Questions tagged [smoothing]

Smoothing a signal or data set approximates the data to reveal patterns and exclude noise, fine-scale structure and rapid changing phenomina.

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26
votes
5answers
8k views

Is there a technical term for this simple method of smoothing out a signal?

Firstly, I am new to DSP and have no real education in it, but I am developing an audio visualization program and I am representing an FFT array as vertical bars as in a typical frequency spectrum ...
23
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4answers
4k views

Bag of Tricks for Denoising Signals While Maintaining Sharp Transitions

I know this is signal dependent, but when facing a new noisy signal what is your bag of tricks for trying to denoise a signal while maintaining sharp transitions (e.g. so any sort of simple averaging, ...
17
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6answers
13k views

Savitzky-Golay smoothing filter for not equally spaced data

I have a signal that is measured at 100Hz and I need to apply the Savitzky-Golay smoothing filter on this signal. However, on closer inspection my signal is not measured at perfectly constant rate, ...
11
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3answers
6k views

Savitzky–Golay filter vs. IIR or FIR linear filter

A traditional IIR / FIR filter (lowpass to remove the high freq oscillations), e.g. moving average, or a Savitzky-Golay filter can all be useful to smoothen a signal, such as an envelope signal: ...
10
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2answers
4k views

Finding local peaks in-between samples

I have $n$ discrete samples of a seismic signal $y[n]$: I want to find local maxima in the signal. A naive test for if $y[n]$ is a maximum would be: $$y[n]: maxima \textbf{ if } y[n] > y[n-1] \...
10
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2answers
12k views

How to find smoothed estimates of the derivative and second derivative of a signal?

I have a signal sampled at $\Delta t$: $f_i(t_i=i\Delta t)$ where $i = 0,\ldots,n-1$. I want to find the first and second derivative of the signal: $f'(t)$ and $f''(t)$. My first thought was to ...
9
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2answers
2k views

IIR Filter for Smoothing (Low Pass Filter)

I am using IIR filter for smoothing $$y[n] = ax[n]+(1-a)y[n-1]$$ My question is, if I add another IIR filter, will it be the second order of IIR filter? If not, what it can be called? My second ...
9
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1answer
7k views

1/n octave smoothing

Given a frequency response obtained with FFT, I would like to apply a 1/n octave smoothing. What filter should I be using and how? Maybe someone could point to a good reference (a paper or book on the ...
9
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1answer
2k views

Directly compare subpixel shifts between two spectra — and get believable errors

I have two spectra of the same astronomical object. The essential question is this: How can I calculate the relative shift between these spectra and get an accurate error on that shift? Some more ...
9
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1answer
4k views

How do I use a Savitzky Golay filter to find local maxima (in between samples) in a discretely sampled 1D signal?

I have a seismic signal y(i): Here I have found one maximum: i=152.54, y=222.29 manually and plotted it in red. I want to find all maxima automatically. I read that the Savitzky Golay Filter (SGF) ...
9
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1answer
959 views

Calculating smoothed derivative of a signal by using difference with larger step=convolving with rectangular window

I have a signal sampled at $\Delta t: fi(ti=i\Delta t)$ where i = 0..n-1. I want to find the first derivative of the signal: f'(t). My first thought was to estimate this by a central difference: $f&#...
8
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4answers
682 views

Solving Convex Optimization Problem Used for High Quality Denoising

The highest voted answer to this question suggests that to denoise a signal while preserving sharp transitions one should minimize the objective function: $$ |x-y|^2 + b|f(y)| $$ where $...
7
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1answer
942 views

how does this equation correspond to smoothing?

