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

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4
votes
1answer
876 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 ...
0
votes
1answer
55 views

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/...
0
votes
0answers
5 views

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: ...
6
votes
5answers
206 views

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: ...
29
votes
4answers
1k views

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 ...
0
votes
1answer
284 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 ...
0
votes
1answer
98 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
106 views

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 ...
20
votes
3answers
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 ...
11
votes
1answer
214 views

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 ...
3
votes
0answers
85 views

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 : ...
0
votes
2answers
70 views

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 ...
2
votes
0answers
47 views

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 ...
0
votes
1answer
82 views

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 ...
1
vote
2answers
103 views

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 ...
1
vote
1answer
64 views

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 ...
1
vote
0answers
76 views

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 ...
1
vote
0answers
99 views

Wavelet Data Visualization (modus and phase) ListPlot [closed]

Due to ContinuousWaveletTransform[...] I can obtain information about wavelet-coefficient for example ...
3
votes
1answer
111 views

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 ...
1
vote
0answers
86 views

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 ...
0
votes
0answers
69 views

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 ...
1
vote
0answers
70 views

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:...
2
votes
3answers
270 views

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 ...
5
votes
1answer
191 views
1
vote
2answers
102 views

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: ...
15
votes
3answers
1k views

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 ...
6
votes
6answers
271 views

How do I build a patterned matrix (high-pass and/or low-pass filter bank)?

I would like the shortest code to build the following matrices, of arbitrary dimension $N$: A Low-Pass filter bank matrix is of the form $ \begin{bmatrix} 1 & 1 & 0 & ...
16
votes
2answers
502 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 ...
31
votes
3answers
3k views

Implementing continuous phase/Arg function

In MATLAB there's a function called phase that is just like our Listable friend Arg, but ...
0
votes
1answer
102 views

Phase spectrum of a linear chirped signal

I am calculating the phase spectrum of a linear chirped signal. I actually don't know how the phase spectrum should be, but I would expect something in the range of interest (the bandwidth) at least ...
5
votes
3answers
244 views

Find when two lists are parallel with autocorrelation

I am working on a signal processing project with two oscillators. The first oscillator has a frequency $f_1$ that is independent, and the second oscillator has a frequency $f_2$ that increases, and ...
0
votes
0answers
58 views

ButterworthFilterModel consumes the memory too much

I have a simple filter which is a result of the these questions here and here I have to use this filter in a Do loop but I found that this filter consume the ...
11
votes
1answer
320 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 - ...
7
votes
2answers
421 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 ...
2
votes
1answer
69 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 ...
2
votes
1answer
191 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"]] ...
3
votes
2answers
147 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 ...
0
votes
0answers
97 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
84 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
64 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: ...
3
votes
0answers
219 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 ...
0
votes
0answers
37 views

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? ...
16
votes
6answers
5k views

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 ...
1
vote
0answers
415 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 ...
2
votes
0answers
68 views

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. ...
0
votes
0answers
86 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. ...
4
votes
0answers
54 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
51 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. ...
7
votes
1answer
222 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
365 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 ...