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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

so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
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
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
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele 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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