# 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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### 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 ...
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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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### 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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### 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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### 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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### 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 ...
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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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### 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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### 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 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 < \...
1 vote
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### 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 ...
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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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### 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 ...
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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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### 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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### 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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### 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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### 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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