Baseband Analysis

Baseband analysis involves applying the FFT to each component of a time-domain signal from the minimum resolvable frequency, 0, to the maximum resolvable frequency.

The sampled time waveform input to an FFT determines the computed spectrum. If an arbitrary signal is sampled at a rate equal to f sover an acquisition time T, N samples are acquired. Compute T with the following equation:

T = N f s

where

T is the acquisition time

N is the number of samples acquired

f s is the sampling frequency

Compute N with the following equation:

N = T ⋅ f s

For FFT, the spectrum computed from the sampled signal has a frequency resolution df. Calculate the frequency resolution with the following equation:

d f = 1 T = f s N
Note The frequency resolution is determined solely by the acquisition time. The frequency resolution improves as the acquisition time increases.

The resolution bandwidth (RBW) is an additional property that describes the minimum frequency spacing required to distinguish between two closely spaced frequency components. The following equation defines RBW:

R B W = d f ⋅ E N B W

where ENBW is the equivalent noise bandwidth.

You often apply a window to the time-domain signal prior to the FFT. A key parameter of the window is the ENBW.

The sampling rate of a time waveform determines the maximum resolvable frequency. According to the Shannon Sampling Theorem, the maximum resolvable frequency must be half the sampling frequency. To calculate the maximum resolvable frequency, use the following equation:

f max ⁡ = f N y q u i s t = f s 2

where

f max is the maximum resolvable frequency

f Nyquist is the Nyquist frequency

f s is the sampling frequency

The minimum resolvable frequency is 0 (DC). The analysis from 0 to fNyquist is the baseband analysis.