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

learn more… | top users | synonyms

1
vote
1answer
63 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 ...
1
vote
0answers
38 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 ...
3
votes
0answers
69 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 ...
0
votes
0answers
19 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 ...
3
votes
1answer
52 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} = ...
1
vote
2answers
122 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 ...
1
vote
2answers
47 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 ...
0
votes
0answers
15 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
vote
1answer
118 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 ...
1
vote
3answers
139 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 ...
1
vote
1answer
63 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
votes
2answers
281 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 ...
2
votes
1answer
136 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
votes
2answers
71 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
votes
1answer
121 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 ...
1
vote
1answer
138 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
votes
0answers
122 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
votes
1answer
77 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
votes
1answer
940 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 ...
1
vote
2answers
8k 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 ...
1
vote
1answer
71 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
votes
2answers
1k 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 ...
0
votes
1answer
105 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.
0
votes
1answer
169 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 ...
1
vote
2answers
310 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 ...
5
votes
2answers
429 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. ...
1
vote
2answers
126 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 ...
1
vote
1answer
132 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 ...
5
votes
1answer
246 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: $$ ...
7
votes
4answers
290 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 ...
4
votes
1answer
469 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 ...
12
votes
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, ...
8
votes
1answer
475 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 ...
4
votes
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: ...
5
votes
2answers
379 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 ...
7
votes
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) ...
6
votes
2answers
918 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
votes
4answers
1k 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
votes
1answer
464 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: ...
6
votes
2answers
2k 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 ...
7
votes
1answer
223 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 ...
5
votes
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 ...