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Questions tagged [signal-processing]

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

14
votes
1answer
1k views

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 - ...
2
votes
1answer
93 views

Digital filter. Why do these two methods produce such different results?

I am trying to produce a transfer function with a peak=3000 and gain=1 first order on the high pass side and second order on the low pass side. I believe the below two methods should produce ...
4
votes
2answers
243 views

How can I filter this signal in mathematica

Given the transfer function $H(z) = \frac{1}{4}(1+z^{-1}+z^{-2}+z^{-3})$ and the input signal $x[n] = \cos(\frac{\pi}{50}n)+\cos(\frac{4\pi}{5}n)$, how can I find the output signal $y[n]$ in ...
2
votes
3answers
868 views

How can I convert a Sound created with SoundNote to a list of samples?

I have a Sound created with SoundNote, as follows: simpleSound = Sound[SoundNote["C"]] ...
1
vote
0answers
128 views

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 ...
3
votes
0answers
256 views

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 ...
-1
votes
1answer
73 views

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: ...
4
votes
0answers
704 views

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 ...
1
vote
0answers
1k views

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 ...
0
votes
0answers
205 views

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. ...
6
votes
1answer
166 views

Do 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. ...
4
votes
0answers
75 views

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 <...
3
votes
0answers
56 views

What are all the elements of the expression returned by KalmanEstimator used for?

The first "Application" in the documentation for KalmanEstimator is copied below with additional variables for clarity. ...
17
votes
2answers
1k views

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 ...
7
votes
1answer
1k views

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 ...
8
votes
1answer
2k 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 ...
4
votes
0answers
498 views

Nonuniform Savitzky-Golay filter for smoothing and differentiation

The classical Savitzky-Golay filter works only with uniformly sampled data and currently we have at least two good implementations of it for Mathematica published on our site. But in many practical ...
0
votes
1answer
125 views

How to find the starting point of an oscillation (with noise)?

I've got a series of coordinates which start to oscillate from some time (and with noise), like this: ...
0
votes
1answer
712 views

Are there any open source projects related to signal processing

I am going to make a program related to audio signal processing . Are there any open source projects related to it?
1
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0answers
152 views

PeriodogramArray or PowerSpectralDensity?

could anyone explain what is the difference between PowerSpectralDensity[data,omega] and PeriodogramArray[data]? When I plot them (starting from the same set of data of course) I get two different ...
15
votes
4answers
2k 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 ...
1
vote
1answer
564 views

Extracting out the Fourier modes of a series, and using these to reconstruct data series

I would like to extract the most important frequency modes from a data set which exhibits strong annual periodicity, as well as some (less) important shorter-term frequency components. The following ...
6
votes
0answers
1k views

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....
9
votes
2answers
896 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 ...
1
vote
0answers
401 views

Is there an equivalent of “pmtm” of MATLAB?

Recently I'm spending my time implementing some patients' analysis using Mathematica Classify function. But I need to rewrite some MATLAB functions for computing ...
2
votes
0answers
365 views

Position from 3 dimensional acceleration data? [closed]

Per a previous post on Mathematica StackExchange here I'm trying to utilize 3-axis accelerometer data to determine approximate 3D position. I wanted to start with a simple case. To this end I've ...
2
votes
1answer
847 views

Is there any function in Wolfram Mathematica simmilar to fft.fftfreq (Python)

Here is an explanation of fft.fftfreq I have data with random noise: ...
4
votes
0answers
390 views

Can Mathematica reconstruct an audio signal from a given spectrogram

I just realized that Mathematica can easily construct a spectrogram for a given .wav file. My question is, to what extent can this process be inverted in Mathematica? Namely, lets say I have the ...
5
votes
2answers
817 views

FindPeaks does not smooth noise on peak?

I have experimental data which is noisy. My objective is to find the peaks. Here is a short part of the data: ...
4
votes
2answers
181 views

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): <...
1
vote
1answer
385 views

How to use a Butterworth bandpass filter to generate a chirped signal [duplicate]

As there is no ChirpSignal function in Mathematica, I wrote a simple code to generate a sinusoid with a frequency that changes continuously from frequency ...
5
votes
3answers
2k views

How to generate a chirped signal

As there is no ChirpSignal function in Mathematica, can anyone tell me how to write a custom function to generate a sinusoid with a frequency that changes ...
12
votes
4answers
826 views

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 ...
6
votes
3answers
6k views

How can I obtain a smooth curve from my data but preserve two inversion points

I have a list of data points, {x, y}, my data. When I plot them, the curve is jagged. I want to smooth the curve and preserve the two sharp corners. This is a plot ...
3
votes
1answer
2k views

Wavelet vs instantaneous power spectrum

Following on from a previous question posted by @xslittlegrass and answered by @Sector and others, Extracting information from the result of ContinuousWaveletTransform I'd like to know if it is ...
7
votes
1answer
350 views

Working example for the built-in SavitzkyGolayMatrix for doing polynominal smoothing

Have been using various packages SavitskyGolay.m for Savitsky-Golay polynomial smoothing but just noticed the built-in matrix kernel. I am looking for an example ...
0
votes
1answer
516 views

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 ...
4
votes
1answer
231 views

How do I bandpass a signal in Mathematica 8

I would like to use the bandpassing function that is available in newer versions of Mathematica but not Mathematica 8: ...
4
votes
0answers
355 views

Bandpassing EEG's using Mathematica's Bandpass Function

Let's say we have an EEG signal approximated using a fractional Brownian motion: ...
5
votes
4answers
2k views

Why does Fourier give a shifted frequency?

I have a signal that I want to identify the frequencies in it, I used the Fourier function but I can't get the frequency correctly. Here is a simplified example: ...
0
votes
0answers
36 views

Why I am not getting the same frequency when sampling a waveform? [duplicate]

I am trying to simulate the sampling of a waveform to then apply FFT Analysis to it. Here is the sample code I have now using a square wave: ...
2
votes
2answers
631 views

How to generate a random signal consisting of the specified functions

Let's assume that I have some particular signal on the finite time interval which is described by function $f(t)$. It could be, for instance, a rectangular pulse with amplitude $a$ and period T; Gauss ...
6
votes
0answers
292 views

Resources for Sound Synthesis & Design

Are there any resources for sound synthesis using Mathematica? This page, Mathematica: Audio Synthesis Software, refers to other software packages, e.g. Max/MSP and Csound, for real-time synthesis. ...
5
votes
1answer
2k views

Data filtering using Butterworth filter

I want to filter data using Butterworth filter. I am currently using Matlab and I want to know how to do it in Mathematica. I have the following data: ...
15
votes
0answers
329 views

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 ...
4
votes
1answer
649 views

Butterworthfilter data filter

I am currently doing a signal analysis and filtering using Matlab. The filter I am using is Butterworthfilter model to filter scattered data (vector data). I am using Matlab as follows: ...
20
votes
4answers
15k views

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 ...
0
votes
1answer
140 views

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. ...
3
votes
1answer
963 views

Plotting power spectral density from transfer function

I am new to signal processing. The equations below are given in $LaTeX$. I have the following transfer function (from the Dryden Model) for the two-sided Power Spectral Density: $$S(w) = \frac{\...
10
votes
2answers
2k views

Correct Fourier scaling and high-resolution frequency identification

I have a dataset of amplitude versus time $(t,A(t))$ and I need to extract the dominant frequency and amplitude, and also get the amplitude at one other specific frequency. My data looks like this: <...