processes
asked Dec 21 '18 at 1:27
AvedisAvedis
667
$endgroup$
add a comment |
$begingroup$
I have a noise process v(t) which is wide sense stationary (WSS) and uniformly distributed with autocorrelation $R_{vv}(tau)=c^2e^{-betamidtaumid}$ where c =0.1.
How would I find $E[v(t)]$, the expected value of v(t)?
I think the way to solve is to take the Fouier transform ($FT$) of $R_{vv}$ and evaluate the function at 0, the DC value. I.e. $S_{vv}(omega)=FT{R_{vv}}$, $E[v(t)] = S_{vv}(0)$
Next, I want to determine the amplitude range of v(t). I believe this is equivalent to finding the bounds of the uniform distribution. I am unsure how to proceed with finding this. Here is what I have tried:
I would think the autocorrelation function would help because $R_{vv}=E[v(t)v(t+tau)]$ but I don't see how to derive PDF properties from this.
The power spectral density (PSD) contains the same information as $R_{vv}$ so if 1 can't help me, this can't either.
Any ideas?
2.
stochastic-processes random-variables stationary-processes
asked Dec 21 '18 at 1:27
AvedisAvedis
667
$endgroup$
I have a noise process v(t) which is wide sense stationary (WSS) and uniformly distributed with autocorrelation $R_{vv}(tau)=c^2e^{-betamidtaumid}$ where c =0.1.
How would I find $E[v(t)]$, the expected value of v(t)?
I think the way to solve is to take the Fouier transform ($FT$) of $R_{vv}$ and evaluate the function at 0, the DC value. I.e. $S_{vv}(omega)=FT{R_{vv}}$, $E[v(t)] = S_{vv}(0)$
Next, I want to determine the amplitude range of v(t). I believe this is equivalent to finding the bounds of the uniform distribution. I am unsure how to proceed with finding this. Here is what I have tried:
I would think the autocorrelation function would help because $R_{vv}=E[v(t)v(t+tau)]$ but I don't see how to derive PDF properties from this.
The power spectral density (PSD) contains the same information as $R_{vv}$ so if 1 can't help me, this can't either.
Any ideas?
2.
stochastic-processes random-variables stationary-processes
stochastic-processes random-variables stationary-processes
asked Dec 21 '18 at 1:27
AvedisAvedis
667
asked Dec 21 '18 at 1:27
AvedisAvedis
667
asked Dec 21 '18 at 1:27
AvedisAvedis
667
asked Dec 21 '18 at 1:27
AvedisAvedis
667
asked Dec 21 '18 at 1:27
AvedisAvedis
667
667
add a comment |
add a comment |
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