Please help me understand smoothing of data. This is a follow up to my previous question posted here. Especially the top answer by Junuxx where he says a way of smoothing a function $f(x)$ is: $$ f'[...
7
votes
2answers
12k views

Savitzky-Golay filter parameters

I am trying to smooth a series of data in order to obtain a continuous function that could represent that given data set. It came out that the Savitzky-Golay method could be a good way. Now, I don't ...
7
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1answer
428 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 ...
6
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4answers
331 views

Make a signal that fits another the best possible with a limitation in the 2nd derivative

Consider this step function: The signal that "fits" this should look like the following (in green): The corners are now smooth because the maximum second derivative allowed is not infinite anymore. ...
6
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1answer
198 views

A Simple Algorithm to Filter / Smooth / Denoise a Noisy Staircase Graph

Is there a way to remove the noise and smooth the graph into a staircase graph.
6
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1answer
906 views

$1/n$ octave complex smoothing

An excellent answer to this post explains how to do $1/n$ octave energy smoothing and mentions complex smoothing can be done as well, but it's tricky business because of phase wrapping. How is phase ...
6
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1answer
1k views

Issues with the smoothing operator in coherence estimation using the complex Morlet (Gabor) wavelet

The goal I wish to compute the coherence estimate using the continuous wavelet transform (CWT) of a real-valued signal with the complex Morlet (a.k.a. Gabor) wavelet. I compute the cwt of the signal ...
5
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2answers
4k views

Why should an image be blurred using a Gaussian Kernel before downsampling?

I recently read that before downsampling an image, it should be blurred using a Gaussian Kernel. This way, the downsampled image is better than just picking a single pixel out of a NxN block or ...
5
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2answers
724 views

What are the characteristics of a “good” smoothing convolution kernel?

At work we were smoothing a signal by convolving with either f1=[0.2000 0.2000 0.2000 0.2000 0.2000] or ...
5
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2answers
3k views

Fitting piecewise splines to noisy data

I have a system that gives me a noisy data set similar to the one generated by this matlab/octave code. The y-axis represents the signal intensity and the x-axis represents spatial distance. ...
5
votes
1answer
2k 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 ...
4
votes
1answer
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: ...
4
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2answers
5k views

When should the sum of all elements of a gaussian kernel be zero?

I found an approximation of a 5x5 2D convolution kernel like this : Here, the sum of the elements is zero and this one was used for Laplacian of Gaussian! Another one here : This one has all ...
4
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5answers
8k views

Derivative of noisy signal

My input signal is phase vector. I want to differentiate it to get frequency vector. My input signal is somewhat noisy. Here is the input signal. This is the derivative of the input signal as ...
4
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2answers
12k views

How to remove the boundary effects arising due to zero padding in scipy/numpy fft?

I have made a python code to smoothen a given signal using the Weierstrass transform, which is basically the convolution of a normalised gaussian with a signal. The code is as follows: ...
4
votes
5answers
27k views

Noise Removal from an Image Using OpenCV (Comparison to Neat Image)

I tried removing noise from the image shown below using Median Blur in OpenCV. But i'm not able to remove the colour noise completely as it is done in Neat Image. Any suggestions.? 1. Original Input ...
4
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1answer
1k 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 ...
4
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1answer
975 views

The Meaning of the Terms Isotropic and Anisotropic in the Total Variation Framework

The isotropic TV is defined as the estimation of 2-norm of gradients $\sqrt{(y_{i+1,j}-y_{i,j})^2+(y_{i,j+1}-y_{i,j})^2}$, while the anisotropic TV is defined as the estimation of 1-norm of gradients $...
4
votes
1answer
92 views

oversampled coefficient for existing exponential smoothing

Say I have an exponential smoothing for certain $\Delta t$, $t_{i+1} = t_i + \Delta t$. In this sampling, I choose a particular $\alpha$ to filter signal $z_i$ like $$ v_1 = z_0 \\ v_{i+1} = \alpha\:...
4
votes
2answers
8k views

Smoothing data by using Kalman filter

I would like to ask about smoothing data by using Kalman filter. Due to quantization, I have data that is not smooth. How can I smooth this data by using Kalman Filter. For your information, the data ...
4
votes
1answer
370 views

Smoothing 3D Data for the Second Derivative

I am not a signal processing expert and my feeble attempts at solving this problem have come up short. I have a C++ application which is being fed regularly-spaced (in time) 3D position samples. The ...
4
votes
1answer
854 views

How Can I Detect Peaks and Regions of Highest Variance in a 1D Signal?

