# 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 smooth wiener deconvolution result in Python?

I'm wondering if it is possible to smooth the estimated response from a Wiener deconvolution in order to have a better representation of the original signal and to remove the side lobes. (Here an ...
44 views

### How to measure smoothness of a signal

Lets say I have two signals with a different number of data points - a step function and a smooth spline as you can see below. What is mathematical operation I can use to quantify the "smoothness&...
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### Constrained interpolation/smoothing of multi-dimensional time series

Consider an $N$ dimensional time series $x_i(t),~i\in\{0,1,\cdots, N-1\}$ where $x_i(t)$ is smooth. It turns out that for all $t$: $x_i(t)>x_{i-1}(t)$. The multi-dimensional series is sampled at ...
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### Peak detection in noisy waveforms

I have a set of 1-dimensional time-series, a subset of which contain either one or two peaks, and the remainder of which are pure noise. I've smoothed these data by ...
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### Is there a technical term for smoothing or flattening the floor of an amplitude envelope?

I am working with the speech envelope, and I have been trying to make it act a little more like a bilevel signal by exaggerating the peaks and flattening out the floor. I detrended and smoothed my ...
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### Is there any complex-valued function used to smooth signals?

To obtain a smoother signal, we usually convolve the original signal with a real-valued kernel function, such as Gaussian and Top-hat. Is there any complex-valued kernel function to smooth signals?
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### Calculate moving RMS with exponential averaging

This is moving RMS, now how to add exponential averaging in this df['signal'].rolling(21*24*60).apply(lambda x: np.sqrt(x.mean()))
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### What are the kernels that are used in the Smooted Psuedo Wigner-Ville distribution?

Defined in Matlab's docs for WVD, SPWVD is given by: $\int_{-\infty}^\infty g(t) * H(f) x(t + \frac{\tau}{2}) x^*(t - \frac{\tau}{2}) e^{-j2\pi\tau\,f} \, d\tau$ H(f) and g(t) are the smoothing ...
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### Data smoothing in temperature measurements from MLX90614 BCC IR sensor

I am trying to measure temperature with the MLX90614 BCC IR sensor for my project, and I am having problems with my precision requirement. I had taken data for 1 second then took the mean of these ...
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### Smoothing contours for contour analysis for character recognition

I am making a character recognition library using contour analysis. Contours are sequencies of complex numbers X + j*Y (in fact in contour analysis they are defined ...
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### Choose the right Sigma for Gaussian filter

I have the following problem: I have a time series with counted data. I now want to smooth it using a Gaussian low-pass filter. Is there a method to determine the sigma value? The window should have a ...
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### Following a smoothing filter of a biological signal

)Following a smoothing filter of a biological signal. y[n] = Ay[n − 1] + Bx[n − 2] Please find the transfer function in the z-domain and find the impulse response function of this filter.
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### Box function signal filtering in python

I am trying to produce a box function filter of a signal in python. I expected to find this functionality in scipy.signal, but I can't find any solutions. What I am trying to do is this. I have 2 ...
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### Smoothing power spectrum by convolution with boxcar function

I am trying to smoothing a signal's power spectrum by convolving the spectrum with a boxcar function in frequency domain. However, the result is obviously not what I expected: original two frequency ...
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### Smoothing peak spectra in time domain

I would like to smooth amplitude spectra of signals around their peak frequencies. I could perform FFT, find the peak frequency, and smooth around the peak in frequency domain, then inverse FFT back ...
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### Deriving a Kalman Filter Equation for a Linear Gaussian Filtering Model with Non Zero Mean Noise

I am trying to answer an exercise question from the book Simo Sarkka - Bayesian Filtering and Smoothing. The question is: Does anyone know if there is a resource that has the solutions for this book?
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### The Effect of the Standard Deviation ($\sigma$) of a Gaussian Kernel when Smoothing a Gradients Image

I am trying to understand why smoothing an image with a gaussian kernel of different sigma values and then computing the gradients of the smoothed image leads to "thicker" trails. In the ...
286 views

### What is the point of smoothing an FFT or spectral density plot, and how does that affect the noise floor?

It appears that smoothing the FFT or spectral density plots of a noisy signal is a common practice. I see that common tools like MATLAB and Python have functions built in to their FFT tools to do just ...
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### Is it applicable to implement a cascaded moving average filter with variable window on real-time?

