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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2answers
35 views

The difference of downsampling an image and smoothing an image?

I am, at the moment, trying to read up on some simple computer vision elements, in which i have become a bit comfused on the terms downsampling and smoothing, and whether there is a difference between ...
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1answer
41 views

midpoint smoothing spline

Suppose we have a time series which have peaks and troughs.(The red curve below) I would like to get an algorithm which is able to identify the peaks and troughs locations, then find the midpoint ...
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1answer
45 views

Is there a name for this smoothing formula?

Hi: I am reading a book called "lectures on wiener and kalman filtering" by Professor Thomas Kailath. On page 18, it says the following: To carry through this approach, let us first note that a ...
3
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1answer
28 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 ...
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2answers
54 views

What criteria should be used for smoothing

Actually I have some measurement which I want to get rid of noise I want to use different filter techniques but I am wondering what criteria I should use to check if I am removing noise or not or if ...
2
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2answers
44 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 ...
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0answers
36 views

Why does increased kernel bandwidth equate to increased SNR values?

If I apply a Gaussian Kernel to an image with some noise applied to it and I want to remove that noise, why does the Signal to Noise Ratio increase as I apply kernel's with higher and higher sigma ...
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1answer
82 views

Structuring Kalman filter for tracking problem where only position is known

I'm new to Kalman filters and my extensive web search about them has helped me understand the majority of it (or so I think). However I still need some light shed on my problem formulation. I have a ...
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0answers
17 views

Proximal operator of image Laplacian

Let $\alpha, \beta > 0$ and $\Delta := \nabla^T \nabla$ be the discrete laplacian operator, $$\nabla: \mathbb{R}^{n_x \times n_y \times n_z} \rightarrow \mathbb{R}^{3 \times n_x \times n_y \times ...
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1answer
61 views

Implementing a 1-D Kalman Filter Regression, Missing the smoothing action (getting the opposite)

I am implementing the 1D Kalman Filter in Python on a fundamentally noisy set of measurement data, and I should be observing a large amount of smoothing...but, instead, my Kalman Filter is doing the ...
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1answer
82 views

Get phase information from bursty time series with amplitude variability and sharp edges

I have time series like this one, and I am trying to get the phase information from it. If it matters why, because I need to compute the precision of the cycles and amplitude variability is ...
4
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2answers
164 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 ...
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2answers
145 views

Compute the time derivative of a noisy digital signal?

The issue is that my signal is very noisy. I need extract its time derivative as accurate as possible. P.S. I do not have any prior knowledge on the signal (black box). On forums some suggested ...
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1answer
98 views

how to smooth estimated velocity

I have a manipulator that provides the position and the velocity of its end-effector. The velocity is noisy. I've implemented a filter in C++ to determine the derivative of the position. In the below ...
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1answer
19 views

What is the equivalent smoothing function to running the same Gaussian 8 times?

Suppose there is an image which is to be smoothed by convolving it with a Gaussian kernel with standard deviation $\sigma$. If the image is then smoothed with this kernel 8 consecutive times, is the ...
3
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1answer
52 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 ...
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1answer
71 views

Cascaded one-pole sections and relationship to time constant

I have implemented a typical one-pole lowpass filter to smooth out some control signals. The form of the filter is: $$ y1 = x0 + b1\centerdot(y1 - x0) $$ x0 is the current input sample. y1 is the past ...
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0answers
60 views

Smoothing out data with DIY Spectral Analysis in Excel VBA Limitations, What are they?

I am trying to leverage DFT and IDFT for some noise filtering on some data I am collecting. I am trying to do this in a user friendly/cheap manner by coding this in excel (I know this is not the best ...
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4answers
84 views

How to obtain round peaks instead of triangular peaks when smoothing an input?

I have a signal (in blue) that I would like to smooth out (in red, moving average). I would like to get red peaks to look more round than triangular and at the same time their width would become ...
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0answers
54 views

Spatial resampling, how to smooth?

Sorry if this is not the right forum. Having a velocity grid in which a wave propagates, and given a certain spatial sampling of the grid, what kind of smoothing/interpolation should be used if the ...
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0answers
49 views

Computationally 'lightweight' smoothing in realtime

I have a pitch tracker that can be quite unsmooth in its output (in Hz). A Savitzky-Golay filter has been good at smoothing but it looks like it adds a lot of multiplies on top of the already ...
4
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1answer
329 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 ...
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2answers
74 views

SURF feature extractor and descriptor

I am trying to understand how SURF extracts features using a Hessian matrix. What I am a bit confused about, is why a second derivative Gaussian filter is used, rather than a standard Gaussian filter?...
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5answers
3k views

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
91 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
62 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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2answers
193 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
205 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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2answers
75 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 $X$,$Y$ (...
3
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3answers
229 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
101 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 ...
4
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0answers
227 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 ...
3
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1answer
63 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\:...
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5answers
973 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
68 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
48 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 ) \...
1
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1answer
959 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
425 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
93 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 ...
3
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2answers
530 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....
2
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1answer
263 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: ...
0
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2answers
107 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 ...
2
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1answer
130 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
270 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
263 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 ...
0
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1answer
84 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 ...
6
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1answer
2k 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 ...
2
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2answers
31k 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
77 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: ...
2
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2answers
3k 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 ...