AN4173

Application code structure

Doc ID 023727 Rev 3

17/22

3.4.1

Degradation of the signal acquisition

When the sampling frequency is choosen only 2 times higher than the frequency of the input

signal, as Nyquist-Shannon’s sampling theorem suggests, the process of reconstruction of

the acquired signal is guaranteed but not perfectly.

Indeed the sampling theorem provides only a sufficient condition but not a necessary one

for a perfect reconstruction.

The condition is that the signal obtained from this reconstruction process cannot have any

frequencies higher than one-half the sampling frequency. According to the theorem, the

reconstructed signal will match the original one provided if the original signal contains no

frequencies at or above this limit. This condition is called the Nyquist criterion.

if the condition is not satisfied, the resulting reconstructed signal may have a component at

the frequency, but the amplitude and phase of the component generally will not match the

original one.

The Figure 8 shows the acquired sinusoidal signal using a sampling frequency only 2 times

higher than the frequency of the input signal:

Figure 8.

Reconstructed signal at 10 Khz with sampling frequency 20Khz

In this case the reconstructed signal in red cannot be considered a perfect copy of the

original input signal in green.

The Figure 9 shows a correct acquisition using a sampling frequency 10 times higher than

the input signal.