Questions tagged [averaging]
Averaging is a signal processing technique applied in the time domain, intended to increase the strength of a signal relative to noise that is obscuring it.
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Does the determination of the ergodicity of a signal force any changes in methodology?
In mathematics, the term ergodic is used to describe a dynamical system which, broadly speaking, has the same behavior averaged over time as averaged over space. -from wikipedia
From the perspective ...
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Why does signal averaging reduces noise levels by more than $\sqrt{n}$?
I have an electrophysiology signal, which is time-based. It basically measures neural activity in the form of potential differences over time.
The noise in this signal is assumed to be a random ...
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What is averaging and how can it be done?
I'm studying about the analysis of (mainly) fMRI and EEG data. Multiple times it's mentioned that to reduce noise, you can use averaging, but nothing more detailed than that.
There never is literally ...
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Exponential weighted moving average time constant
I think it is an easy question but I am stuck.
I want to derive that $$ \alpha = -e^{\frac{-T}{\tau}}\,. $$
Can someone provide me with an answer?
[EDIT] Sorry guys, this was really a senseless ...
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How to derive the results that averaging $N$ signals yields a $\sqrt{N}$-fold increase in signal-to-noise ratio?
If I have understood correctly, averaging $N$ noisy independent segments or signals increases the signal-to-noise $\sqrt{N}$-fold.
How does one derive this result?
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Averaging multiple FFTs in matlab
I have multiple, real, audio signals which I am taking the FFTs. Although they don't come from the same recording, those signals represent the same thing (biologically). I was told that I could ...
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Weight vector of an exponential moving average?
With weight vector I mean the vector with weights that you have to multiply the observations in the window that slides over your data with so if you add those products together it returns the value of ...
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Is it possible to remove the non-random noise in the signal by averaging?
Ex: We're measuring vibration Frequency response of a structure, and at the same time there is a constant source of vibration (noise) from a pump. The pump is exciting the structure by sinusoid ...
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Lowpass : What is wrong with average filtering?
The question is : What is wrong with averaging as low pass filter ?
The details :
I want to lowpass filter a signal to downsample it.
The constraints are : I have no RAM available and I work in ...
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Is there an algorithm for second order filtering of data where the filter frequency is not known a priori?
It is well known that a moving average algorithm done in the time domain is equivalent to a filter with frequency response $\mathrm{sinc}(\omega\tau)$ where $\tau$ is the averaging time. (see this ...
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Larger FFT vs multiple averaged FFTs for detecting small CW signals
I am writing an SDR application which searches for CW signals at various predefined frequencies. Currently, the radio tunes to the appropriate LO frequency and calculates a number of FFTs to produce ...
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Processes: Orthogonal, Uncorrelated, Statistically Independent
How are they all related? You can define them as:
Orthogonal Processes: $E[XY] = 0$
Uncorrelated Processes: $E[XY] = E[(X - \mu_x)(Y - \mu_y)] = 0$
Statistically Independent Processes: $E[XY] = E[X] \...
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RMS averaging in spectrum analyzers
While studying spectrum analyzers I ran into the concept of RMS averaging as a mean to reduce dispersion of data without affecting power spectral density (PSD).
What is not really clear to me is how ...
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Time synchronous averaging - MATLAB
I have a time domain signal that corresponds to a vibration signal of a machine. I have a second signal that corresponds to a tachometer signal (There is a pulse every one revolution of the shaft).
I'...
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Averaging over bins in frequency domain
I have a sound file with a computed spectrogram from 0 to 8000 Hz (spanning about 5 octaves). The spectrogram has 128 logarithmically spaced frequency bins. How can I reduce the number of bins so that ...
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How to average coherences estimated using Welch's method in MATLAB
I'm trying to estimate the average coherence of discontinuous snippets of a signal in MATLAB. For Welch's spectrum estimates, the following works:
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Is it correct to subtract two signals acquired over different times and trials to remove the common signal in them?
I have two signals that represent the response of a neuron under two different conditions.
Signal 1 (S1): response to Stimulus A
Signal 2 (S2): response to Stimulus A+B
The response to stimulus A is ...
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How do I average frequency spectra?
How did letter d.) become letter e.)? How do we perform this averaging process? Its clear the averaging the signal causes some noise to be reduced.
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How to predict the final noise after adding two or more noisy discrete signals?
Is it possible to accurately predict the noise level if we add two or more noisy signals. For the sake of simplicity, let us say, the noise is independent and Gaussian.
Suppose we wish to add signals $...
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Slow sampling of signal and averaging over n periods
Can one in theory achieve as high accuracy as needed by sampling a sinusoidal signal over n Periods? Is there a formula that connects the signal frequency (f), sampling frequency (fs), periods (P) and ...
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Allan deviation to determine averaging time
Thanks in advance for the help. I don't post on here often, so I hope I can convey my question properly.
I think I understand what the Allan deviation (same as IEEE Allan variance?) does. You take a ...
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Averaging of a phase flipping signal
Suppose I want to average a signal $s(t)$ which consists of several spectral components without any DC offset. I sample $M$ points in the time domain. I am interested in the power spectrum which I get ...
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Generalized/Power means in DSP
Generalized/power means may be used to construct moving-average filters with different properties than regular one which is based on arithmetic mean. This observation seems to be trivial - even ...
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What is the intuition of "averaging is a low pass filter"?
As I know, the shape of a low pass filter in time and frequency are as follow:
But how averaging work like a normal function in time domain?
Is there any intuition in it?
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Averaging data from 2 sensors
Suppose we take a reading of a single rotating axis using 2 identical sensors. Intuitively, I think that averaging the outputs of both sensors will yield a less noisy result. But what if sensor A has ...
