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Douglas C. Smith

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Technical Tidbit - August 2003
Sin(x)/x, the Forgotten Setting - Part One

  Acquisition dialog box
Figure 1. Acquisition Setup for Scope

Abstract: Digitizing oscilloscopes have many settings that affect the accuracy of measurements. One of these settings is Sin(x)/x interpolation. The effect of this setting on the display is discussed. For many measurements, this feature should be disabled.

Discussion: Figure 1 shows the menu for signal acquisition in an Agilent 54845a digitizing oscilloscope.  The Sin(x)/x interpolation option is easy to overlook. Sin(x)/x interpolation is used to smooth a digital waveform display. Often the waveform is more pleasing to look at with this interpolation enabled, but it can hide the fact that a single shot waveform may not be displayed accurately.

Figure 2 shows a waveform displayed with Sin(x)/x interpolation enabled. Notice that the time scale is 500 ps/div and yet the sample rate (displayed in the upper left above the waveform) is only 2 GSa/sec (gigasamples/second). The scope is capable of much faster sampling, but for this example the sampling rate has been slowed down to a rate similar to many digitizing scopes now in use.  A sampling rate of 2 GSa/sec yields a sample every 500 ps so there is only one sample per horizontal division of the display, but one would never guess this to be the case from the smooth waveform in Figure 2.


waveform with sin(x)/x on
Figure 2. Waveform With Sin(x)/x On
(500 ps/div)

Figure 3 shows the same waveform with Sin(x)/x interpolation turned off. There is quite a difference compared to Figure 2. The individual samples, one per horizontal division, can be seen connected by straight lines. The sharp corners in the waveform show that the sampling rate is not nearly fast enough to properly display this waveform. In fact, it cannot be known what happens to the waveform between samples. The waveform could (and does, in this case) contain oscillations between the samples that cannot be seen. This effect of under sampling is often called aliasing and the waveform is referred to as aliased.

waveform with Sin(x)/x off
Figure 3. Waveform With Sin(x)/x Off
(500 ps/div)

For many uses, I prefer to disable Sin(x)/x interpolation to avoid hiding sampling problems such as shown above. This is especially important as many forms of EMI, like electrostatic discharge, can produce very fast waveforms and signals on circuit boards get faster with each new generation of hardware.

Summary and Conclusion: Use of Sin(x)/x interpolation can hide the fact that the sampling rate used is not fast enough to display a waveform. In many cases, it should be disabled to insure an accurate measurement.

Equipment used in this article include:

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Copyright © 2003 Douglas C. Smith