Hi,

i am not sure if i understand right, but if you use common DFT implementations the coefficents with low indices will belong to the low frequencies (you just might have to consider that the spectrum of a real valued function is symmetric in frequency domain, i.e. even the highest indices belong to low frequencies if your implementation outputs the symmetric spectrum; however, the information of the upper half of indices is redundant).

Off course you have to take care that the time interval has sufficient length in order to analyze low frequencies adequately.

Greetings, Sebastian

Hi,

you might need to use a window (e.g. hamming window) in time domain, especially for short signals as the fourier transform only works perfectly fine for infinte periodic signals, which can be decomposed into sin-waves. Sharply cutting the signal at the beginning and the end will introduce errors. Furthermore, you can use zero-padding to artificially improve frequency resolution (especially required for shorter signals), but on the downside you will have to deal with artefacts introduced by this method. Finally you can eliminate a high DC component by mean-adjustment of the time-domain data.

The result of the DFT/FFT in usually complex. To calculate the ampitude spectrum you need the absolute value of the complex inices (mostly devided by the length of the time-domain data, depending on the algorithm).

Example from MATLAB:

Compute DFT or FFT:

Y = fft(X)

Compute two-sided spectrum P2 (L ist the length of X):

P2 = abs(Y/L)

Compute one-sided spectrum P1 (as Sebastian explained, the second half of P2 is redundant):

P1 = P2(1:L/2+1)

P1(2:end-1) = 2*P1(2:end-1)

Calculate the frequency axis values:

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

Plot the amplitude spectrum:

plot(f,P1)

This example is based on the MATLAB implementation of FFT. In some other implementations might not need to devide by L.

Best regards,

Daniel

Reference: https://de.mathworks.com/help/matlab/ref/fft.html

Hello Muhamad,

check the attached document.  it will be useful if you uses matlab

What means low frequency depends strongly on the type of signal analyzed. In any case, the use of DFT is often associated with the discretization of a signal via the sampling theorem. In these cases, the fundamental relation f [n] F [k] must be formulated in terms of the frequencies of the sampled signal: f [nTs] F [k / nTs] where Ts = 1 / Fs the Nyquist rate, fs = 1 / 2fm (fm is the highest frequency present in the analyzed signal).

Thus, when adopting a DFT of length N, the lowest frequency discriminated is 1 / NTs = 2fm / N. The initial components of the DFT, associated with the values of V0, V1, V2, ... estimate the frequency content in multiples of Delta = 2fm / N Hertz, i.e., the components dc, Delta, 2Delta, 3Delta ...