Frequency_Content_of_Signal

# Frequency_Content_of_Signal - How to Analyze the Frequency...

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How to Analyze the Frequency Content of a Signal Author: John M. Cimbala, Penn State University Latest revision: 11 October 2007 Introduction When the frequency content of a signal is known , or at least approximately known , 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 unknown (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 filter the signal before taking the digital data. o In particular, a low-pass filter is used; thus, a low-pass filter is often called an anti-aliasing filter . o Here is how this anti-aliasing-filter technique works: ± A low-pass filter lets low frequency components of the signal pass through (that’s why it is called a “low-pass” filter), but cuts off frequency components above some specified cutoff frequency . ± An ideal low-pass filter abruptly 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, f cutoff = f s /2 (following the Nyquist criterion). ± That way, 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 . o 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. o 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 by sampling at several different sampling frequencies, and comparing the corresponding frequency spectra . o Principle : If we sample at two different sampling frequencies, and the peaks in the frequency spectra appear at different frequencies, we can be sure that aliasing errors are occurring . o In this case, the sampling frequency must be continually increased until the peaks in the spectra do not change , and 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

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## This note was uploaded on 07/23/2008 for the course ME 345 taught by Professor Staff during the Spring '08 term at Penn State.

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Frequency_Content_of_Signal - How to Analyze the Frequency...

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