What is FFT frequency spectrum?

The frequency resolution is just the sample frequency divided by the number of samples (which is also the number of steps in the DFT sine table). If we have a sample rate of 10240 Hz for our 1024 samples, for instance, we will get 10 Hz resolution.

For the DFT, the resolution is equal to f s/N , from Equation 4.8. So, for a given sampling frequency, the more samples (N) in the signal, the smaller the frequency increment between successive DFT data points. The more points sampled, the higher the spectral resolution.

The spectrum is the basic measurement of an FFT analyzer . It is simply the complex FFT. Normally, the magnitude of the spectrum is displayed. The magnitude is the square root of the FFT times its complex conjugate. (Square root of the sum of the real (sine) part squared and the imaginary (cosine) part squared.)

The frequency resolution of each spectral line is equal to the Sampling Rate divided by the FFT size . For instance, if the FFT size is 1024 and the Sampling Rate is 8192, the resolution of each spectral line will be: 8192 / 1024 = 8 Hz.