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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

what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
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
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
Got questions? Join the online conversation and get instant answers!
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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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