I am using a 3-pass cascaded moving average filter for smoothing noisy data. I applied some optimization algorithms to determine the optimal length of the MAF window. For different amplitudes of data ...
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### Error introduced by smoothing filter at the end of a processing block

I'm running analysis on a multichannel audio signal and due to the size have decided to process it in blocks (my computer doesn't have enough memory to process it in one go). Some of the data produced ...
220 views

### A Simple Algorithm to Filter / Smooth / Denoise a Noisy Staircase Graph

Is there a way to remove the noise and smooth the graph into a staircase graph.
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### Possible to get transfer function coefficients from window?

I am hoping to use scipy.signals.filtfilt() to smooth some signals in Python, and wanted to build the filter based on a window like a hanning window or whatever. E....
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### Reversing the Order of Operators for Edge Detection?

Usually, for edge detection, we perform smoothing and then pass it through difference filter. What if application of difference filter happens first and then smoothing. How the math behind the same ...
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### I want to get tilt sensor value for a given time t_0, but the tilt sensor data points are discrete. How do I interpolate between the discrete points?

I have 3-dimensional readings from a tilt sensor (specifically these are rotational angles about X, Y, and Z axes) over time. Let's call these angles S. I want to infer S at a specific time t_0, but ...
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### Slew Rate Filter With Different Smoothing Factors in Each Direction

I'm smoothing the output of an ADC with a simple first order low pass filter. Of course the smoothing rate is the same whether the signal is rising or falling. Preferably the smoothing rate needs to ...
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### Algorithm for smoothing the output of an object detector operating on a video?

Please could you point me towards an algorithm that takes a series of object detections performed on a frame by frame basis as input and outputs a filtered series of object detections in which the ...
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### Selected bin oscilation in STFT

I am looking for a noisy signal using STFT. My window length is 128 and I am using 75% overlap. I am using a Hanning window before running the FFT process. I am using Quinn's 2nd estimator for ...
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### temporal smoothing: FWHM of Gaussian kernel vs. window length of moving average

Suppose in one case I convolve Gaussian kernel with FWHM=10 samples. I would like to compare the result with moving average. My question: should I take the moving average window also 10 samples? In ...
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### Continuous time double exponential filtering in state space form?

I'm trying to determine the continuous time formulation of the double exponential filter so that I can adapt it more flexibly for my particular problem. Typically, this model is expressed as a pair ...
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### Difference Between a 1st Order SG Filter And a Least Squares Moving Average

I have been studying SG filters and i recently found another filter which seem to be commonly used in financial data smoothing which is the least-squares moving average, this filter is also called ...
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### Implementing Edge Preserving Diffusion (Anisotropic Diffusion)

I am trying to implement edge preserving diffusion. Recall the general diffusion equation to be: $$\DeclareMathOperator{\Div}{div}\delta_t u = \Div(g \nabla u)$$ Where $g$ is the speed of the ...
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### Chromatogram peak detection - bunching vs others?

Reading presentations from existing tool providers I noticed that in order to detect peaks they first use bunching (average N points) and then use slope and curvature to detect peaks. I'm guessing ...
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### Are there any applications using absolute Savitzky-Golay filter to smooth data and preserve non-negative properties?

I want to smooth peaks for non-negative matrix factorization (NMF). Since Savitzky-Golay has polynomial smoothing, I think it is good for narrow peak shape in my signal profile. But NMF needs to be ...
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### 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 ...
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### 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: ...
I have a simple first-order reaction batch system for which I have some discrete measurements ($0<t_{k}\le t_{endbatchsample}$). I have an initial guess for $x_0$ and $P_0$ and from here I ...