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We then plot the results on a 2-D plane using imagesc() . This function associates colors with the values in the matrix, so that you can see where the values in the matrix are larger. Thus we get a pretty picture as above.

Testing the spectrogram

For the first test, we will try a simple sin wave.

For the second test, we will use a more interesting function. Below we have plotted sin ( 6 * 2 π t ) + sin ( 20 * 2 π t ) + 2 * sin ( e t / 1 . 5 ) over [ 0 , 10 ] .

a dog on a bed
An interesting signal to decompose.

This function is interesting because it contains a frequency component that is changing over time. While we have waves at a constant 6 and 20 Hertz, the third component speeds up as t gets larger and the exponential curve gets steeper. Thus for the plot we expect to see a frequency component that is increasing. This is exactly what we see in [link] –two constant bands of frequency, and one train of frequency that increases with time.

>> dt = 1e-4;>> t = 0:sr:10;>> y = sin(6*2*pi*t)+sin(20*2*pi*t)+2*sin(exp(t/1.5));>> my_stft(y, dt, 5000);
a dog on a bed
The spectrogram of the above function

Application to eeg data

For the final section, we will analyze actual brain waves. We recorded from and EEG, and got the signal in [link] .

a dog on a bed
An EEG wave.

To analyze, we find the time-step in the data, then call mysgram(). This gives us the plot below.

a dog on a bed

Compare the spectrogram to the raw signal. What do you notice? Perhaps the most notable change is the significant increase in signal magnitude near 18 seconds. This is reflected in the spectrogram with the brighter colors. Also, several "dominant" frequencies emerge. Two faint bands appear at 10 Hz 4 Hz for the first half of the signal. In the last section, a cluster of frequencies between 6 and 10 Hz dominate. Many of the patterns are hidden behind the subtleties in the data, however. Decoding the spectrogram is at least as difficult and creating it. Indeed, it is much less defined. The next section will explore these rules in the context of an interesting application.

Application: driving a car

One application of decoding brain waves is giving commands to a machine via brainwaves. To see developing work in this field, see this video of the company NeuroSky. Of the many machines we could command, we choose here to command a virtual car (some assembly required) that goes left or right. As above, the decision rule for such a program is not obvious. As a first try, we can find the strongest frequency for each time section and compare it to a set value. If it is lower, the car moves left, and if higher, the car moves right. The following code implements this rule:

   %load dataload bwave N = numel(eeg_sig);win_len = 3 * round(N / 60); n = 0;freq_criterion = 8; while (n+3) * win_len / 3<= N %for each time window %define the moving window and isolate that piece of signalsig_win = eeg_sig(round(n * win_len / 3) + (1:win_len));%perform fourier analysis [freq raw_amps]= myfourier(sig_win, dt, 1); %only take positive frequenciesfreq = freq((end/2+1):end); %add sine and cosine entries togethefamps = abs(sum(raw_amps(end/2:end,1), 2));%find the maximum one [a idx]= max(amps);%find the frequency corresponding to the max amplitude max_freq = freq(idx);%decided which way the car should move based on the max frequencyif max_freq<freq_criterion; fprintf('Moving left.... (fmax = %f)\n', max_freq);%this is where we put animation code elsefprintf('Moving right.....(fmax = %f)\n', max_freq); %this is where we put animation codeendpause(.5); %for dramatic effect :) n = n + 1;end

Questions & Answers

Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, The art of the pfug. OpenStax CNX. Jun 05, 2013 Download for free at http://cnx.org/content/col10523/1.34
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