how can I get fast Fourier transform of a signal from a continuous time ?

Hi,

first, do I need to discretize the signal and then get "fft" in MATLAB?

Or any suggestion?

thanks

[David Goodmanson]

Hi Adnan,

By 'continuous time' do you mean that you have the signal as a known function of t, such as sig = t.*exp(-t.^2) or whatever?

[ADNAN KIRAL]

Hi David,

I do have a ground motion which is an earthquake. I was wondering is that discretized ? do ı still need to discretize my ground motion ? if I directly use that in "fft", is that reasonable ?

I have used my ground motion in "fft" matlab, but the output is not making sense.

like;

FFTT=fft(ground_motion);

can you please tell me where the problem is.

cheers.

[David Goodmanson]

Hi Adnan,

Your ground motion is discretzed because you will have a file with data taken at discrete times. Analysis is easier if the time intervals are equally spaced, because then you can use the fft directly. To get the right answer you have to know the sampling rate, or equivalently the time interval between measurements (if they are equally spaced).

The data itself, velocity or whatever it is, is discretized in a different sense, because you only have so many bits to describe each data value. If each data point has has several decimal places then this is not a problem.

[ADNAN KIRAL]

Thanks David,

helped a lot, in your mail you said "Analysis is easier if the time intervals are equally spaced"

if i wanna make 0.01 sampling time in my data, which command should i use to make my signal having 0.01 sampling time to be able to use "fft" ?

thanks in advance

[David Goodmanson]

Is your data equally spaced already, and if it is do you know what the time interval is (or equivalently the sampling frequency)?

[ADNAN KIRAL]

I see, ok, the time is already spaced as 0.01 sec. So that I do not need to change anything, I will use in my "fft". Am I right?

Also, if you have a sinusoidal signal, do I need to discretise the data ? can I directly use that directly in "ff"?

let's say

k=1:0.1:30;

t=0:length(k);

y= sin(2*pi*f*t)

cheers, David.

[David Goodmanson]

I thought you had data already, so is what you are doing here just for example purposes, instead of using the actual data?

[Walter Roberson]

fft() does not know or care what the sample rate is provided that it is uniform . The interpretation of the output of fft does depend on the sample rate: the sample rate and the length together are used to calculate the frequency resolution of what was output from fft.

It is typically not desired to apply fft to the entire ground movement information because doing so would presume that the ground movement was acting uniformly during the entire recording time .It would be more common to assume that the waveform itself was changing over time .To analyse for that situation you would typically need aa short time Fourier transform which is known as stft . AA major MATLAB tool for that is spectrogram()

[ADNAN KIRAL]

thanks all of you for your kind replies. i see.

[ADNAN KIRAL]

thanks @David Goodmanson

I have already had the data. that question was just asked for additional information.

[David Goodmanson]

The code you have is the right idea, but not correct.

f0 = (whatever)
t = 0:.01:30;
y = sin(2*pi*f0*t);

will give you a signal that you can take the fft of. I used f0 instead of f so that the fixed frequency of the sine wave will not be confused with the frequency array that is associated with the output of fft. That frequency array is

fs = 1/.01;     % sampling frequency 100 Hz in this case
n = length(y);
f = ((0:n-1)/n)*fs;  

[ADNAN KIRAL]

I see, thanks @ David.