Questions tagged [random]

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1answer
65 views

Correlation of independent random processes

Suppose $X(t)$ and $Y(t)$ be two independent random processes. Is $E(X(t_1)Y(t_2))$ necessarily zero?
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1answer
23 views

Power contained in a random process $X(t)$

How do we calculate the AC and DC power of random process $X(t)$ , provided we have $R_x (\tau)$, and $S_x(f)$ ?
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0answers
33 views

How to Derive Rayleigh distribution using transformation formula

Consider a complex random variable $Z=X+\jmath Y$, where the probability density function of $X$ and $Y$ are given by $$p(x) = \frac{1}{\sqrt{2\pi\sigma^2}} {\rm e}^{-\frac{x^2}{2\sigma^2}}\quad\mbox{...
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1answer
30 views

Variance of function of random variable

Is their an easier way to find variance of function of random variable? Till now what I am doing is first find probability density function of (function of random variable) then integrate over range.
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0answers
20 views

Independence of ergodic process [closed]

I am given two random process x and y out of which x is considered to be ergodic and its probability distribution function is not given while y is considered to be non ergodic and its probability ...
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2answers
44 views

Independence of Functions of random Variable

Consider I am given two functions of one random variable each for example x=cos(at),y=rect(bt) where a and b are random variables.And I am given Probability density function for a and b then if I am ...
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0answers
29 views

What is a simple smoothing filter for signals sampled at non-uniform times?

An answer: A simple smoothing filter for signals that has a DC gain of one, is a simple RC low pass filter. This filter has a exponentially rising step response, $$O(t) = 1 - e^{\frac{-t}{\tau}},$$ ...
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2answers
54 views

Random Process at a particular time instance

I was studying Random Process and I thought I understood what it was all about until I came across this example. Consider a random experiment of tossing a coin with sample space S = {H, T} The sample ...
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0answers
37 views

CDF of product of two *translated* exponential variables

It is known that the CDF of the product of two exponential random variables is given by this answer If $X$ and $Y$ have rate parameters $\mu$ and $\lambda$, so their pdf's are $f_X(x) = \mu e^{-\...
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1answer
235 views

How can I generate time-variant Rayleigh channel in MATLAB

One of known models for channel simulation is called Rayleigh Fading channel, it's usually used to simulate wireless channel in time variant/invariant. As I know, Rayleigh fading channel can be ...
2
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1answer
58 views

Does a collection of Gaussian random variables necessarily constitute a Gaussian Process?

If $\{X(t)\}$ is a Gaussian Process then the random variables $X(t_k)$ where $k = 1,2,3...n$, are jointly Gaussian. If each random variable $X(t)$ is a Gaussian variable, then will the random ...
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0answers
57 views

Is the output of function of two ergodic processes ergodic?

Let $\{\xi_k\}_{k\in \mathbf{Z}}$ and $\{\epsilon_k\}_{k\in \mathbf{Z}}$ be two independent zero-mean Gaussian processes (i.i.d.). Is the output of the function $f$ such that $y = f(\dots,\xi_{k-1},\...
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0answers
38 views

How to randomly generate a realistic hourly temperature series given historic data

I have 20 years of historic hourly temperature data in Omaha. I want, given just a seed, to be able to generate a pretty realistic year of hourly temperatures. (I have a program that takes such ...
1
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1answer
59 views

Doubts and some confusion on variance for complex rv

This question is in continuation of the one asked here. Let's say that the measurement noise $w$ or any random variable is circularly Gaussian complex. If the imaginary and real components each has ...
3
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1answer
151 views

How can I calculate the entropy of a signal that's not independent from itself?