I'm not a signal processing person at all so hopefully I'm not asking an obvious question (if I am, I'd appreciate any resources that would help give more context). I have a 1D vector where the ...
3
votes
1answer
247 views

Does this Signal Smoothing algorithm have a name?

We are reverse engineering some 20 year old software. Original developers were laid off years ago, and cannot be found. In this code, there is a signal that is getting smoothed as follows: $P_{new} ...
3
votes
2answers
5k views

detect to rising, stable and falling point in non-smooth rectangular wave

I am working on basic signal processing problems in MATLAB. I have found a signal from the internet (i don't remember the site exactly). The data is organized in column wise. 1st and 2nd column is ...
3
votes
2answers
566 views

Convolution for non-signal-processing background

I am a civil engineer and am analyzing traffic data recorded by capturing vehicle movements over a highway for a specified time period. The database I am dealing with contains observations at every 0....
3
votes
2answers
2k views

Find smoothed first derivative from signal with noisy slope

How can I get filtered first derivative from a noisy signal that has slowly changing slope in form of y=kx+b? k can slowly ...
3
votes
3answers
86 views

Reversing the Order of Operators for Edge Detection?

Usually, for edge detection, we perform smoothing and then pass it through difference filter. What if application of difference filter happens first and then smoothing. How the math behind the same ...
3
votes
2answers
2k views

How do I smooth this noisy signal?

I have a numerical solution to a problem in mechanics. I am computing the force applied to an object as a function of its deformation and in the problem, there is an instability, due to which the ...
3
votes
2answers
208 views

Smooth 2D Data with Discontinuous and Artificial Jumps

I have some data $(X,Y,Z)$, which is a set of measurements $Z$ over a $2D$ space $X$,$Y$. The $Z$ data on this space is continuous except for some discontinuous jumps in certain domains of $X$,$Y$ (...
3
votes
1answer
138 views

Chromatogram peak detection - bunching vs others?

Reading presentations from existing tool providers I noticed that in order to detect peaks they first use bunching (average N points) and then use slope and curvature to detect peaks. I'm guessing ...
3
votes
1answer
2k views

Gaussian Pyramid - How is Subsampling Rate Related to Sigma?

I found a gaussian pyramid implementation in a MOPS paper (feature detection). They use sampling rate $s=2$ and $\sigma=1$ - i.e. to generate a new level of the pyramid, the current level is smoothed ...
3
votes
3answers
581 views

Filtering data so that only rising edge is left

I have data that looks like this: Sometimes the data has a higher point in the middle of the shallow slope I want to find a way to filter the data such that it smooths it and leaves the first rising ...
2
votes
2answers
71k views

How to apply Hamming Window?

I am new in matlab and signal processing. The time series that have been used are obtained from accelerometer in a building. As far as I understand both the time series' length and window function ...
2
votes
2answers
1k views

Effect of Gaussian Blur on Different Frequency Components of an Image

Gaussian blur is lowpass filter which means it pass the low frequency components and stop the high frequency component but the point I am not getting is that if it is lowpass filter then how it is ...
2
votes
2answers
1k views

Smoothing a staircase

I have some data from a position encoder, so naturally i want to estimate its speed. However, the data is very quantized, so it's difficult to smooth enough to differentiate easily: Each step level ...
2
votes
1answer
146 views

How to append two bandlimited signals and make the result bandlimited without modifying the first signal

I need to append (not add) a bandlimited signal F(b) to a bandlimited signal F(a) and keep the result bandlimited without modifying the part that corresponds to F(a). Both are bandlimited to the same ...
2
votes
1answer
210 views

Fast Recursive 1D Signal Smoothing - IIR / Auto Regressive Implementation of Gaussian Smoothing

I have just begun to dive into the field of signal processing, but there is the need to program a digital filter, that has to smooth a realtime signal from a sensor device. As far as I know, in my ...
2
votes
1answer
168 views

What Are Different Approaches to Realize a Gaussian Blur (Smoothing) Step on an Image? [closed]

Could some review some methods to apply Gaussian Filter (Blur) on an image besides the direct one using Truncated FIR (classic convolution with Truncated Kernel) approximation?