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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Noise Removal from an image using Opencv

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 ...
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1answer
21 views

Transfer function of double exponential smoothing?

Double exponential smoothing a.k.a. Holt-Winters smoothing tracks level and trend of a time series in coupled IIRs: $\qquad$ In: $Y_t$, t = 0 1 2 ... $\qquad$ State: $L_t, T_t \quad$ -- level and ...
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0answers
19 views

Effect of Gaussian Smoothing to mean image intensity

I am implementing Perona-Malik Diffusion in using the formulas: Creating image at time k+1 using equation This is my implementation: ...
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1answer
59 views

Calculating Savitsky-Golay filter coefficients - normalization

using the matrix equations found on Wikipedia i wrote some Python code to compute the Savitsky-Golay coefficients for m data-points, using a polynomial of degree k, here it is: ...
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1answer
62 views

Calculate Damping using FFT

Given the following signal I would like to calculate the rate of damping. I presume that I need to find out where the peaks are using some kind of smoothing on the sample data. After performing an ...
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1answer
44 views

Smooth X,Y,Z data with discontinuous, 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 $X$,$Y$ ...
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2answers
136 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 ...
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0answers
56 views

Edge-preserving smoothing

I'm searching for a method that can smooth a 3D volume whilst preserving the edges in my volume. I researched anisotropic diffusion filtering and bilateral filtering but I'm having trouble to evaluate ...
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115 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. So how is 1/n ...
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0answers
25 views

Super-Resolution of depth map without loss of data

I'm applying super resolution algorithms in disparity maps, as they do in Lidarboost 1 and (2). The problem is that when I apply the term of ...
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1answer
55 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} = ...
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3answers
374 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 ...
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2answers
55 views

Non-cyclic smoothing of a 2D image

I was wondering if there was a simple approach to smooth images, e.g using a Gaussian Kernel without introducing boundary effects which are also present when using Discrete Fourier Transforms? For ...
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0answers
36 views

How to smooth gradient estimates for steepest descent optimization

In steepest descent methods of minimizing a function $f(x), x \in \mathbb{R}^d$, it's common to approximate the gradient by finite differences: $\qquad\qquad \nabla f(x) \approx gradest( x; h ) ...
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1answer
286 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 ...
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3answers
207 views

filter and resample or resample and smooth?

Currently doing some signal analysis in python for a major project in my physics degree which is due really soon. I need some help! Say I have two signals, f(t) and g(t) which are recorded over the ...
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1answer
73 views

Standard deviation of Gaussian corresponding to perfect low pass filter [1,1]

For a time discrete signal, the rect-filter (for 1D signal [1,1]) is a perfect low pass filter. I was wondering, what is the best gaussian approximation of this filter? For a current problem, I ...
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2answers
524 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 ...
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1answer
193 views

MATLAB gradient derivative troubleshooting

I have an array $A$ having the next 145 values I would like to calculate the $\frac{dA}{dX}$, having a 1D grid, $x$: 1:286:41468 I use the function gradient: ...
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2answers
78 views

Calculating information loss in a signal after smoothing?

I have a signal. I applied Gaussian smoothing to it and then for baseline reduction I appied Tophat filter to the smoothed version. This is the original signal: This is the final signal: I read ...
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1answer
123 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 ...
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1answer
175 views

How to do smoothing without affecting phase

I have signals captured from two channels of a measurement system. There is phase and magnitude differences between these two signals. I want to apply nonlinear smoothing to the magnitude, but the ...
2
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0answers
162 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 ...
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1answer
81 views

What technique could I use to smooth the right amount these signals?

I'm developing an application which one of its capabilities is peak detection. I expect to handle three types of the similar data (Acceleration vs Frequency) but measured in different laboratories ...
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1answer
1k 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 ...
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2answers
15k 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 ...
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1answer
73 views

Is there a need of Point interpolation before proceeding for gaussian smoothing of an incomplete distribution?

Suppose there is a distribution that has values sampled on the interval 1-25 with corresponding sample values that have to be smoothed. For example: ...
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2answers
2k 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 ...
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1answer
123 views

How i can smooth a sinusoidal signal using it's local maximum

I have a signal that it is like a Sinusoidal signal with many local maximum, I want to smooth this signal with almost connecting it's local maximum to each other.
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1answer
210 views

Estimating number for iterations for gaussian smoothing

I have some data sets on which I applied Gaussian smoothing using [1 4 6 4 1] kernel. In my program I iterated this kernel 50 times on the data sets. But only a few ...
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2answers
510 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 ...
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2answers
538 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. ...
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2answers
137 views

filter for reducing background noise in image

I have images where there is a lot of "black" background (few shades of black). (In many images at least half the pixels are background). I need to get interest points from the image, but because the ...
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1answer
141 views

Help me in understanding smoothing

Follow up to the question here This is a screen shot of an intermediate step in the middle of my calculation The dotted line called MY is supposed to be a smoothed version of db pow y db pow y is ...
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1answer
272 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: $$ ...
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4answers
321 views

Solving 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 ...
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1answer
533 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 ...
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4answers
1k 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, ...
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1answer
648 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 ...
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2answers
2k 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: ...
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2answers
415 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 ...
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1answer
1k 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) ...
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2answers
1k 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 if y[n] > y[n-1] and y[n] > y[n+1]. ...
8
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4answers
2k 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, ...
9
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1answer
538 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: ...
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2answers
3k 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..n-1. I want to find the first and second derivative of the signal: f'(t) and f''(t). My first thought was to estimate the ...
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1answer
250 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 ...
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1answer
1k 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 ...