Signal Processing Stack Exchange
Signal Processing Stack Exchange

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.

144 questions
27
votes
5 answers

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 visualization. The problem I had was that the audio…
Michael Bromley
  • 373
  • 3
  • 7
23
votes
4 answers

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, i.e. convolving with a gaussian, is out). I…
John Robertson
  • 1,082
  • 1
  • 8
  • 13
21
votes
6 answers

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, the delta between measurements ranges between 9.7…
VLC
  • 313
  • 1
  • 2
  • 5
11
votes
3 answers

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: For which application would a Savitzky-Golay…
g6kxjv1ozn
  • 441
  • 3
  • 11
10
votes
1 answer

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 subject).
Psirus
  • 101
  • 1
  • 5
10
votes
2 answers

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 estimate the derivatives by central…
Andy
  • 1,647
  • 1
  • 16
  • 26
10
votes
3 answers

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: $$y[n]: maxima \textbf{ if } y[n] > y[n-1] \textbf{ and } y[n] > y[n+1]$$ However the maxima are…
Andy
  • 1,647
  • 1
  • 16
  • 26
9
votes
1 answer

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'(t_i) =\frac{f(t_{i+1})−f(t_{i−1})}{2\Delta…
Andy
  • 1,647
  • 1
  • 16
  • 26
9
votes
2 answers

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 filter is $$y_2[n] = ay[n] + (1-a)y_2[n-1] $$
user4234
  • 133
  • 1
  • 4
9
votes
2 answers

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 averaging over the block. After searching in this site…
Nagabhushan S N
  • 377
  • 3
  • 16
9
votes
1 answer

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 details if you are still with me. Each spectrum will…
JBWhitmore
  • 191
  • 2
9
votes
1 answer

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) can be used to find smoothed estimates of both a…
Andy
  • 1,647
  • 1
  • 16
  • 26
8
votes
4 answers

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 $x$ is the noisy signal, $y$ is the denoised signal, $b$ is…
John Robertson
  • 1,082
  • 1
  • 8
  • 13
8
votes
2 answers

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 know much about smoothing and/or interpolate, but…
Py-ser
  • 205
  • 1
  • 2
  • 6
7
votes
1 answer

"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 signal. -- L. Sörnmo and P. Laguna, Bioelectrical…
user42
1
2 3
…
9 10