# Tagged Questions

Digital signal processing of sound, video or other single or multidimensional data

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### Wavelet Transform Modulus Maxima (WTMM) method

Has anyone already coded the Wavelet Transform Modulus Maxima (WTMM) method for computing the singular spectrum using multi fractal formalism in Mathematica? The goal is to analyse 1D, 2D and 3D data....
877 views

### How do you use Fourier transforms to perform a deconvolution

I've been trying to teach myself about deconvolution through Fourier transforms, but I seem to be missing something simple, as my results are garbage. I start by defining a test function and a window ...
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### Power spectrum density calulation with ARProcess

I have a measurement of $x$ coordinates of an oscillating particle at presence of noise taken at constant time steps of 1/60 s. The corresponding data set can be obtained here: http://goo.gl/...
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### What does ℜn mean? [migrated]

I came across the symbol ℜ in the Kalman introduction: http://www.cs.unc.edu/~welch/media/pdf/kalman_intro.pdf x∈ℜm It was used in this context: ...
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### Why isn't LowPassFilter working for these parameters?

First I define a function, just a sum of a few sin waves at different angular frequencies: ...
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### Filtering beat-to-beat heart rate data

From an experiment, I have a dataset of beat-to-beat heart rate data: a list of the time between each heart beat in [ms]. The data is measured using an infrared optic sensor at the finger tip. The ...
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### Extracting filter coefficients from a transfer function

What is the correct way to extract coefficients (in a form I could use in RecurrenceFilter) from a filter which I have represented as a Mathematica transfer ...
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### Implementation of a Hanning filter

I'm implementing a package for in-house signal processing. I wrote here a quite trivial function implementing a Hanning windowing of the signal. ...
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### Identify a note in a song using Mathematica

I'm trying to figure out how to use Mathematica to identify a note from a song. The short .mp3 file found here or here contains a bass-note that I'd like to identify. I can find it through ...
3k views

### Savitzky-Golay Filter to smooth noisy data

I do have noisy data and want to smooth them by a Savitzky-Golay filter because I want to keep the magnitude of the signal. a) Is there a ready-to-use Filter available for that? b) what are ...
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### Extracting signal from gaussian noise

I am trying to extract a signal, $X$, from a noisy source of data, $Z$: $Z = X + Y$ where I know that $Y\sim N(0,\sigma)$, and I know the standard deviation $\sigma$. I am starting with a surrogate ...
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### Filtering in frequency domain

I'm trying to modify a transfer function in the frequency domain by filtering it with a Butterworth filter. For example, let's say my transfer function is of the form : ...
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### Applying a window over a list

The window functions state that they tread over lists, but when I try to do: HammingWindow/@list, I do not get the expected results. What is the best way to apply a window over an arbitrary length ...
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### FindPeaks error “ Expecting an image or graphics instead of”

I'm running Mathematica 10.3.1.0 on windows 7 Professional Sp.1 when I try to use FindPeaks I keep getting the following error, even when trying the example in the ...
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### Problem with Sin and ListPlot

In order to produce a smooth sine wave (Sin) and visualize it (ListPlot), I seem to need a very high sample rate (much higher than Nyquist). I want to know if this is a artifact of ListPlot or Sin ...
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### Plotting amplitude spectra of modulated message signal

I'm trying to plot the amplitude spectrum of the modulated message signal, I have managed to plot it by working through the maths, expanding out each trig function, and then drawing onto a graph ...
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### Why there is a click sound when I play a sound?

When I consider this simple code: ListPlay[RandomReal[1, {2000}], SampleRate -> 1000] I hear a click at the beginning of the sound sample and at the end of ...
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### Mapping the MATLAB SP Toolbox to Mathematica

We have some work and people where I am doing signal processing using the signal processing toolbox in MATLAB and it comes up how to translate one or another of the large number of functions in that ...
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### Wavelet Data Visualization (modus and phase) ListPlot [closed]

Due to ContinuousWaveletTransform[...] I can obtain information about wavelet-coefficient for example ...
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### Getting correct amplitudes with Periodogram

I'm having some trouble with the function Periodogram, mainly with getting it to produce correct amplitudes for the spectrum it returns. My question is how to fix ...
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### Is oscillation seen in data signal or noise? [closed]

I have some experimental data which is well-fitted by 40 terms of a Fourier series. I want to know if the oscillation exhibited is signal or noise. I evaluated the code shown below to plot my data in ...
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### Engineering spectral densities using filtered white noise

My goal is to create time-spectrum noise signals with spectral densities $S_{xx}(f)$ for pretty much arbitrary spectral densities (think white noise, lorentzian, $1/f$). In finding advice on how to do ...
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### Constructing the spectral density of white noise

My goal is to find the spectral density $S_{XX}(f)$ from a time domain noise signal $X(t)$. The approach should work for general time series, but to illustrate what I've been doing I'll keep it simple:...
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### Using BandpassFilter

https://drive.google.com/file/d/0B7G3oUuZG1TwRHNNV1RFZjFWUXM/view?usp=sharing Above I have linked a data set containing a 2 seconds EEG sample I have recorded of someone "blinking". This data set was ...
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### How to fit data to a convolution equation

How to fit data to a convolution equation: ...
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### How to obtain the magnitude with dB in DFT?

I want to do a DFT of a fragment of music,and then plot the magnitude with dB instead of amplitude. For example: ...
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### What is Mathematica's equivalent to MATLAB's filter function?

The MATLAB code filter(0.5,[1, -0.5], [1:10]) is equivalent to Rest@FoldList[(#1 + #2)/2. &, 0, Range[10]] I don't ...
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### Absurd solution by LinearSolve

I am trying to find curve that passes through all the data points.To do this i am doing interpolation using LinearSolve. No. of equations vary from 1000 to 3000. LinearSolve gives me values of ...
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### Application of lowpass Butterworth filter

I'm trying to design a Butterworth lowpass filter with a cutoff frequency of So far what I did is ...
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### Mathematica nested loops [closed]

I can write down the following Python code: for j1 > 2: time1 = i1 for i2 > i1: if j2 < 2: time2 = i2 break Purpose of the above code: ...
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### Estimating Power Spectral Density from Autocorrelation

I have been tasked with computing the power spectrum of a noisy signal. Specifically, I am asked to do so through first attaining the autocorrelation function. From what I have read, the PSD is simply ...
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### 1D phase unwrapping [duplicate]

I want to unwrap a signal but I don't know where to add the 2 Pi. How should I unwrap the phase? ...
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### How do you find the frequency and amplitude from Fourier?

Edit This is a popular question with several answers. This edit organises the answers and gives links. Fourier just gives y values (ordinates) if you wish to read off frequencies and amplitudes you ...
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### How to compute the Power Spectral Density of an EEG signal [closed]

I have an EEG signal of length N on a given channel (FP1). I would like to compute the power spectral density of the signal. More specifically, once the PSD is computed, I would like to sum the ...
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### We need to know the input signal when we use KalmanEstimator?

The first "Application" in the documentation for KalmanEstimator is copied below with additional variables for clarity. ...
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### How does KalmanEstimator update the Kalman gain, process noise and state variable mean?

The first "Application" in the documentation for KalmanEstimator is copied below with additional variables for clarity. ...
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### What does OutputResponse[sys, { {u1,u2,u3}, {v1,v2,v3} } ] do?

I am puzzled by the result of OutputResponse[sys, {{u1,u2,u3},{v1,v2,v3}}]. OutputResponse is used this way in the first "Application" in the documentation for <...