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.
131
questions
26
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5answers
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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
votes
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
votes
6answers
14k 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
votes
3answers
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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
votes
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:
$$y[n]: maxima \textbf{ if } y[n] > y[n-1] \...
10
votes
2answers
12k views
How to find smoothed estimates of the derivative and second derivative of a signal?
I have a signal sampled at $\Delta t$: $f_i(t_i=i\Delta t)$ where $i = 0,\ldots,n-1$.
I want to find the first and second derivative of the signal: $f'(t)$ and $f''(t)$.
My first thought was to ...
9
votes
2answers
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IIR Filter for Smoothing (Low Pass Filter)
I am using IIR filter for smoothing
$$y[n] = ax[n]+(1-a)y[n-1]$$
My question is, if I add another IIR filter, will it be the second order of IIR filter? If not, what it can be called?
My second ...
9
votes
1answer
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1/n octave smoothing
Given a frequency response obtained with FFT, I would like to apply a 1/n octave smoothing. What filter should I be using and how? Maybe someone could point to a good reference (a paper or book on the ...
9
votes
1answer
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Directly compare subpixel shifts between two spectra — and get believable errors
I have two spectra of the same astronomical object. The essential question is this: How can I calculate the relative shift between these spectra and get an accurate error on that shift?
Some more ...
9
votes
1answer
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How do I use a Savitzky Golay filter to find local maxima (in between samples) in a discretely sampled 1D signal?
I have a seismic signal y(i):
Here I have found one maximum: i=152.54, y=222.29 manually and plotted it in red.
I want to find all maxima automatically.
I read that the Savitzky Golay Filter (SGF) ...
9
votes
1answer
966 views
Calculating smoothed derivative of a signal by using difference with larger step=convolving with rectangular window
I have a signal sampled at $\Delta t: fi(ti=i\Delta t)$ where i = 0..n-1. I want to find the first derivative of the signal: f'(t).
My first thought was to estimate this by a central difference:
$f&#...
8
votes
4answers
694 views
Solving Convex Optimization Problem Used for High Quality Denoising
The highest voted answer to this question suggests that to denoise a signal while preserving sharp transitions one should
minimize the objective function:
$$ |x-y|^2 + b|f(y)| $$
where $...
7
votes
2answers
5k views
Why should an image be blurred using a Gaussian Kernel before downsampling?
I recently read that before downsampling an image, it should be blurred using a Gaussian Kernel. This way, the downsampled image is better than just picking a single pixel out of a NxN block or ...
7
votes
1answer
962 views
how does this equation correspond to smoothing?
Please help me understand smoothing of data. This is a follow up to my previous question posted here. Especially the top answer by Junuxx where he says a way of smoothing a function $f(x)$ is:
$$
f'[...
7
votes
2answers
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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
votes
1answer
429 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
votes
4answers
338 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
votes
1answer
202 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
votes
1answer
931 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
votes
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
votes
2answers
731 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
votes
2answers
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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
votes
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
votes
5answers
9k 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
votes
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
3answers
91 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 ...
4
votes
5answers
28k 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
votes
2answers
243 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 $X$,$Y$ (...
4
votes
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
votes
1answer
1k 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
94 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
373 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
869 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
248 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
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 ...
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
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 ...
3
votes
2answers
567 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
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
1answer
143 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
Smoothing a power spectrum
My question is regarding how one could/should smooth a rather noisy power spectrum obtained from measurements. There are various methods one can use (a moving average, binning, etc) and I am not sure ...
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
599 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
72k 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
4k views
Generating smoothed versions of square wave, triangular, etc
I'm trying to get functions depicting smoothed out versions of wave forms(triangle,square, sawtooth, reverse sawtooth) which have the same amplitude and frequency as $cos(x)$.
I found a few ...
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 ...
