2.1 Dsp00104-sampled time series  (Page 10/10)

Illustrates the folding frequency

Hopefully this illustration will make the concept of the folding frequency easier for you to understand. The folding frequency is one-half the samplingfrequency. The entire spectrum below the folding frequency folds around the folding frequency and the peaks in that spectrum appear in mirror-image formatabove the folding frequency.

The frequency information for all frequency components above the folding frequency is lost when the signal is sampled. In addition, the energy associatedwith those components will fold around and can corrupt the information for frequency components that are below the folding frequency.

The bottom line

The bottom line is that you must be very careful when sampling analog signals for later processing using DSP. In order to avoid erroneous results, you mustsample sufficiently fast to ensure that your sampling rate is greater than twicethe highest frequency components contained in the analog signal.

On the other hand, the greater your sampling rate, the more computer-intensive will be most of the DSP techniques that you apply to the datalater. For economy reasons, therefore, you don't want your sampling frequency to be excessively high.

Using an analog low-pass pre-filter

A common approach to sampling is to feed the analog signal into an analog-to-digital (AtoD) converter. This is a device that measures the amplitude of the analog signal at a uniform sampling frequency. It is commonpractice to place a low-pass analog filter immediately ahead of the converter to suppress any analog frequency components that are greater than one-half thesampling frequency.

Digital re-sampling

Another common approach is to initially sample the analog signal at a sufficiently high rate to ensure that the sampling rate is greater than twicethe highest frequency contained in the analog signal. Then, if you really don't need all of that high-frequency information, you can apply a low-pass digitalfilter to suppress the high-frequency energy. Then you can re-sample the data to a lower sampling frequency simply by discarding samples. The data with the lowersampling frequency can then be used for further DSP analysis.

Summary

I explained the meaning of sampling, and explained some of the problems that arise when sampling and processing analog signals.

The problems generally relate to the relationship between the sampling frequency and the high-frequency components contained in the analog signal.

I explained the concept of the Nyquist folding frequency, which is half the sampling frequency.

I illustrated the frequency folding phenomena by plotting sampled time series data as well as spectral data.

Miscellaneous

This section contains a variety of miscellaneous information.

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