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Another approach would be to find the center of mass of the data. This decision rule is more comprehensive because it takes into account all data from the Fourier transform, not just the maximum value. In order to find the average weight of all amplitudes, we change the inner part of code to the following (starting with "%find the maximum one"):

... %find the frequency corresponding to the "average" amplitudeavg_freq = sum(freq.*amps)/(sum(amps)*df);%decided which way the car should move based on the max frequency if avg_freq<freq_criterion; ...

One can imagine myriad other ways to approach this problem. Many strategies have been developed, but the question is open-ended. A natural next step is for the reader to think of new ways to interpret spectrogram data. The most effective characterizations probably have yet to be discovered!


In this module we developed the tools to decompose an arbitrary signal, such as an EEG, into is component frequencies. We began with sine waves, established the trapezoid scheme, and finally introduced Fourier analysis. This same flavor of analysis is used in many other settings, too–see the related documents.


Code for mytrapz.m

function curve_area = mytrapz(x, y, fast) % function curve_area = mytrapz(x, y, fast)% % mytrapz.m performs the trapezoid rule on the vector given by x and y.% % Input:% x - a vector containing the domain of the function % y - a vector containing values of the function corresponding to the% values in 'x' if nargin<3 curve_area = 0;%loop through and add up trapezoids for as many points as we are givenfor n = 2 : numel(x) height = (y(n) + y(n-1))/2; %average height of function across intervalbase = x(n) - x(n-1); %length of interval trap_area = base * height; %area of trapezoidcurve_area = curve_area + trap_area; %add to continuing sum endelseif fast%alternate (fast) implementation xvals = x(3:end) - x(1:end-2);yvals = y(2:end-1); curve_area = yvals(:)'*xvals(:);curve_area = curve_area + y(1)*(x(2) - x(1)) + y(end)*(x(end) - x(end-1)); curve_area = curve_area/2;end

Code for myfreq.m

% myfreq.m %% find the frequencies and amplitudes at which a wave is "vibrating" %% Contrast simple (but laborious) trapezoid computations to the fast % and flexible built-in fft command (fft stands for fast Fourier% transform). % To make full sense of this we will need to think about complex% numbers and the complex exponential function. %T = 5;% duration of signal dt = 0.001; % time between signal samplest = 0:dt:T; N = length(t);y = 2.5*sin(3*2*pi*t) - 4.2*sin(4*2*pi*t); % a 2-piece wave plot(t,y)xlabel('time (seconds)') ylabel('signal')for f = 1:5, % compute the amplitudes as ratios of areas a(f) = trapz(t,y.*sin(f*2*pi*t))/trapz(t,sin(f*2*pi*t).^2);end figureplot(1:5,a,'ko') % plot the amplitudes vs frequency hold onplot(1:5, [0 0 2.5 -4.2 0], 'b*')figure(34) f = (0:N-1)/T;% fft frequenciessc = N*trapz(t,sin(2*pi*t).^2)/T; % fft scale factor A = fft(y);newa = -imag(A)/sc; plot(f,newa,'r+')y = y + 3*cos(6*2*pi*t); % add a cosine piece figure(1)hold on plot(t,y,'g') % plot ithold off legend('2 sines','2 sines and 1 cosine')figure(2) A = fft(y); % take the fft of the new signalnewa = -imag(A)/sc; plot(f,newa,'gx')b = real(A)/sc; plot(f,b,'gx')xlim([0 7]) % focus in on the low frequencieshold off xlabel('frequency (Hz)')ylabel('amplitude') legend('by hand','by fft','with cosine')

Code for myfourier.m

% function [mag freq] = myfourier(y, dt, use_fft)% % myfourier.m decomposes the signal 'y', taken with sample interval dt,% into its component frequencies. %% Input: %% y -- signal vection % dt -- sample interval (s/sample) of y% use_fft -- if designated, use matlab's fft instead of trapezoid method %% Output: %% freq -- frequency domain % mag -- magnitude of frequency components of y corresponding to 'freq'function [freq mag] = myfourier(y, dt, use_fft)y = y(:); N = numel(y); %number of samplesT = N*dt; %total time t = linspace(0,T,N)'; %reconstruct time vectorhalf_N = floor(N/2); %ensures that N/2 is an integer if mod(N,2) %treat differently if f odd or evenfreq = (-half_N:half_N)'/T; %fft frequencies elsefreq = (-half_N:half_N-1)'/T; %fft frequencies endif nargin<3 %perform explicit Fourier transform sinmag = zeros(size(freq)); %vector for component magnitudescosmag = zeros(size(freq)); %vector for component magnitudes%loop through each frequency we will test for n = 1 : numel(freq)%obtain coefficient for freqency 'freq(n)' sinmag(n) = mytrapz(t, y.*sin(freq(n)*2*pi*t), 1);cosmag(n) = mytrapz(t, y.*cos(freq(n)*2*pi*t), 1); end%scale to account for sample lengthscale_factor = mytrapz(t, sin(2*pi*t).^2); sinmag = sinmag / scale_factor;cosmag = cosmag / scale_factor; mag = [sinmag(:) cosmag(:)];elseif use_fft %use built-in MATLAB fft() for speed fft_scale_factor = mytrapz(t, sin(2*pi*t).^2) * N / T;A = fft(y); mag(:,1) = -imag(A)/fft_scale_factor;mag(:,2) = real(A)/fft_scale_factor; mag = circshift(mag, half_N);end

Code for mysgram.m

% % function [stft_plot freq tm]= my_stft(y, dt, Nwindow) %% my_stft splits the signa 'y' into time windows, the breaks each % segment into its component frequencies. See "Short-time Fourier Transform"% %% Input: % y -- signal% dt -- sample interval % Nwindow -- number of time intervals to analyze% % Output:% stft_plot -- values plotted in the spectrogram % freq -- frequency domain% tm -- time domain function [stft_plot freq tm hh]= mysgram(y, dt, Nwindow) %count the number of windowsN = numel(y); win_len = floor(N/Nwindow);sm = zeros(win_len, Nwindow); cm = zeros(win_len, Nwindow);tm = linspace(0, numel(y) * dt, Nwindow); %for each windowfor n = 1:Nwindow %isolate the part of the signal we want to deal withsig_win = y((n-1)*win_len + 1 : n*win_len); %perform the fourier transform[freq mg] = myfourier(sig_win, dt, 1);sm(:,n) = mg(1:win_len,1); cm(:,n) = mg(1:win_len,2);end stft_plot = abs(sm + cm);stft_plot = stft_plot(end/2:end, :); %plot the fourier transform over timehh = imagesc(tm, freq(round(end/2):end), stft_plot); title('Spectrogram', 'FontSize', 20)xlabel('time', 'FontSize', 16) ylabel('frequency', 'FontSize', 16)set(gca, 'ydir', 'normal') %just look at lower frequenciesylim([0-win_len/2 50+win_len/2])

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
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
ya I also want to know the raman spectra
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
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
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.
Berger describes sociologists as concerned with
Mueller Reply
what is hormones?
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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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