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averaging power spectrum from multiple signal of different length
I have multiple physiological signals (EMG - muscular electrical activity) that are all of different length (one may even be 2/3 times longer than the smallest one). These signals are from 2 types of ...
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Why averaging in Spectral magnitude domain not in complex domain to estimate spectrum of a process
Consider we need the magnitude spectrum of the signal. Signal is recorded in $N$ trials to a certain stimuli. Signal varies from each trial because of noise. So, to estimate the actual magnitude ...
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low pass filtering for smoothing
I am using the following code in Matlab, from some source (sadly I cant remember).
The code is used for smoothing signals using a low pas filter.
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What is the average of $\DeclareMathOperator{\rect}{rect} \rect(\cos(\pi t/2)) $?
We have this signal:
$$\operatorname{rect}\left(\cos\left(\frac{\pi t} {2}\right)\right) $$
I must find the average power , how can i get there ?
My solution:
I have seen that
$$-\frac 12 < \...
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Downsampling by block averaging
Many spectroscopic detectors used to study light absorbance as a function of time. These detectors cab sample data at 160 to 250 Hz. There is an option of choosing lower sampling rates such 80, 40, 20,...
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Spectral averaging without phase information
In the context of signal averaging to reduce uncorrelated noise:
Is it possible to perform signal averaging from just the magnitude spectrum of certain signals? Or that would only work if we know ...
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Is there an equivalent time-domain operation to the spectrum averaging in Welch's method?
In Welch's method a time-series is segmented and then the subsequent FFTs of the segments are averaged. Is there an equivalent time-domain operation?
I guess doing the the Welch estimate and ...
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Smoothing of Log Data Plots in Octave
I have some frequency based data that I'm plotting with Octave's semilogx that looks like this:
The amplitude of peaks does not increase with frequency over the linear scale. But with a log scale, ...
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is there upper limit on averaging window size for images?
An amateur question. I take an image and average pixels over a window 3 by 3, thus obtaining a smoother image. Then I increase the averaging window size - obtain an image with even less details, but ...
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Bit accuracy improvement versus sample averaging
Supposing we have multiple samples of a scaled signal $x$ given by $y_i=a_ix+n_i$ where $n_i$ is AWGN how does the bit accuracy of estimation of $x$ improve with averaging of samples $y_i$ (number of ...
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Averaging Different Length Speech Signal
I have around 10 wav audio files all containing same word spoken i.e. 'Hello' but all having different length.
So lets say 1st file when loaded consist of 20000 samples, 2nd of 15000, 3rd of 18000 ...
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FFT to work out optimum number of samples to average
I have a magnetometer, a LIS3MDL to be precise, and I am taking readings from it every second. As expected there is variation in the readings. For example, if I take five readings I get:
1164,
1190,
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Why is Error Vector Magnitude (EVM) measured as an RMS value?
I do understand Voltage/Current measurement of a Sine Wave is in RMS, as average yields a zero, and RMS gives a true 'DC equivalent' value. But I do not understand why an EVM measurement could be in ...
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Averaging 2D signal with ignored samples
I have a 2D signal, and I want to compute a new signal by calculating a weighted mean of each sample's neighbours. However, I also have a 2D bitmask, the same size as the original signal, which ...
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Coherent averaging of polyphase components of a signal
I want to subsample a multi-band signal to introduce controlled aliasing. My frequency components are uniformly distributed across the spectrum (comb structure) and occupy a relatively narrow ...
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Removing the Multiples of Decrease and Increase in a Spike
I have a signal shown below. I got this signal from a glove, where I want to detect the movement of a finger. What I am planning to do is to threshold the signal, so I can get a binary signal ...
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Why is it necessary to average signals with filters?
As someone who is new in working with filters, why do signals need to be averaged? What are the advantages, by performing filters on signals? As I know, there are different types of filters for ...
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Power spectral density of melodic contours
DESCRIPTION OF SIGNALS
I have several sung melodies under each of nine experimental contexts ("conditions"). The melodies are all of slightly different lengths (ranging more or less from 3s ...
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Usefulness of Allan deviation with DC signals
This is a follow-up question to Allan deviation to determine averaging time
I was under the impression that with DC signals I couldn't capture or average a signal forever to get better SNR, because of ...
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Artefactual results in the Welch PSD (FFT) of melodic contours (pitch profiles)
DESCRIPTION OF SIGNALS
I have several sung melodies under each of nine conditions. The melodies are all of slightly different lengths (ranging more or less from 3s to 12s), and each is encoded as a ...
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Get shape of a recurring pulse event in my plant video signal
I'm studying plants - specifically how the color of their leaves change throughout a day. I have a camera pointing at a leaf which takes a picture every 47 minutes and calculates the average green ...
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How to interpret Allen Deviation with increasing negative slope
I was calculating the Allan deviation (utilizing the Python module allantools.adev, which relies on eq. (6) in https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=50505). The expected behavior is a ...
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How to deal with noise near saturation
If I have a noisy signal which I know is approaching the saturation limit of my sensor, then the measurement will sometimes be saturated. It seems that if I try to estimate the true data by averaging ...
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On number of samples needed
Suppose we get $m+1$-bit signed noise samples $n_i$ with magnitude of noise as high as $m$ bits.
Does averaging say $m\log m$ samples suffice to get average of $n_i$ to magnitude within few LSBs?
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Lower bound of weighted average of sequence
Can anyone prove that
$$\mathrm{avg}\left(\frac {a_i}{\left(1+a_i\right)^2}\right) \ge \frac{\mathrm {avg}({a_i})}{\left(1+\mathrm{avg}{(a_i)}\right)^2}$$
for a sequence of positive valued elements $...
