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34 votes
2 answers
62k views

What is the cut-off frequency of a moving average filter?

I need to design a moving average filter that has a cut-off frequency of 7.8 Hz. I have used moving average filters before, but as far as I'm aware, the only parameter that can be fed in is the number ...
CaptainProg's user avatar
12 votes
3 answers
32k views

Moving average vs. Moving median

I have read in many places that Moving median is a bit better than Moving average for some applications, because it is less sensitive to outliers. I wanted to test this assertion on real data, but I ...
Basj's user avatar
  • 1,277
11 votes
5 answers
11k views

How should a moving average handle missing data points?

I'm writing a program that averages the user's weight across different days. I'm planning to use a 5-point moving-average (current day, two before and two after). Sometimes, a data point is missing ...
Anna's user avatar
  • 357
8 votes
7 answers
81k views

How to implement a moving average in C without a buffer?

Is it possible to implement a moving average in C without the need for a window of samples? I've found that I can optimize a bit, by choosing a window size that's a power of two to allow for bit-...
tarabyte's user avatar
  • 395
7 votes
5 answers
7k views

3dB-Cut off frequency of moving average

I've read the thread: Cut off frequency of moving average And I use the second answer in my algorithm to calculate the 3dB cut off frequency of my filter, which works great, as my filter length is ...
Slev1n's user avatar
  • 157
7 votes
5 answers
12k views

What Is the Transfer Function of a Moving Average (FIR Filter)?

To make post-processing easier, I export scope measurements as CSV files, which are then post-processed (mostly in Microsoft Excel, which is not the best tool for the job, but it is all I have at my ...
Sclrx's user avatar
  • 271
7 votes
3 answers
186 views

Why use an ARMA process theory instead of just performing linear regression?

I am studying ARMA processes. At the end of the course the professor told us that estimating the next sample in an arma process using past of length $p$ (so performing a projection of $X_t$ on $\text{...
Robert Laplace's user avatar
7 votes
1 answer
454 views

"Ensemble averaging ... cannot track dynamic changes"?

A book claims this as a motivation for introducing exponential averaging: A disadvantage of ensemble averaging is that the resulting estimate cannot track dynamic changes occurring in the observed ...
user avatar
6 votes
3 answers
2k views

Moving average before downsampling: effect on Nyquist frequency?

First the simple questions: Is there an effect on the Nyquist frequency when I apply a moving average filter on the raw data before I downsample? And what does this do to aliased frequencies? ...
W_vH's user avatar
  • 163
6 votes
1 answer
7k views

Difference between Gaussian and moving average filters for peak detection and doppler shift detection?

Consider having a signal in the time domain, and you want to smooth the signal. Moving average and Gaussian filters that are used. How do you choose which is used for what? What are the conditions ...
DVG's user avatar
  • 171
5 votes
6 answers
2k views

Optimal $ n $ -th Order IIR /AR Approximation of a Moving Average Filter

I would like to approximate a moving average filter with an IIR filter of much lower order than the tap-length of the moving average filter. Optimality shall refer to the $L_2$ norm of the impulse ...
burnpanck's user avatar
  • 169
5 votes
1 answer
3k views

How to decide whether to use AR or MA for smoothing data?

Imagine I've got some offline data that I want to smooth. I could use an auto-regressive or moving-average filter of some appropriate order for conducting the smoothing. On which criteria should I ...
Andreas's user avatar
  • 1,968
5 votes
1 answer
318 views

Model Validation After Estimation for System Identification Task (Assistance with MATLAB Code)

QUESTION: I want to determine how well the estimated model fits to the future new data. How do I validate the estimated model...what is the procedure? After system identification, how to do model ...
Ria George's user avatar
5 votes
3 answers
570 views

Frequency response of a rolling linear regression

I am looking for a way to characterise the frequency response of the slope from a linear regression. We are exploring the effect of window length of the regression to the magnitude of the slope of the ...
Dan's user avatar
  • 163
4 votes
1 answer
1k views

How does this "simple filter" work?

I'm new to DSP, and I'm using this basic "1-pole LPF" Param Smooth filter which "smooth" param when I change it. The code is pretty simple: ...
markzzz's user avatar
  • 45
4 votes
3 answers
247 views

Box filter with non integer length

I'm trying to model a sensor system that has an averaging behaviour. The frequency response is almost identical to a box filter and looks roughly like this: Transferring this into a discrete time ...
LoveDaOOP's user avatar
4 votes
1 answer
736 views

moving average rounding error analysis

I have implemented a moving average, similar to the Hogenauer Filter, with a reduced number of computation operations. I expect the expected error to behave as the random walk and its STD to be of ...
Gideon Genadi Kogan's user avatar
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 ...
MisterH's user avatar
  • 317
4 votes
1 answer
2k views

How can I smoothly interpolate between 2 position?

