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0
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2answers
42 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 ...
0
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0answers
78 views

Generate time-domain random signal from PSD

Given an analytical description of the PSD, for example (MATLAB "pseudocode"): ...
0
votes
2answers
84 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
votes
1answer
54 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
vote
1answer
57 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 & ...
-1
votes
2answers
96 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 ...
3
votes
1answer
428 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
votes
1answer
198 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 ...
1
vote
1answer
171 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, $x(t)$ ...
0
votes
2answers
117 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 ...
1
vote
1answer
74 views

A special case of 2 jointly WSS stochastic processes

I know that 3 conditions must be met in order a pair of stochastic processes X(t) and Y(t) to be characterized as jointly WSS: 1. X(t) WSS 2. Y(t) WSS 3. Rxy(t1,t2) = Rxy(t1 - t2) = Rxy(t2 - t1) ...
2
votes
2answers
922 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 ...
0
votes
0answers
97 views

Variance of this 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 $(x[n] + x[n-1] + ...
0
votes
1answer
111 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
votes
1answer
2k 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 ...
5
votes
0answers
106 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. ...
3
votes
2answers
1k 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, ...
0
votes
2answers
105 views

Random signal power spectrum

I have a signal $X(t)=\sum_{n=-\infty}^{\infty} Z_n \delta(t-n\tau)$, $Z_n$ is a random variable with equal possibility of +-1 and I know the power spectrum of this signal is $\frac {1}{\tau}$ from ...
6
votes
1answer
145 views

How to tell how likely a signal is present in another one? (variance unknown)

I know this is probably a simple question, but I haven't been able to find a satisfactory answer anywhere... Say you have a time series signal of finite length N. Call it $y[n]$. It looks like a ...
1
vote
0answers
80 views

Gauss Markov Process

I am trying to generate a random signal that represents a gyroscope drift. I know the Allan Variance characteristics of the signal (ARW, RRW, Bias Instability and Cluster Time for for Bias ...
1
vote
1answer
87 views

Probability of random numbers

This is the question i found on internet under DSP section so thats why i am posting it here. Help me understand it please. "A computer adds 1000 random numbers that have each been rounded off to ...
3
votes
2answers
411 views

Can Kalman Filter be used to track Randomly Moving Target?

i want to track random moving object with a camera using kalman filter...i have the following questions... Randomly moving target means $Corelation(t) = E[ x(T)x(T+t) ]$ is very low...where $x(T)$ ...
9
votes
3answers
536 views

Implementing Gaussian random variable by using a uniform random variable

I'm trying to write a C++ function that will return Gaussian random values, given their means and variances. There is a library function rand(), which returns ...
6
votes
2answers
388 views

Probability distribution of windowed cross-correlation

This question is in the context of time-delay estimation. Say I have a stationary Gaussian stochastic process $g$, and I know its autocorrelation function $R_g(\tau)$. To do time-delay estimation, I'm ...
19
votes
5answers
13k views

What is the distinction between ergodic and stationary?

I have trouble distinguishing between these two concepts. This is my understanding so far. A stationary process is a stochastic process whose statistical properties do not change with time. For a ...
11
votes
2answers
2k views

Pink ($1/f$) pseudo-random noise generation

What are some algorithms for generating a good pseudo-random approximation to $1/f$ (pink) noise, yet suitable for implementation with low computational cost on an integer DSP?