FFT-based[edit]
With an FFT based spectrum analyzer, the frequency resolution is Δ ν = 1 / T {displaystyle Delta
u =1/T} , the inverse of the time T over which the waveform is measured and Fourier transformed.
With Fourier transform analysis in a digital spectrum analyzer, it is necessary to sample the input signal with a sampling frequency ν s {displaystyle
u _{s}} that is at least twice the bandwidth of the signal, due to the Nyquist limit.[5] A Fourier transform will then produce a spectrum containing all frequencies from zero to ν s / 2 {displaystyle
u _{s}/2} . This can place considerable demands on the required analog-to-digital converter and processing power for the Fourier transform, making FFT based spectrum analyzers limited in frequency range.