# Tag Info

Accepted

### Understanding of Random Process, Random Variable and Probability Density Function

when we observe the Random Process at a specific time $t_k$, that is the value at $X(s_1,t_k), X(s_2,t_k),\ldots,X(s_n,t_k)$, if we denote them by $(a_1,a_2,\ldots, a_n)$. Now the mapping between ...
Accepted

### Understanding Ergodicity and Ensemble Averaging

I will try to explain this practically using MATLAB notation. Yet before that I must say the ergodic property sometime is limited to a level of moment, namely ergodic in the 1st , 2nd, 3rd moment, etc....
Accepted

Accepted

### The Standard Deviation of The Derivative of a Signal

Since the signal is discrete and the operation is linear it be formed using a Filter. Assuming the signal is given by $x \left[ n \right]$. Then its derivative is given by:  y \left[ n \right] = \...
Accepted

Accepted

### Understanding of Random Process/Random Variable

Let me explain it in another way. Consider you have 6 different function of time. You only throw your dice once and regarding the outcome you choose on of six functions and the chose one is one ...
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### Random process $X(t)$ with autocorrelation function given find the mean and the variance

The limit $\lim_{\tau\to\infty} R_x(\tau)$, if it exists, equals $E^2[X(t)]$ and so $E[X(t)]=0$ in this case. More generally, the mean of a WSS process is nonzero only if the power spectral density ...

### The Standard Deviation of The Derivative of a Signal

It depends on the frequency content of the signal. Consider sinusoidal signals with an amplitude of 1 and frequencies of 1Hz and 1kHz. Both have the same standard deviation, but the standard ...
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### Doubts and some confusion on variance for complex rv

If the imaginary and real components each has a variance of 0.5, then what would be the total variance? The variance of the complex RV in that case would be $0.5 + 0.5 = 1$. If on the other hand, ...