How to Analyze the Frequency Content of a Signal
Author: John M. Cimbala, Penn State University
Latest revision: 11 October 2007
When the frequency content of a signal is
, or at least
, it is easy to choose the
sampling frequency – we choose a sampling frequency larger than twice the maximum expected frequency of
the signal (using the Nyquist criterion).
In this learning module, we discuss what to do in situations in which the frequency content of a signal is
(as in many typical laboratory situations). In particular,
how then can we avoid aliasing errors
Apply a low-pass (anti-aliasing) filter
The best way to eliminate aliasing errors entirely is to
taking the digital data.
In particular, a
is used; thus, a low-pass filter is often called an
Here is how this anti-aliasing-filter technique works:
A low-pass filter lets low frequency components of the signal
through (that’s why it is called a
“low-pass” filter), but cuts off frequency components above some specified
ideal low-pass filter
cuts off the high frequency content of the signal –
all content of the
signal at frequencies greater than the cutoff frequency is removed
Ideally then, the cutoff frequency of the ideal low-pass filter is set to one-half of the sampling
frequency to avoid aliasing,
/2 (following the Nyquist criterion).
all frequencies that would have produced aliasing errors are removed from the signal
before the digital data are sampled, and therefore no aliasing is possible
Unfortunately, real-life low-pass filters do not cut off high frequencies abruptly; instead, the attenuation
of higher frequencies falls off rather slowly with frequency.
Because of this, most real-life data acquisition systems employ a cutoff frequency
several times smaller
than the sampling frequency to ensure proper anti-aliasing.
Low-pass filters are discussed in more detail in another learning module.
Sample at different sampling frequencies
Even without a low-pass anti-aliasing filter, we are often able to analyze the frequency content of the signal
sampling at several different sampling frequencies, and comparing the corresponding frequency spectra
If we sample at two different sampling frequencies, and the peaks in the frequency spectra
frequencies, we can be sure that aliasing errors are occurring
In this case,
the sampling frequency must be continually increased until the peaks in the spectra
the aliased peaks can be consistently explained
. An example is provided below.
In many practical applications, such as measurement of turbulent fluctuations in a fluid flow, there are