Signal Processing Stack Exchange
Signal Processing Stack Exchange

Questions tagged [random]

69 questions
61
votes
6 answers

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 strict-sense stationary process, this means that its…
Matt
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3 answers

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?
hotpaw2
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3 answers

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 random numbers between 0 and RAND_MAX. RAND_MAX does not have a fixed value, but it is…
hkBattousai
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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 sine-gaussian perhaps but with some random effects. …
bill_e
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8
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1 answer

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 15 of these slides, but I can't really make…
Arrow
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7
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3 answers

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 even though we know that real-life signals…
Likely
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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 I understood from the book in the link is as…
Srishti M
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2 answers

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 computing a windowed cross correlation between…
Matt
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6
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1 answer

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, $x(t)$ is a truncated monolateral exponentially…
Aglar
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6
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2 answers

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 measurement of the responses that shows me at which…
Sturm
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5
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1 answer

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 consider a sample space $S$ consisting of $n$ outcomes…
sundar
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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 to the other by an about $\delta t$. Sometimes…
JesseC
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2 answers

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 statistical behaviour of the output signal. I was…
dexterdev
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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. For a given sequence of time points $\{t_i\}$, we…
kerzol
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4
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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 $x(T)$ is the position of the target at time = $T$ along…
rotating_image
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