Does the DFT calculate spectral components up to half the sampling frequency, $f_s/2$?

1. What is sampling frequency in DFT?
2. How do you find the frequency of a DFT?
3. What is the result of DFT?
4. What is spectrum analysis using DFT?

What is sampling frequency in DFT?

Data are sampled discretely at a sampling frequency of 0.5 Hz. Starting at time t = 0, N = 4 data points are taken. Here, T = 8 s, Δt = T/N = (8 s)/4 = 2 s, and fs = 1/Δt = 0.5 Hz. The discrete data used to calculate the DFT are those at t = 0, 2, 4, and 6 seconds.

How do you find the frequency of a DFT?

calculate the magnitude of each DFT output bin: magnitude = sqrt(re*re+im*im) find the bin with the largest magnitude, call its index i_max . calculate the equivalent frequency of this bin: freq = i_max * Fs / N , here Fs = sample rate (Hz) and N = no of points in FFT.

What is the result of DFT?

In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency.

What is spectrum analysis using DFT?

The DFT can thus be used to exactly compute the relative values of the N line spectral components of the DTFT of any periodic discrete-time sequence with an integer-length period. negative frequencies due to the periodicity of the DTFT and the DFT.