how to convert pressure versus time to pressure versus frequency using fft function

I have tried to convert pressure versus time data to pressure versus frequency using FFT function

This is the pressure versus time signal

after using fft

deltaT=2.5e-6;
fs=1/deltaT;
pxx0 = fft(p);
n = length(p);         % number of samples
f = (0:n-1)*(fs/n);   % frequency range
mag=abs(pxx0);
figure(1)
semilogx(f,mag)
ylabel ('magnitude');
xlabel ('frequency');

This is the output of FFT function

How to convert the magnitude of FFT to corresponding pressure value like this graph ? in form of pressure versus frequency

[BALAJI KARTHEEK]

u should scale the pressure and frequency axis to get what u wanted for i need the pressure data or i can given an of how to convert the pressure and frequency axis. Good luck. if you want any help you can free to contact me

%T18EE009 D J K S S BALAJI
%DETERMINE THE MAGNITUDE OF FUNDAMENTAL SIGNAL OF SINUSODIAL AFTER USING FOURIER TRANSFORM
%INPUT DATA
clc
clear all
f=50;%frequency
FM=50;%FREQUENCY TO OBTAINED
T=0.2;%TIME OF THE SIGNAL
N=1024;%NO OF SAMPLES
S=0.02/N;%SAMPLE TIME
fs=1/S;%SAMPLING FREQUENCY
t=0:S:T-S;%timeinterval
O=30*(pi/180);%phase angle
X=200;%MAGNITUDE
for j=1:N*(T/0.02)
    x1(1,j)=0;
end
for k=1:20
    A=(X/k)*sin((2*3.141*k*t*f)+(O));%CREATION OF HARMONICS
    x1=A+x1;
end
t1=1;
t2=0;
for i1=1:(T/0.02)
for i=t1:t1+N-1
    A(1,i-t2)=x1(1,i);
end
y=fft(A);%APPLYING FFT
c=abs(y);%CONVERTING COMPLEX VALUES TO ABSOLUTE VALUES
Q=2*c/N;%CONVERSION OF SAMPLING DOMAIN TO MAGNITUDE DOMAIN
B1=(FM*N/fs)+1;%OBTAINING THE FUNDAMENTAL FREUENCY FROM BINS
op(i1)=Q(1,B1);%OBTAINING FUNDAMENTAL MAGNITUDE FROM FFT
ph(i1)=angle(y(1,B1))*(180/pi)+90;
t1=t1+N;
t2=t2+N;
end
t5=0.02:0.02:0.2;
yyaxis left
plot(t5,op)
yyaxis right
plot(t5,ph,'--')

[zein]

I do not understand your answer?in my case if i got the results as magnitude domain, how can i convert it to pressure?

Answer 1

[Mehmed Saad]

• set xlim between 30 and 1e6
• set you xtick as [30 300 3e3 3e4 3e5]
• turn off xMinorTick
• turn off xMinorGrid
• turn on grid
• change linewidth to 1.5

Although it looks like window is also applied on the pressure data and fft size is also greater than the size of signal (next2pow is used)

[zein]

the x-axis is in log scale

[Mehmed Saad]

see the updated answer

[zein]

it is related to editing?i am asking about converting the p(f) to corresponding pressure value?

so i was expecting to have at frequency of 100 Hz, pressure magnitude of 0.752 like the last figure, i mentioned.

t=2.5e-6:2.5e-6:0.2;%time 
R=0.1;% radius of sphere
f=100;% freq. of velocity
u0=0.01;%amplitude of velocity
U=u0.*sin(2*pi*f.*t);%velocity
c=100;% sonic speed
rho=14.1855;%density
w=2*pi*f;
k=w/c;
r=1;%location of reciever

A=(-1i*w*rho*u0*R^2)/(r*(1-1i*k*R));
p=A*exp(1i*(r-R));
pmag=abs(p);
pReal=real(pmag.*exp(-1i.*(w.*t-65*pi/180)));
pReal=pReal';
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%plotting%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
figure(1);
%plot(t,pReal,'r',t1,p1,'k')
plot(t,pReal,'r');
xlabel('time (sec)');
ylabel ('pressure (N/m^2)');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%FFT%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

deltaT=2.5e-6;
Fs=1/deltaT;
L = length(pReal);          % number of samples
n = 2^nextpow2(L);
Y = fft(pReal,n);
f = Fs*(0:(n/2))/n;
Pp = abs(Y/n);

figure(2)
semilogx(f,Pp(1:n/2+1))
ylabel ('magnitude');
xlabel ('frequency');

[Mehmed Saad]

deltaT=2.5e-6;
Fs=1/deltaT;
L = length(pReal);          % number of samples
n = 2^nextpow2(L);
Y = fft(pReal,n);
f = Fs*(1:n)/n;
Pp = abs(Y/L*2);

figure(2)
semilogx(f,Pp,'LineWidth',1.5)
xlim([30 1e6])
grid on
a = gca;
a.XTick=[30 300 3e3 3e4 3e5];
a.XMinorGrid = 'off';
a.XMinorTick = 'off';
ylabel ('magnitude');
xlabel ('frequency');

[zein]

Thanks a lot for your help.

I have run it and i got the same results you post, but i want to ask you a question

why the peak value if i change the time 0:2.5*e-6:0.1? instead of 0:2.5e-6:0.2

[Mehmed Saad]

n = 2^nextpow2(L)*2;

[zein]

how you change the equations for n and Pp ?

Is there any reference? i do not know how you adjust these equation to give the correct results?

I do not understand how you modify them?

[Mehmed Saad]

fs = 1000;
t = 0:1/fs:1-1/fs;
s = exp(2j*pi*10*t);
L = length(s);
n = 2^nextpow2(L);
Y = fft(s,n);
Pp = abs(Y)/L;

figure,plot(Pp)
s = real(s);
Y = fft(s,n);
Pp = abs(Y)/L;
figure,plot(Pp)

Pp = abs(Y)/L*2; % because we take fft of real componnet only
figure,plot(Pp)