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# Questions tagged [white-noise]

White noise has constant power spectral density for all frequencies. Because there is no bandlimit to white noise, it has infinite overall power.

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1 vote
101 views

### Show that the impulse response of an LTI system can be determined by observing the output and inputting white noise

Problem Show that the impulse response of an LTI system can be determined by observing the output and inputting white noise. Attempt Let $x(t)$ be the input signal (white noise) and $y(t)$ be the ...
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1 vote
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### Minimum Number of Base Accelerations Needed to Simulate Gaussian White Noise in Structural Dynamics?

I am currently working on a scientific paper where I subject a structure to base accelerations modeled as Gaussian white noise. I am relatively new to signal processing and would appreciate some ...
1 vote
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### Symmetry of white noise

I am fairly new to signal processing and the concept of noise. I recently started working on a project related to data gathered from some cheap sensors. I have therefore been trying to gather some ...
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1 vote
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### Flatten noise floor of spectrum by reference/dark measurement

I'm currently stuck with a problem and would appreciate any input or guidance in this regard. Background information In a laser experiment, an amplitude signal in volts and a position signal are ...
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24 views

### Identification of the spectrum color of a coded video signal

I have two encoded video signals (MPEG and H.263). In each file, I have information about the frames of the video. I calculated the autocorrelation and then did the Fourier transform to find and plot ...
88 views

### How should I go about completely decorrelating a digital signal?

So I'm working on real time signal compression, and I need to come up with the best convolution to minimize the entropy of incoming data (which I will then compress), which I understand is achieved by ...
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### Intuitive understanding of the relationship between the variance of a Wiener process and the variance of white noise

The Wiener process $W(t)$ is said to be the integral of white noise $\xi(t)$ from $0$ to $t$. That is, $$W(t) = \int_{0}^{t} \xi(t')dt'$$ However, the variance of $\xi(t)$ is infinite, but the ...
127 views

### Rigorous derivation of autocorrelation of white noise

It is said that the autocorrelation of white noise is the dirac delta function $\delta(\tau)$, but I don't know how to derive that... Since white noise is a function with constant power spectral ...
40 views

### Generating a whitening filter using MATLAB cceps() function

I have a few thousand realisations of a discrete stochastic process. I am trying to generate a whitening filter from these realisations. I am expected to use the MATLAB cceps() function to generate ...
45 views

### Unbalanced binary sequences for system identification?

I have a physical system that I'd like to obtain the frequency response for. I can only provide binary sequences as inputs to the system. Normally, I'd use a MLS (maximal length sequence) and ...
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### Estimating noise power from sensor signal

I'm a beginner in signal processing and a bit lost. I have sensor readings from a load sensor of real system. I want to replicate the noise inherent in the signal in simulink using the Bandlimited ...
1 vote
120 views

### Why is white noise uncorrelated for any two different samples?

Consider white noise with spectrum density $N_0/2$, it is known that the autocorrelation is given by: $$R(\tau) = \frac{N_0}{2}\delta(\tau)$$ Meanwhile the definition of delta function in the ...
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1 vote
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### Simultaneous removal of all noises in all channels?

Can MATLAB be able to look at all 16 channels of a bio-amplifier simultaneously and look for the common factor which is the noise which affects all channels simultaneously, and the noises removed from ...
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81 views

### White noise vs low-pass filters

It seems common that people assume white (aka Gaussian) additive noise. Yet it is also common to use low-pass filters to remove noise. But white noise shows up equally on all frequency bands. So it ...
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119 views

### Jitter model does not behave as expected after FFT

So I'm currently trying to understand the relationship between jitter and phase noise. To help my understanding I did write a little simulation in matlab. I used this model in the time domain, relying ...
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### How to produce a noise spectrum from an rms velocity specification?

For a dynamic model I am looking at the appropriate input to analyse the performance under the influence of floor vibrations. The norm is an ISO VC-C floor spectrum as displayed in the image. However, ...
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1 vote
152 views

### What is the best method to filter a signal where baseline and the signal of interest have overlapping frequency range?

I am reading out the movement of a motor arm using a Hall sensor and a magnet pair. The hall sensor measures the distance between the sensor and the magnet. The motor arm is being moved with a band-...
49 views

### How does the sampling rate of a digital filter limit the sampling rate that can be used for replay of filtered signal?

I need a band-limited white noise to characterize a biological sensor that senses mechanical movement. For that, I am generating a Gaussian white noise (MATLAB Communications toolbox) of length 10 ...
1 vote
111 views

### What duration of a white noise burst is required for it to be "white" at a given frequency or frequency range?

I am running white noise bursts (with very short ramps on/off to prevent discontinuities) through underdamped resonant bandpasses which are tuned to any given $f_0$ and an underdamped $Q$. Continuous ...
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48 views

### Why different noise terms are read at specific sampling interval in Allan Variance plot?

I was trying to identify Quantization Noise, Angle Random Walk, Bias Instability, and Rate Random Walk from Allan Variance plot which as Allan deviation on y axis and Sampling Time Interval ...
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1 vote
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### Is a white noise always zero mean and uncorrelated?

It seems to be silly, but is it possible to deduce mathematically that a white noise is necessarily zero mean and uncorrelated? I have seen some people defining a white process as a zero-mean and ...
95 views

### Reducing Noise Floor by Sampling Larger BW or Noise Shaping White Noise

If I am sampling a sensor with white noise (Johnson) that is the noise floor of the system could I drive the noise floor down by sampling a larger bandwidth than I care about and then using a digital ...
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246 views

### Predicting distribution of integral of random process from power spectral density?

Suppose I have a random process $X(t)$ and I know the power spectral density of $X(t)$, $S_{XX}(f)$. What can be said about the distribution of $Y(t) = \int_{t'=0}^T X(t') dt'$? Bear in mind I have a ...
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### White noise does not contradicts Wide Sense Stationarity?

I am studying White Noise. But I am really beginner level, so I have a confusion with its construction. White Noise is usually defined as a Wide Sense Stationary process $N=\{N_t\}_{t\in T}$ (for $T$ ...
241 views

### Why does adding white noise improve the calculation of frequency of a sine wave in the time domain?

I created short audio files with a sine wave (tone) having a set frequency, and added varying white noise to it generated by a random number generator. I wanted to code and test the simple algorithm ...
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426 views

### Variance of Integral of a real white Gaussian Noise Process

In this question, is the answer not equal to infinity ? Answer is mentioned as 6. But my doubt is cant we think of it like a linear combination of many independent random variables each having ...
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4k views

### White Gaussian Noise Spectrum and Power

White Gaussian noise has constant power spectral density $N_0/2$. I know that the area under the power spectral density curve between two points gives the power of the signal between these two points. ...
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I´m stuck in a deduction analysis of the variance of a gaussian white noise signal in a "integrate-and-dump detector" of a baseband data transmission receiver, where $n(t)$ is white noise ...