39 votes
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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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20 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)\,...
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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 ...
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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 ...
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7 votes
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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 ...
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6 votes
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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 ...
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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 ...
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  • 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. ...
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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 ...
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  • 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 ...
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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). ...
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6 votes
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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 ...
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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 ...
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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 ...
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5 votes
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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
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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. ...
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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
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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 ...
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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: ...
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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 ...
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  • 22.5k
4 votes
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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 ...
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  • 1,023
4 votes
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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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