How can I get the central frequency out of a fft?

For an analysis I have the following script. Everything is fine and working. My Prof now wants to know the central frequeny out of the fft.

How di I get the central frequency?

Fs= 1.9* 10^6 ; %sampling frequency
T = 1/Fs; %sampling period
L = 15000 ; %time in ms
t= (0: L-1) * T; %time vector

% load holz.mat

ti= fliese90cm.time;
a= fliese90cm.ampli;

plot(ti,a)
y=fft(a);
P2 = abs( y /L );
P1 = P2 (1: L /2+1);
P1(2: end-1)=2*P1(2:end-1);

f = Fs*(0:(L/2))/L;

plot(f,P1)
xlim([0 2*10^5])
title ( 'FFT Fliese, 100 cm')
xlabel('Frequency [Hz]')
ylabel('Amplitude [V]')
% stem(f,P1)
Q=trapz(f,P1);

[dpb]

Some observations...

L = 15000 ; %time in ms
t= (0: L-1) * T; %time vector

You comment that L is time in ms, but have used L as in the example from the documentation for FFT as the length of the signal. Those two are imcompatible---the time record will be something like 7.89 msec based on your computed vector t.

The actual signal length of the data collection and sampling rate will determine the actual time...

ti= fliese90cm.time;
a= fliese90cm.ampli;
...

The structure/table/timetable(?) flies90cm is not defined in the script...that makes very fragile...

Those comments aside, regarding the subject question, I guess the first question to answer is what does the prof mean by "central" frequency?

It's used to describe the midpoint of a bandpass filter as between upper/lower frequency cutoff points and various other ways, but just as a general term without context, "I dunno!".

[Image Analyst]

Isn't the central frequency at index 1, and the value there is y(1)? That's the zero frequency location and will be in the center once you use fftshift() on it. Or do you mean something completely different?

[Leo Dokoza]

In the picture you can see what i mean by center frequeny. It was false translated so the true word is center frequency. It ts the square root of the product of frequency index 1 and frequency index 2 or index low and high.

On this basis it would be also helpful to get to know how do I get frequency index 1 and frequency index 2.

[Image Analyst]

OK, so it's the center frequency of the spectrum signal within some particular frequency band. And is defined by the geometric mean of the starting frequency and ending frequency of that particular band.

So I guess you have the spectrum, and now you're needing to find the starting and ending frequency of some "hump" you see in the spectrum, right?

Did you see the answers below?

[Leo Dokoza]

Correct. After an analysis of some objects I have now different frequency spectrums. With the answers here I consider to take the max. and min. values of my spectrum and with them to calculate the center frequency

Answer 1

[Star Strider]

Not possible to run your code.

One option is to use islocalmax, specifically using 'FlatSelection','center'.

[dpb]

Or, alternatively, findpeaks optional 'widths' output with the 'WidthReference','halfheight' input named parameter option.

ADDENDUM:

Actually, findpeaks isn't as helpful as could be -- it returns the widths but not the locations of the reference-level crossings. There was another thread just a week or so ago on same issue--I showed there how to find the points.