# Tagged Questions

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

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### Implementing continuous phase/Arg function

In MATLAB there's a function called phase that is just like our Listable friend Arg, but ...
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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 ...
1k views

### Graphical representation of a moving sound source

Some explanation since I have got a specific and another more open-ended question: I used two microphones in a 90° arrangement (see picture below) to capture sound from a source moving around the room ...
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### Computing and plotting a spectrogram in Mathematica

How can I compute and plot the spectrogram of a signal/time series/data in Mathematica? I have a WAV file, sampled at 44100 samples/second and I want to generate a spectrogram of that data. Something ...
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### Implementing discrete and continuous Hilbert transforms

What is an efficient and accurate Mathematica implementation of the Hilbert transform, for both continuous and especially discretely sampled functions? This transform relates phase and amplitude in ...
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### How to find the phase difference of two sampled sine waves?

I'm trying to measure a phase difference between two Sine functions I've acquired with a computer. I'm uploading one of the .txt files with the data I'm working with here: txt file. To remove the ...
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### 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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### Can one find the beat of a tune with Fourier analysis?

I'm trying to find out if it's possible to find the beat of a tune by Fourier analysis with Mathematica. I'm taking a 44.1 kHz sample sound and hoping that I might get a nice peak for a frequency ...
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### How to demodulate an FM signal in continuous-time?

I'm not sure if this is a math or Mathematica question, but I'm posting it here because I'm interested in possible Mathematica tools/functions to solve the problem. I'm stuck. I want to simulate ...
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### Numerical Fourier transform of a complicated function

Say I have a function $f(x)$ that is given explicitly in its functional form, and I want to find its Fourier transform[1]. If $f$ is too complicated to have an analytic expression for $\hat f(k)$, how ...
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### Plotting Fourier spectrum versus frequency of a signal

I have looked around here, and i am sure this has been answered, but i don't understand it. The thing is, I have taken a introductory signal processing course, and we had to use Mathematica, and i had ...
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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 ...
501 views

### Cluster a signal into areas of equal intensity

Introduction I have a greyscale photograph that I want to partition into areas of equal intensity. This means, that the integral over each partition should be (roughly) equal. There is no unique ...
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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 ...
723 views

### Cross-Correlation with TimeSeries

How to find hidden relationship between two TimeSeries data sets? I normally compute the Cross-Correlation function, but I cannot find an easy way of doing this on the TimeSeries objects in ...
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### Segmentation of a microscopy image with uneven illumination

I am trying to do a little image segmentation on some cells taken from microscopy images that have uneven illumination. I am having trouble getting the background of the image cleaned up after ...
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### Strategies to find curves on messy data using FindCurvePath

I have a set of data points that correspond to roots of a transcendental equation with respect to a parameter (the abscissa) which, by the properties of the system, define continuous curves (might be ...
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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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### How can I use Mathematica to numerically compute a Wigner spectrogram of an optical pulse?

This question was inspired by this question where it is necessary to numerically compute the Fourier transform of a Gaussian optical pulse with a Gaussian chirp function. E(t)=e^{-t^2} \cos(50 t - ...
414 views

### Wavelet transform order problem

I have a signal that I'm trying to study its time-frequency features by continuous wavelet transform. By choosing different wavelet order, I get some differences in the results. ...
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### How does Mathematica's LowpassFilter work?

I don't really understand the documentation for the LowpassFilter[] function in Mathematica. In the course I have about signal processing, low-pass filters come in ...
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### Hilbert-Huang transform package

I am trying to learn Hilbert-Huang transform (HHT) and its applications (especially in ECG signal processing). There are several HHT packages (scripts) HHT for R and Matlab. Is there any known ...
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### Why the BandpassFilter is different than applying LowpassFilter then HighpassFilter

If I generate some data with noise, and use a filter to filter the noise, why does BandpassFilter not produce the same results as using ...
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### How to make sense of LowpassFilter, SampleRate and the cutoff frequency ωc in different Mathematica versions?

How do you make sense of the scale of "time" and "sampling" when using LowpassFilter and SampleRate ? Given the test data with ...
419 views

### How to extract notes and chords from audio?

I have a 3-second recording of a guitar chord which you can safely download here. I'm trying to use Mathematica's wavelet features to find out the notes in the chord, at least the docs says that ...
412 views

### Building Butterworth Bandpass Filters

In order to bandpass filter data it is necessary to use ButterworthFilterModel, followed by ToDiscreteTimeModel and RecurrenceFilter. I have two questions: I wish to specify the order of the ...
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### Compare two shifted signals

I have one set of original data (signal A) and a second set of derived data (signal B) which was computed from A by position rotation (circular shift). Here are the data for the signals (A and B): <...
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### PrincipalValue option of Convolve not working in 9.0.1?

The PrincipalValue option of Convolve is used in this question to define the Hilbert transform. However, in Mathematica 9.0.1, ...
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### Obsolete Signal Processing functions

I need some tools to detect the fundamental frequency and pitch of a sound. I Googled for "pitch detect" and found some .nb files that do these tasks, but all the files are in Mathematica 3.0 format. ...