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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How to Mesure the smoothness of a signal

so how can i determine if a signal is smooth or not ? And if its possible to get something indicating the level of the smoothness of my signal. I looked at the r-squared and hurst exponent but i ...
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68 views

Should zero element be considered to calculate mean when smoothing spectrogram by window?

My (mass spectrometry) spectrogram does not measure the intensity constantly. I obtain the spectrogram, for example, ...
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132 views

What is limit on performance of edge-preserving filters for low signal-to-noise regimes?

Let's say I have a signal, $x(t)$, defined as such, $ x(t) = \begin{cases} 0 &\text{if} \,\,\, t < -\alpha/2 \\ \frac 1\alpha t+\frac12 &\text{if} \,\,\, -\alpha/2 \leq t \leq \alpha/2 \...
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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 ...
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400 views

Smoothing or bigger FFT bins?

I have an FFT of a radio signal, to look at "what's happening" in the frequency domain. I'm interested in signals that are "wide enough", eg 1MHz, and thus would like to smooth the result to filter ...
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58 views

Removing the Multiples of Decrease and Increase in a Spike

I have a signal shown below. I got this signal from a glove, where I want to detect the movement of a finger. What I am planning to do is to threshold the signal, so I can get a binary signal ...
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393 views

smooth noisy irregularly spaced data containing peaks

I've got a set of scans of an object (human body) from different angles, which are being combined to reconstruct a 2D-representation. The raw measurements (blue plot below) contain a fair amount of ...
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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 ...
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Estimating the standard deviation of Gaussian filter from smoothed image

Firstly, let's say that in order to smooth an image, I convolve it with a Gaussian function having standard deviation $\sigma_x$ and $\sigma_y$. I am now interested in knowing if there exist methods ...
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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 ...
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2answers
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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 ...
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Fast implementation of LOESS for equally spaced samples (possibly using convolution)

Is it possible to do LOESS smoothing on equally spaced data using convolution? The Wikipedia article on LOESS mentions a possibility of using a FIR filter for LOESS. I could not find anything more ...
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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: ...
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2answers
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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 ...
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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 ...
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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
245 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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111 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 ...
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1answer
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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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101 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 ...
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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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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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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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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
539 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 ...
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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
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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
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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
107 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 ...
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1answer
378 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
345 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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4answers
166 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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289 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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509 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 ...
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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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3answers
539 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
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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 ...
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2answers
679 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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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
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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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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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250 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 $X$,$Y$ (...
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3answers
612 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 ...
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1answer
480 views

Image 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 ...
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1answer
948 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 ...
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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\:...
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5answers
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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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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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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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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 ...