I really don't know how to word this better, sorry if that title is confusing. Basically, I'm wanting to use the noise from an AM radio audio signal to generate random numbers. To do this effectively,...
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1answer
568 views

Rayleigh Fading Simulation

I have a question about simulating Rayleigh Fading channel. I know theory behind the Rayleigh channel and it is sum of two Gaussian random variable where the amplitude is Rayleigh distributed and the ...
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3answers
1k views

Random signals as power signals

Why are random signals considered as power signals (i.e. signals with infinite energy and finite average power)? Does this make any sense? What does it mean for random signals to have infinite energy ...
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1answer
74 views

SD of a function of signals

Say $a_x$, $a_y$, $b_x$, $b_y$ are signals with values in $\mathbb{R}$. Say they are independednt, normally distributed variables with given SDs $\sigma_{a_x}$, $\sigma_{a_y}$, $\sigma_{b_x}$, $\...
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1answer
125 views

Understanding of Random Process/Random Variable

At a simpler level to my previous question, I wanted to confirm my understanding on Random Process based on Random Variables using an example. So, I took this example: If we consider a dice, which ...
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1answer
2k views

Understanding of Random Process, Random Variable and Probability Density Function

I just wanted to confirm my understanding of a Random Process, Random Variable and the its Probability density Function. Here is the way that I looked a Random Process/Random Variable: If we ...
2
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0answers
95 views

Distribution of a Filtered Signal

For a given input signal, for each discretized sample, $dt=1$: $$ x(t) \sim N(0,1)$$ and a given LTI low order filter with transfer function: $$ H_{fil}(f)$$ which would be is the a priori ...
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2answers
1k views

Addition of signal variance and noise variance

Can I add two variances directly? I have my noise variance $\sigma_{noise}=-10 \ \mathrm{dB}$ and signal variance, $\sigma_{signal}=40 \ \mathrm{dB}$. So, can I say the total variance is $\sigma_{...
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1answer
1k views

Random process $X(t)$ with autocorrelation function given find the mean and the variance

Autocorrelation function is $$R_{xx}(\tau)=\frac{20}{1+2\tau^2}$$ So at $\tau=0$$$R_{xx}(0)=20=E[X(t)X(t)]=E[X^2(t)]$$ The variance is $$\mathrm{Var}[X(t)]=E[X^2(t)]-E^2[X(t)]=20-E^2[X(t)]$$ As $X(t)$...
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1answer
187 views

What is the value of the standard deviation $\sigma$? [closed]

I am using the following formula to add the additive Gaussian noise. noise= (x/255)*(randn(size(image))), where x is the ...
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1answer
2k views

Random sampling vs uniform sampling

In this paper of Lustig, he speaks about a something which appears unintuitive: sampling at random may exhibit better performance than sampling uniformly. I tried to understand this starting from page ...
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1answer
122 views

How to measure noise, consonance, dissonance of a sound?

How can I make a graph of the noisiness of some audio durations of 100ms - 10s with 100% being white noise and 0% being a sine wave. I have FFT at the moment, are there other ways to know the ...
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1answer
303 views

Detection of sine signals with random amplitudes

Problem statement: I am designing a NP detector for the following detection problem: $\mathcal H_{0}: x[n] = A_0\cos(2\pi f_0n) + w[n]$ $\mathcal H_{1}: x[n] = A_1\cos(2\pi f_0n) + w[n]$ where: $...
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0answers
36 views

How to determine if output signals represent the same process with different unknown random inputs

This is a question about how to determine if two different output signals represent the same process with different random inputs. This is related to validating ship motion modeling. When ship motion ...
4
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3answers
626 views

Estimate changing time lag between signals

Suppose I have two timeseries $x_1(t)$ and $x_2(t)$, shown in the image that I drew below. They look almost identical in general form, except some features are shifted slightly in time from one series ...
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1answer
364 views

Relation between Covariance matrix & Energy of a random signal

Let's say I have the below random signal: $ Y[n] = [y(n), y(n-1), y(n-2), \ldots, y(1)] $ I have two random variables now: The first one $X_1 $ which express the maximum eigenvalue of the covariance ...
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1answer
567 views

Uniform quantizer for gaussian input signal

I have a gaussian signal $x$ with zero mean and unit variance. I am quantizing it by using a uniform quantizer of step size $q$ calculated by $$q = \frac{x_\mathrm{max} - x_\mathrm{min}}{2^{M_\mathrm{...
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1answer
178 views

Plotting uniform and Gaussian random variables

I want to create uniform and Gaussian (normal) random variables in MATLAB via rand and randn syntax. And I would like to plot ...
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2answers
445 views

What is the entropy for these cases?

