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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

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
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
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.
what is the actual application of fullerenes nowadays?
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.
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.
is Bucky paper clear?
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.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
I'm interested in nanotube
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
what is system testing
what is the application of nanotechnology?
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
anybody can imagine what will be happen after 100 years from now in nano tech world
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
I'm interested in Nanotube
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
can nanotechnology change the direction of the face of the world
Prasenjit 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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