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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How do you average the power spectra across multiple samples to compare 2 conditions?

I have physiological signals from samples under 2 conditions and want to compare the difference in frequency content between the conditions. Specifically,I'd like to compare the average power spectrum ...
1 vote
0 answers
102 views

average after Kalman filter and how to deal with drift

This is in the context of mobile device localization. The mobile device does not move. All I have is the delay estimated from the signal sent by the mobile device ('measure' in blue). With a simple ...
0 votes
0 answers
64 views

Are longer integration times equally good or better than averaging over several shorter timespans?

Consider the signal of e.g. a photodiode or a spectrometer, where a dark measurement has been taken to account for baseline noise. The signal we want to measure is quite weak, so we need a decently ...
1 vote
2 answers
109 views

Averaging a Signal with a delayed version of itself

I am working on a problem that requires interpolating between two music files. One music file is very similar to a delayed version of the other. I would like the 'average' of the two signals to sound ...
0 votes
1 answer
67 views

Signal averaging of a digitized noisy signal

If I have a signal that is lower than the noise power, I may want to use signal averaging over time to increase SNR. However, when the signal has been obtained after digitization, there is ...
2 votes
0 answers
30 views

Event-related EEG (epoch averaging) as a form of inter-harmonic bandstop filtering?

There is a matter that comes to my mind from time to time, now I describe it in detail. Anyway I am a first year PhD student, doing research in the field of cognitive neuroscience, but yet I only have ...
2 votes
1 answer
28 views

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 ...
2 votes
1 answer
227 views

Average of a set of transfer functions: how should I treat the phase?

I have a set of transfer functions obtained by impacting an instrumentation hammer against a mass, measuring the acceleration on a set of accelerometers; the result is shown below. I want to get a ...
0 votes
1 answer
70 views

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 ...
3 votes
2 answers
364 views

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 ...
1 vote
1 answer
117 views

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 ...
2 votes
1 answer
440 views

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 ...
0 votes
0 answers
130 views

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 ...
0 votes
1 answer
31 views

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 ...
1 vote
2 answers
959 views

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 ...
1 vote
1 answer
200 views

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. ...
2 votes
1 answer
160 views

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 ...
4 votes
5 answers
3k views

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'...
-1 votes
1 answer
180 views

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 $...
1 vote
2 answers
138 views

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, ...
-1 votes
1 answer
79 views

Recoverable continuous function after average sampling

I have a personal interest in this question, but I don't know if it is unfounded. Suppose I have a continuous function x (t), which is sampled using an average sliding window, which performs a ...
6 votes
2 answers
9k views

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 ...
1 vote
1 answer
166 views

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 ...
0 votes
1 answer
99 views

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 ...
0 votes
1 answer
156 views

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 ...
1 vote
3 answers
11k views

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?
2 votes
1 answer
291 views

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 $...
1 vote
3 answers
1k views

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 ...
4 votes
2 answers
330 views

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 ...
1 vote
1 answer
143 views

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 < \...
4 votes
1 answer
1k views

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] \...
4 votes
3 answers
6k views

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 ...
1 vote
1 answer
1k views

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,...
1 vote
0 answers
161 views

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, ...
0 votes
1 answer
431 views

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 ...
8 votes
3 answers
6k views

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 ...
0 votes
0 answers
283 views

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 ...
1 vote
2 answers
2k views

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 ...
4 votes
1 answer
1k views

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: ...
1 vote
2 answers
354 views

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 ...
3 votes
2 answers
683 views

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 ...
2 votes
1 answer
178 views

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 ...
4 votes
1 answer
5k views

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 ...
0 votes
1 answer
115 views

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 ...
0 votes
1 answer
67 views

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 ...
3 votes
2 answers
651 views

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 ...
-1 votes
1 answer
212 views

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? ...
7 votes
1 answer
860 views

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 ...
1 vote
0 answers
104 views

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 ...
3 votes
2 answers
4k views

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 ...