This question stems from an article, "Entropy estimation of symbol sequences" download link where the abstract mentions the need for using symbols in information theory. Random chains of ...
2
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1answer
869 views

Complex normal Gaussian noise

I would like to create complex normal Gaussian noise with dimensions $(M,N)$. The noise should be zero mean and the variance should be equal to one. How can I do so?
3
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2answers
541 views

Filtering random Signal

My question is easy one actually. First, I generate a random signal using randn() function of MATLAB like this: Then, I design a FIR filter of order 200 of pass-...
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0answers
2k views

Generate time-domain random signal from PSD

Given an analytical description of the PSD, for example (MATLAB "pseudocode"): ...
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2answers
562 views

Reproducing MATLAB's randn

Gentlemen! I have to reproduce MATLAB random normal generator (randn) with some fixed seed. Also, I have to reproduce it in an external script, without MATLAB itself. Has anyone done this? What ...
2
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1answer
282 views

Gaussian, Rayleigh, and Exponential RVs

I am doing some simulations on the performance of OFDM systems in multi-path channels and I am confused about something. It is explained below: Assume that we have a multi-path channel with a number ...
1
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1answer
207 views

WSS Ergodic Process with Power Spectrum

I was given a WSS ergodic process $x(t)$ with power spectrum : $$ \begin{array}{rcl} G_x(f) &=&1−\left|\frac{f}{B}\right| &\mbox{for } |f|<B\\ G_x(f) &=& 0 & \...
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3answers
985 views

The Standard Deviation of The Derivative of a Signal

Given a signal with zero mean and a standard deviation of 0.1 sampled at 5000 Hz. What would be the Standard Deviation of its 1st, 2nd and 'n' derivative? For instance, let's say we measure the ...
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1answer
2k views

Difficulty in understanding ergodicity and ensemble averaging

Literature says that a stationary signal is ergodic, if its ensemble average = time averages. Should it be the statistics computed by time averaging = statistics computed by ensemble averaging?The way ...
2
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1answer
2k views

Digital Gaussian White noise signal generation in C++

I am trying to generate a band limited noise signal on a Raspberry Pi. I calculate samples at every 1/48000 sec on the Pi. If I generate normally distributed random numbers as data points at every ...
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1answer
1k views

Autocorrelation of the product of deterministic and random signal

I was wondering how to calculate the autocorrelation of a deterministic signal $x(t)$ multiplied by a stochastic process $M(t)$, whose autocorellation $R_M(\tau)$ is known a priori. In my case, $x(t)$ ...
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2answers
130 views

number of possible component in sinusoidal model

Suppose that we have the following model $y(t) = A_1\sin(\omega_1 t+\phi_1) + A_2\sin(\omega_2 t+\phi_2) + ... + A_p\sin(\omega_p t+\phi_p) + z(t)$ My question is not related to how to determine the ...
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2answers
2k views

Sampling low pass filtered white noise

If we filter out ideal white noise using an ideal LPF of cutoff frequency 10 KHz and then sample it at 30 KHz , is the resulting discrete signal statistically independent? I would like to know the ...
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0answers
302 views

Variance of a random discrete sequence

If $x[n]$ is a discrete random sequence with uniform distribution having mean $\mu = 2$ and variance $\sigma^2 = 3$, if passed through a moving average filter to get an output of $$\frac{x[n] + x[n-...
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1answer
421 views

Why is random noise amplitude inversely proporional to the frequency?

http://astarte.csustan.edu/~tom/SFI-CSSS/info-theory/info-lec.pdf compares a bacteria DNA vs a random string: My first step was to generate for myself a "random genome" of comparable size to ...
4
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1answer
14k views

Why the RMS of a PSD curve is the root of the area below

I will try to explain what is my level of understanding of this problem, please correct me if I'm wrong: RMS is the Root Mean Square, it represent the mean value of the input signal. PSD is the ...
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0answers
164 views

Stochastic process inference from partial observations

Consider a set $U$. My signal is a piece-wise constant "function" $Sig: t \mapsto s$, i.e. the signal at time $t$ equals to some subset $s \subset U$. One can see $Sig(t)$ as a stochastic process. ...
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3answers
2k views

Gaussian random generator

I have quite a straight-forward question. What I aim for is the generation of a certain set of random numbers with a normal distribution (mu = 0, ...