39
votes
Accepted
Is there a technical term for this simple method of smoothing out a signal?
What you've implemented is a single-pole lowpass filter, sometimes called a leaky integrator. Your signal has the difference equation:
$$
y[n] = 0.8 y[n-1] + 0.2 x[n]
$$
where $x[n]$ is the input (...
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votes
Is there a technical term for this simple method of smoothing out a signal?
Warning: include some history, old papers (I love them) and punch cards!
You used, with $a=0.2$ the form:
$$y(n) = y(n–1) + a[x(n) – y(n–1)]\,,$$
sometimes written as:
$$y(n) = ax(n) + (1 – a)y(n–1)\,...
- 29.9k
19
votes
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Why should an image be blurred using a Gaussian Kernel before downsampling?
An image "should not be blurred using a Gaussian Kernel" in general.
This however can be a safe bet for a lot of basic image processing needs, and a smoothing is almost mandatory when you ...
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10
votes
Is there a technical term for this simple method of smoothing out a signal?
Are there better approaches or further study on solutions to this which I should look at?
The normal approach for audio meters is a "lossy peak detector".
...
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9
votes
Why should an image be blurred using a Gaussian Kernel before downsampling?
According to (digital) sampling theorem, signals should be properly bandlimited, before they are (down) sampled.
A practical digital filter approximately limits the bandwidth of the signal and makes ...
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8
votes
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How does this "simple filter" work?
In more standard DSP terms, you have the following filter:
$$
y[n] = (1-a) x[n] + a y[n-1]
$$
where $x[n]$ and $y[n]$ are the input and output signals at time $n$ respectively.
The transfer ...
- 4,701
8
votes
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The Meaning of the Terms Isotropic and Anisotropic in the Total Variation Framework
In the Total Variation framework we define 2 flavors:
$$ \text{Isotropic TV} \; {TV}_{ {L}_{2} } \left( X \right) = \sum_{ij} \sqrt{ { \left( {D}_{h} X \right) }_{ij}^{2} + { \left( {D}_{v} X \right) ...
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7
votes
Is there a technical term for this simple method of smoothing out a signal?
Around US DoD contractor circles, this particular filter is frequently called an "alpha filter", because it can be characterized with one parameter that is traditionally named "alpha".
It is directly ...
- 171
7
votes
Accepted
How to Deal with Outliers in Measurement of a Simple Model of Kalman Filter
One classic way to deal with outliers is taking advantage of the statistics behind Kalman Filter.
The state vector is basically the mean value of a Multivariate Gaussian Distribution.
The covariance ...
- 40.7k
6
votes
Accepted
Smooth 2D Data with Discontinuous and Artificial Jumps
If I understand you correctly you want to smooth the data (Namely reduce "Noise") yet regular filters would ruin the data on discontinuities.
What you need is an Edge Preserving Filter.
You can try ...
- 40.7k
6
votes
Derivative of noisy signal
2 point discrete differentiation is bound to produce highly noisy results.
try the 5-points stencil. you can also generate coefficients (i.e. more points) yourself using derivation of Lagrange ...
- 590
6
votes
Savitzky-Golay smoothing filter for not equally spaced data
As techwinder did in C++, I used datageist's algorithm and implemented it in Python. Maybe this will help somebody in the future.
...
6
votes
detect to rising, stable and falling point in non-smooth rectangular wave
The usual approach to change detection is the CUSUM algorithm.
I've done an implementation that just addresses the level (mean) change issue. It's included (in R) below.
The black line is the noise-...
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6
votes
Effect of Gaussian Blur on Different Frequency Components of an Image
Gaussian Blur is Spatially Invariant Linear Filter.
Hence it can be analyzed in the Frequency Domain which in fact shows its Low Pass properties.
Namely it attenuates High Frequency Energy.
In Image, ...
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6
votes
Make a signal that fits another the best possible with a limitation in the 2nd derivative
Hmmmmmmmmm, interesting question.
Since you want to use the second derivative as your criteria, it would seem that you would want to have the maximum second derivative absolutie value for as short of ...