I've got a 1D signal (position of a servo motor over time) and I've extracted 'peaks'/'key' positions picking running average "local extrema" points. Below is are 2 plots from 2 servos and the white ...
George Profenza's user avatar
4 votes
2 answers
425 views

The Logic Behind Cascading a Moving Average Filter After a Median Filter

Why do we cascade a median filter and a moving average filter? I know how each filter performs, but I do not know the difference between these two filters in denoising application and what is the ...
mohammad rezza's user avatar
4 votes
1 answer
343 views

Underdetermined deconvolution of windowed output

Consider a discrete 'blurred' output $h[t]$ given by the convolution of filter $f[t]$ and signal $g[t]$. This question considers recovering $g[t]$ from a window (subset) of $h[t]$. This causes the ...
egg's user avatar
  • 143
4 votes
1 answer
6k 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 ...
Mac's user avatar
  • 51
4 votes
1 answer
243 views

Conceptual Question from Signal Processing - Impulse Response and AR Coefficients

In continuation to the previous question Conceptual questions from signal processing I have a doubt which is: Consider an Autoregressive model (AR(2)): $$ y(t) = ay(t-1) + by(t-2) $$ and a FIR (...
Ria George's user avatar
3 votes
4 answers
648 views

Filtering Angular Measurements

I am trying to apply a filter to reduce noise in angular measurements. Since the data comes with noise, the filter needs to be able to handle measurements that are not smoothly progressing; for ...
c00der's user avatar
  • 131
3 votes
1 answer
532 views

Is it correct to call a Savitsky-Golay filter of degree 0 a simple moving average?

I had this question after seeing that polynomial regressions fit polynomial functions of different degrees to a time-series, since the mean of a time series is a constant and that a constant is also a ...
alexgrover's user avatar
3 votes
1 answer
2k views

Equivalent 2D mask of moving-average

I have the moving-average mask as mask = [1 1 1; 1 1 1; 1 1 1]; and then I compute the convolution 3 times ...
BRabbit27's user avatar
  • 301
3 votes
3 answers
2k views

Averaging filters

If a signal undergoes repeated averaging (n times) with a filter (h) of size m. Is it possible to achieve the same averaging result with an averaging filter(H) of a larger size? h = {1/m, 1/m... m ...
ssb's user avatar
  • 133
3 votes
4 answers
2k views

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 ...
achoo5000's user avatar
3 votes
1 answer
119 views

How to interpret power of a two-point average signal

Consider a DT signal $x[n]$. Define the two-point moving average signal : $$ y[n]:=\frac{1}{2}x[n]+\frac{1}{2}x[n-1] $$ Define : $$ \langle x[n]\rangle:=\lim_{N\to\infty}\frac{1}{2N+1}\sum_{n=-N}^{N}x[...
SPARSE's user avatar
  • 129
3 votes
1 answer
600 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 ...
nedflanders's user avatar
3 votes
1 answer
90 views

Envelop detection with low sample rate?

I have a signal up to $3\textrm{ MHz}$. The ADC that sample it has a rate of $1.5\mu s$. So a full $T$ of the signal is $0.3\mu s$, and I can only sample each $1.5\mu s$. It sounds not enough, but I ...
Curnelious's user avatar
3 votes
1 answer
807 views

Determination of periodicity in data and finding mean

I have to find whether there is any pattern (I mean periodicity or close to periodicity) and if there is, for one cycle i have to perform numerical integration to determine mean. In the first picture ...
Fringe Emanuel's user avatar
2 votes
2 answers
2k views

Moving Average for Notch filtering

I have a periodic signal(ECG) with period of ~1 seconds. It does not have features that are shorter than 0.04 seconds. For removal of 60Hz, I thought instead of implementing a notch filter, doing a ...
doubleE's user avatar
  • 273
2 votes
3 answers
504 views

Determining Loss of Information by Taking Average (Mean of Signal)

So basically information is defined by expected value of Shannon's information i.e. Entropy. I am curious how much information is lost if we simply take the average of the sample given to us. I am ...
GENIVI-LEARNER's user avatar
2 votes
2 answers
995 views

MAD and RMS SNR relation

Recently I've found a formula relating mean average deviation (MAD) SNR to root mean square (RMS) SNR: $$\text{SNR}_\text{MAD} = \sqrt{\frac{2}{\pi}} \text{SNR}_\text{RMS} $$ which assumes Gaussian ...
nadlr's user avatar
  • 123
2 votes
2 answers
627 views

Why couldn't I reapply a LPF to remove more noise?

