Aliasing - TiePie Handyscope HS5 series User Manual

The sampling frequency must be higher than 2 times the highest frequency in the
input signal. This is called the Nyquist frequency. Theoretically it is possible to
reconstruct the input signal with more than 2 samples per period. In practice,
10 to 20 samples per period are recommended to be able to examine the signal
thoroughly.
3.2.1

Aliasing

When sampling an analog signal with a certain sampling frequency, signals appear
in the output with frequencies equal to the sum and difference of the signal fre-
quency and multiples of the sampling frequency. For example, when the sampling
frequency is 1000 Hz and the signal frequency is 1250 Hz, the following signal fre-
quencies will be present in the output data:
Multiple of sampling frequency
...
-1000
0
1000
2000
...
As stated before, when sampling a signal, only frequencies lower than half the
sampling frequency can be reconstructed. In this case the sampling frequency is
1000 Hz, so we can we only observe signals with a frequency ranging from 0 to 500
Hz. This means that from the resulting frequencies in the table, we can only see
the 250 Hz signal in the sampled data. This signal is called an alias of the original
signal.
If the sampling frequency is lower than twice the frequency of the input signal,
aliasing will occur. The following illustration shows what happens.
8
Chapter 3
Figure 3.3: The effect of the sampling frequency
-1000 + 1250 = 250
0 + 1250 = 1250
1000 + 1250 = 2250
2000 + 1250 = 3250
Table 3.4: Aliasing
1250 Hz signal
-1000 - 1250 = -2250
1000 - 1250 = -250
2000 - 1250 =
-1250 Hz signal
0 - 1250 = -1250
750