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6
votes
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Does this Signal Smoothing algorithm have a name?
Not sure if this has a name, but it is a nonlinear low pass filter that uses different smoothing constants depending on the input signal deviation from the filtered output. Small deviations are ...
- 4,324
6
votes
Savitzky–Golay filter vs. IIR or FIR linear filter
Since the discussion in the existing answers and comments has mainly focused on what Savitzky-Golay filters actually are (which was very useful), I will try to add to the existing answers by providing ...
- 80.2k
6
votes
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Reversing the Order of Operators for Edge Detection?
In the classic framework both the Smoothing and the Difference Filter are applied using Convolution.
Since it is done using convolution it implies the operation is Linear Spatially Invariant (LSI).
...
- 40.7k
6
votes
Accepted
The Effect of the Standard Deviation ($ \sigma $) of a Gaussian Kernel when Smoothing a Gradients Image
Let's analyze it in 1D as the intuition is the same.
First, let's have a look on a few different Gaussian Kernels:
As expected, they are wider as the Standard Deviation (STD) increase.
It means that ...
- 40.7k
5
votes
Noise Removal from an Image Using OpenCV (Comparison to Neat Image)
NeatImage probably uses Wavelets based Noise Reduction.
You can look for methods based on that.
Today you need methods which are "Edge Aware", namely they smooth yet keep edges in tact.
Have ...
- 40.7k
5
votes
How to Smooth Gradient Estimates for Steepest Descent Optimization
In the Probabilistic settings we have many methods applied to the Stochastic Gradient Descent in order to decrease the variance of the Gradient Estimation (ADAM / RMS Prop / AdaDelta, etc...).
The ...
- 40.7k
5
votes
Accepted
What Are Different Approaches to Realize a Gaussian Blur (Smoothing) Step on an Image?
You can apply Gaussian Blurring on an image in many ways:
Using FIR Approximation by Convolution.
Using Approximation by Box Blur.
In the Fourier Domain by Multiplication by a Fourier Kernel.
Using ...
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5
votes
Accepted
Fast Recursive 1D Signal Smoothing - IIR / Auto Regressive Implementation of Gaussian Smoothing
Have a look at my Fast Gaussian Blur Project at GitHub.
You will find there implementation of IIR Approximation of Gaussian Blur which implements the following papaers:
Recursive Gabor Filtering.
...
- 40.7k
4
votes
How Can I Detect Peaks and Regions of Highest Variance in a 1D Signal?
I would do the following:
Create a smoothed signal using $ N $ points averaging window to estimate the local average.
On the smoother signal I'd find an approximation which regularizes the $ {L}_{1} $...
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4
votes
Accepted
Smoothing a staircase
Looks like your data is virtually free of noise. That, combined with a very high sampling frequency would mean that at the jumps the data is exactly at the threshold between two quantized values. Set ...
- 12.4k
4
votes
Generating smoothed versions of square wave, triangular, etc
It seems the amplitude is not scaled properly. Rather than (2*A/pi) using (A/atan(1/delta)) seems more appropriate. In other words I propose:
...
4
votes
Find smoothed first derivative from signal with noisy slope
I think least squares is going to be the best approach, and that's not going to be that computationally expensive (I think! Please correct me if I'm wrong).
The gradient can be estimated from a ...
- 22.5k
4
votes
Accepted
How to Mesure the smoothness of a signal
A number of features will return some estimate of the smoothness of a signal. In general, these are all measures of dispersion with slightly different takes on "dispersion".
The choice of the "right" ...
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4
votes
How to smoothen signal with missing values before differentiation?
The best tool for this job is normalized convolution. It can deal with missing samples as well as uncertainty.
The paper describing the method is "Normalized and Differential Convolution -- Methods ...
- 1,023
4
votes
Accepted
How do you do signal averaging on a realtime data?
@Greyfrog. Here are the descriptions of four different kinds of averaging operations:
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Only top scored, non community-wiki answers of a minimum length are eligible