How i can determine sinusoid frequency ?

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Muna Shehan
Muna Shehan 2017-4-1
评论： Star Strider 2017-4-6
Hi; Pleas can anyone explain how i can determine sinusoid frequency if I have a step response where the data form is two vectors one for the acceleration and the other is time, when i transfer the plot from time domain to frequency domain i use fft; however i am confused how i can specify f0 when i read
http://blogs.mathworks.com/steve/2014/09/23/sinusoids-and-fft-frequency-bins/
I will appreciated for any explanation. Thanks in advance

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Star Strider
Star Strider 2017-4-1
编辑：Star Strider 2017-4-2
It could be difficult to get a dominant peak with the signal you posted, since it could be a heterodyne of several frequencies. You will have to take the fft (link) of your signal and use your judgement.
It will be easier if you subtract the mean of the time-domain signal before you take the fft (link). This will eliminate the ‘0 Hz’ peak.
EDIT — 01:48 UCT 2017 04 02
The true resonant frequencies of your system are determined by the eigenvalues of your ‘A’ matrix. For your simulation, they appear to be the eigenvalues of:
Aqcar = [0 1 0 0;-kus/mus -c/mus k/mus c/mus;0 -1 0 1;0 c/ms -k/ms -c/ms];
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Muna Shehan
Muna Shehan 2017-4-6
Thanks again . I mean the code that I posted to Image Analysis's Answer.

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Image Analyst
Image Analyst 2017-4-1
Subtract the mean and take the fft using fft() or pwelch(). Then scan it and look for the max magnitude. You didn't supply data so I can't do much other than speculate some code:
spectrum = fft(yourSignal - mean(yourSignal));
[maxValue, indexOfMaxValue] = max(abs(spectrum));
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Muna Shehan
Muna Shehan 2017-4-1
Thanks for your reply. I have posted the code. I have the dynamic response (Acc.) in time domain for the dynamic system ( quarter car suspension system). Now, I try to transfer this response (Acc.) to frequency domain. How I can do it correctly by using fft?. So far I used the fft example.
https://www.mathworks.com/help/matlab/ref/fft.html I appreciated for any help to transfer my signal from time domain to frequency domain.
ms = 325; % 1/4 sprung mass (kg)
mus = 65; % 1/4 unsprung mass (kg)
kus = 232.5e3; % tire stiffness (N/m)
grav = 9.81; % acceleration of gravity (m/s^2)
v = 12.5; % vehicle velocity (m/s)
dt = 0.001; % simulation time step
% Road profile
sinbump = @(L,A) A*(0.5+0.5*(sin(linspace(-pi/2,pi*3/2,25*L))));
B2 = sinbump(12, 0.10);
road_x=linspace(0,99.99,600);
road_z(1:300)=B2;
road_z(301:600)=0;
% Simulation time
tmax = 5;
x_time = 0:dt:tmax;
dx = road_x(2) - road_x(1); % spacial step for input data
z0dot = [0 diff(road_z)/dt]; % road profile velocity
k=15024.9;
c=1568.2;
dt2 = dx/v; % time step for input data
x = v*x_time; % time/space steps to record output
% Construct linear state space model
Aqcar = [0 1 0 0;-kus/mus -c/mus k/mus c/mus;0 -1 0 1;0 c/ms -k/ms -c/ms];
Bqcar = [-1 0 0 0]'; Cqcar = [1 0 0 0; 0 1 0 0; 0 0 1 0; 0 0 0 1; 0 -1 0 1];
Dqcar = 0;
qcar = ss(Aqcar,Bqcar,Cqcar,Dqcar);
x0 = [0 0 0 0]'; % initial state
uu = interp1(road_x,z0dot,x);umf=1; % prepare simulation input
% Simulate quarter car model
y = lsim(qcar,uu*umf,x_time,x0);
Acc1 = [0 diff(y(:,4))'/dt2]; % sprung mass acceleration
%Time domain plot
figure(1);
plot(x_time,Acc1);
xlabel('Time (sec)','fontsize',14);
ylabel('Acceleration (m/s^2)','fontsize',14);
title({'Sprung mass response to a 0.1 m high step','Vehicle velocity = 45 km, Ks = 15024.9 N/m^{2}, Cs=1568.2 Ns/m'})
%Frequency domain analysis
Fs=1/dt;
Lenght = size(x_time,2);
NFFT = 2^nextpow2(Lenght(1,1)-1); % Next power of 2 from length of b
Y1 = fft(Acc1,NFFT)/(Lenght(1,1)-1);%Y_FREQ = fft(y_time,N2)*T
f = Fs/2*linspace(0,1,NFFT/2+1);
yPower1 = 2*abs(Y1(1:NFFT/2+1)); %magnitude
ydB1 = 20*log10(abs(Y1(1:NFFT/2+1))); %power
spectrum = fft(Y1 - mean(Y1));
[maxValue, indexOfMaxValue] = max(abs(spectrum));
figure(2);
plot(f,yPower1);
set(gca, 'XLim',[0 30])
xlabel('Frequency (Hz)','fontsize',14)
ylabel('Acc.','fontsize',14)
figure(3);
plot(f,ydB1);
xlabel('Frequency (Hz)','fontsize',14)
ylabel('Power (dB)','fontsize',14)

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