Digital Signal Processing Reference
In-Depth Information
Nyquist
Frequency
Sampling
Frequency
Frequency
Axis
Our signal should have a
frequency content only in
this area (below Nyquist)
to avoid aliasing effect
Figure 3.11. Nyquist Sampling
Rule.
twice the frequency of the signal
then the sampled signal will
represent the same frequency as the actual signal prior to
sampling. The critical frequency that the signal must never
exceed, which is one half of the sampling frequency, is called the
Nyquist
e
frequency (see Figure 3.11).
If we follow this rule, then we can avoid the aliasing
phenomenon we demonstrated with the moving wheel example
above. Normally, the ADC converter frequency is set high enough
to sample the signal upon which we want to perform digital signal
processing. To make sure that unwanted signals above the
Nyquist frequency do not get sampled and cause aliasing there
are two options:
The analog signal needs to be filtered through an analog low-
pass filter, which attenuates any unwanted high-frequency
content signals, just prior to the sampling.
The sampling speed is set at least twice as fast as the fastest-
changing components in the analog signal.
A common one-dimensional example is the telephone system.
Our voices are assumed to have a maximum frequency of about
3600 Hz. At the microphone, our voice is filtered by an analog
filter to eliminate, or at least substantially reduce, any frequencies
above 3600 Hz. Then the microphone signal is sampled at
8000 Hz, or 8 kHz. All subsequent digital signal processing occurs
on this 8 kSPS (kilo-samples per second) signal. That is why if you
hear music in the background while on the telephone, the music
will sound flat or distorted. Our ears can detect up to about
15 kHz frequency, and music generally has frequency content
exceeding 3600 Hz. But little of this higher frequency content will
pass through the telephone system.