I have a piece of raw accelerometer data consisted of 10,000 samples to be processed offline. Since the movement or rotation of the object is moderately slow and smooth, I would think that I can ...
KMC's user avatar
  • 207
2 votes
1 answer
524 views

How to approximate a moving RMS without iterating over N samples for each required output?

I have a signal with a sampling rate of F Hertz. From it I want to produce an RMS signal, also with F samples per second with a window size of N samples. Using a standard moving RMS algorithm I must ...
ImJimmi's user avatar
  • 23
2 votes
1 answer
202 views

A general conceptual understanding of moving average

I have a conceptual question here. I understood how to calculate a Moving Average(MA). For example : x(n) = 0, 1, 2, 3, 4, 5 MA = 0, 1/2, 3/2, 5/2,7/2, 9/2, where for calculation of the MA we only ...
gklearning's user avatar
2 votes
1 answer
141 views

Terminologies - lags, order in time series model

I am facing some difficulties with the terminologies - lag ($p$) and sequence length (number of data points) (N) used in time series model such as Moving average and Autoregressive model. Considering ...
Srishti M's user avatar
  • 616
2 votes
1 answer
259 views

How to apply least-squares estimation for sparse coefficient estimation?

The model is expressed as follows $$y(n) = \sum_{i=0}^{p-1} r(i) x(n-i) + v(n) \tag{1}$$ where $\mathbf{r} = \begin{bmatrix} r_1 & r_2 & \ldots &r_p \end{bmatrix}^T$ is the sparse length-$...
SKM's user avatar
  • 621
2 votes
1 answer
7k views

Phase response of moving average filter -- how to interpret?

There are many articles on the frequency response of the moving average filter but they all seem to focus on magnitude. However the phase response is intriguing and I find it hard to interpret. The ...
barnhillec's user avatar
2 votes
2 answers
5k views

Is this code for doing a moving average correct?

Is this code for doing a moving average correct? y=conv(x, ones(1,100)/100); I want to filter my speech signal with moving average filter in code. I think that ...
vida's user avatar
  • 23
2 votes
1 answer
614 views

Gain function calculation (frequency response)

Define moving average process $y_t := 0.5 x_t + 0.5 x_{t-1}$ where $x_t := e^{i2 \pi t}$. Its frequency response is then: $$H(f) = 0.5 + 0.5 e^{-i2\pi f}$$ Recall that the frequency response in ...
Jase's user avatar
  • 163
2 votes
1 answer
595 views

How to filter a signal using a bandpass filter consisted of two moving average filters?

I want to filter a PPG signal on a microcontroller. I have limited memory and a was searching for low computational methods. I found the work of Kazuhiro Taniguchi, Earable POCER: Development of a ...
JasonScientist's user avatar
2 votes
2 answers
578 views

Mean delay for a M tap harmonically weighted filter

I am trying to derive the mean delay for $M$ filter taps harmonically weighted: $$y[n] = \frac{M\,x[n] + (M-1)x[n−1]... + 1 \cdot x[n−M+1]}{\tfrac12 M (M + 1)}$$. For a uniformly weighted filter, I ...
Srilakshmi Alla's user avatar
2 votes
1 answer
194 views

What happens when filter ringing is far longer than the signal itself?

I'm digging into some (quite popular in my field) analytical practice that I find suspicious. The problem is to remove the trend from some very short (eg. 18-40 data points representing 200 - 800 ms) ...
Bartek Kroczek's user avatar
2 votes
1 answer
621 views

autoregressive moving average code implementation

I am new to DSP and i am trying to take a wav (human speech) file and apply ARMA filter and plot its PSD graph in python. I see that there are a lot of AR implementations but almost none ARMA. I ...
Richard's user avatar
  • 31
2 votes
1 answer
179 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 ...
tms's user avatar
  • 21
2 votes
1 answer
192 views

What are the ripple and attenuation in a set of moving average filters?

Ladies, Gentlemen, Consider following set of moving average filters: (1) - 100 coefficients equal to 1/100 (2) --- 95 coefficients equal to 1/95 (3) --- 90 coefficients equal to 1/90 (4) --- 85 ...
George Theodosiou's user avatar
2 votes
1 answer
617 views

Taking the Moving Average of STFT Results

I realize that this seems redundant, but I'm getting consistently better results when performing machine learning techniques that use spectral features extracted using the moving average process below,...
Jay's user avatar
  • 21