how to convert the seismic wave data in Excel to fourier spectra

I want to convert the seismic wave data in the attached Excel file to the frequency [Hz] on the horizontal axis and the magnitude on the vertical axis by performing FFT in MATLAB. I'm sorry, but I'd appreciate your help.

Answer 1

[William Rose]

@Changhyun Kim

data=xlsread('GYEONGJU(MKL).xlsx');
N=length(data);
t=data(:,1);            %vector of times (s)
x=data(:,2);            %vector of x-values
dt=(t(end)-t(1))/(N-1); %sampling interval (s)
f=(0:N-1)/(N*dt);       %vector of frequencies (Hz)
X=fft(x);               %compute FFT(x)
%% Plot results
plot(f,abs(X))
xlabel('Frequency(Hz)'); ylabel('|X(f)|');
grid on

Try the above. As you can see, the FFT is symmetric about the Nyquist frequency, which is always half the sampling frequency . (Actually, the FFT of a real signal is conjugate symmetric about the Nyquist frequency, but we will ignore the phase for now.) Therefore it is common to plot only up to the Nyquist frequency.

[Changhyun Kim]

sorry. It seems my question was not correct.

[William Rose]

@Changhyun Kim, I think your question is fine. Add the command xlim([0,1/(2*dt)]); at the end, to limit the plot to the frequencies below the Nyquist frequency, and you have a nice plot of the magnitude of the FFT of the seismogram.

[Changhyun Kim]

actually, This was exactly the intent of my question.

So I realized that my question was wrong, so I corrected the question and re-posted it.

.

.

Given information

• Time domain signal file : GYEONGJU(MKL).xlsx (attached)
• Sampling rate (frequency): 100Hz
• Acceleration values in g (9.81m/s^2)

I want to convert the ground acceleration data in the attached Excel file to the frequency [Hz] on the horizontal axis and the magnitude on the vertical axis by performing FFT in MATLAB.

Also, it must plot only up to the Nyquist frequency. i.e 100sample(0~50Hz)

In addition, I need the Fourier Spectrum as raw data and the Fourier Spectrum filtered by performing FFT on 100sample seismic wave data with a 20Hz low-pass filter. In other words, I need the 100sample(filtered, 0~20Hz) Fourier Spectrum and the 100sample(raw,0~50Hz) Fourier Spectrum both.

[William Rose]

@Changhyun Kim,

I did answer the quesiton you posted here, so you could accept it, and should acept it, if you agree that I aswered it. You can consider my answer to your other qustion separately. Thank you.

[William Rose]

@Changhyun Kim,

I deleted the file GYEONGJU(MKL).xlsx from my comment, as you requested.