I am trying to use statmodels STL decomposition function to find the seasonalities in my time-series. I have for simplicity superpositioned two sine series, and am trying to get the STL to find both my seasonalities. I am struggling to make it do that, and I do not fully understand the input-parameters to the function.
Is it not so that STL can find "all" the seasonalities in your time series? Or will you have to specify your expected periods for it to decompose?
Below is an example with period 31 and 7 sine series and a STL(df,period=37):
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I'm trying to develop a model to recognize new gestures with the Myo Armband. (It's an armband that possesses 8 electrical sensors and can recognize 5 hand gestures). I'd like to record the sensors' raw data for a new gesture and feed it to a model so it can recognize it.
I'm new to machine/deep learning and I'm using CNTK. I'm wondering what would be the best way to do it.
I'm struggling to understand how to create the trainer. The input data looks like something like that I'm thinking about using 20 sets of these 8 values (they're between -127 and 127). So one label is the output of 20 sets of values.
I don't really know how to do that, I've seen tutorials where images are linked with their label but it's not the same idea. And even after the training is done, how can I avoid the model to recognize this one gesture whatever I do since it's the only one it's been trained for.
An easy way to get you started would be to create 161 columns (8 columns for each of the 20 time steps + the designated label). You would rearrange the columns like
emg1_t01, emg2_t01, emg3_t01, ..., emg8_t20, gesture_id
This will give you the right 2D format to use different algorithms in sklearn as well as a feed forward neural network in CNTK. You would use the first 160 columns to predict the 161th one.
Once you have that working you can model your data to better represent the natural time series order it contains. You would move away from a 2D shape and instead create a 3D array to represent your data.
The first axis shows the number of samples
The second axis shows the number of time steps (20)
The thirst axis shows the number of sensors (8)
With this shape you're all set to use a 1D convolutional model (CNN) in CNTK that traverses the time axis to learn local patterns from one step to the next.
You might also want to look into RNNs which are often used to work with time series data. However, RNNs are sometimes hard to train and a recent paper suggests that CNNs should be the natural starting point to work with sequence data.
All examples that I can find on the Internet just visualize the result array of the function computeSpectrum, but I am tasked with something else.
I generate a music note and I need by analyzing the result array to be able to say what note is playing. I figured out that I need to set the second parameter of the function call 'FFTMode' to true and then it returns sound frequencies. I thought that really it should return only one non-zero value which I could use to determine what note I generated using Math.sin function, but it is not the case.
Can somebody suggest a way how I can accomplish the task? Using the soundMixer.computeSpectrum is a requirement because I am going to analyze more complex sounds later.
FFT will transform your signal window into set of Nyquist sine waves so unless 440Hz is one of them you will obtain more than just one nonzero value! For a single sine wave you would obtain 2 frequencies due to aliasing. Here an example:
As you can see for exact Nyquist frequency the FFT response is single peak but for nearby frequencies there are more peaks.
Due to shape of the signal you can obtain continuous spectrum with peaks instead of discrete values.
Frequency of i-th sample is f(i)=i*samplerate/N where i={0,1,2,3,4,...(N/2)-1} is sample index (first one is DC offset so not frequency for 0) and N is the count of samples passed to FFT.
So in case you want to detect some harmonics (multiples of single fundamental frequency) then set the samplerate and N so samplerate/N is that fundamental frequency or divider of it. That way you would obtain just one peak for harmonics sinwaves. Easing up the computations.
How to compute the maximum of a smooth function defined on [a,b] in Fortran ?
For simplicity, a polynomial function.
The background is that almost all numerical flux(a concept in numerical PDE) involves computing the maximum of certain function over an interval [a,b].
For a 1-D problem with smooth and readily-computed derivatives, use Newton-Raphson to find zeros of the first derivative.
For multiple dimensions, and readily-computed derivatives, you're better off using a method that approximates the Hessian. There are several methods of this type, but I've found the L-BFGS method to be reliable and efficient. There a convenient, BSD-licensed package provided by a group at Northwestern University. There's also quite a bit of well-tested code at http://www.netlib.org/
I am using the accelerate framework FFT functions to produce a spectrogram of a sound sample. This part works great. However, I want to (effectively) manipulate the spectrum directly (ie manipulate the real numbers), and then call the inverse again, how would I go about doing that? It looks like the INVERSE call expects an array of IMAGINARY numbers, but how can I produce that from my manipulated real numbers? I have tried making the realp array my reals, and the imagp part zero, but that doesn't seem to work.
The reason I ask this is because I wish to run an FFT on a voice audio sample, and then run the FFT again and then lifter the low part of the cepstrum (thus hopefully separating the vocal tract components from the pitch) and then run an inverse FFT again to produce a spectrogram showing the vocal tract (formant) information more clearly (ie, without the pitch information). However, I seem to be running into problems on the inverse FFT, into which I am passing in my real values (cepstrum) in the realp array and the imagp is zero. I think I am doing something wrong here and the results are unexpected.
You need to process the complex forward FFT results, rather than the real magnitudes, or else the shape of the IFFT result spectrum will be distorted. Don't consider them imaginary numbers, consider them to be part of a 2D vector containing the required angular phase information.
If your cepstrum lifter/filter alters only the real magnitudes, then you can try using the amount of change of the real magnitudes as scaling factors to alter your forward complex FFT result before doing a complex IFFT.
How to find the following Maximum or supremum by computer software such as Mathematica and Matlab: $\sup\frac{(1+s)^{4}+(s+t)^{4}+t^{4}}{1+s^{4}+t^{4}}$?
Instead of numerical approximation, what is the accurate maximum?
Thanks.
Since the question seems a bit like homework, here's an answer that starts a bit like a lecture:
ask yourself what happens to the function as s and t go to small and to large positive and negative values; this will help you to identify the range of values you should be examining; both Mathematica and Matlab can help your figure this out;
draw the graph of your function over the range of values of interest, develop a feel for its shape and try to figure out where it has maxima; for this the Mathematic Plot3D[] function and the Matlab plot() function will both be useful;
since this is a function of 2 variables, you should think about plotting some of its sections, ie hold s (or t) constant, and make a 2D plot of the section function; again, develop some understanding of how the function behaves;
now you should be able to do some kind of search of the s,t values around the maxima of the function and get an acceptably accurate result.
If this is too difficult then you could use the Mathematica function NMaximize[]. I don't think that Matlab has the same functionality for symbolic functions built-in and you'll have to do the computations numerically but the function findmax will help.
In Matlab, one would create a vector/matrix with s and t values, and a corresponding vector with the function values. Then you can pinpoint the maximum using the function max
In Mathematica, use FindMaximum like this:
f[s_,t_]:= ((1+s)^4 + (s+t)^4 + t^4)/(1+s^4+t^4)
FindMaximum[ f[s,t],{s,0},{t,0} ]
This searches for a maximum starting from (s,t)=(0,0).
For more info, see http://reference.wolfram.com/mathematica/ref/FindMaximum.html