Types of sampling methods

Sampling refers to the process of converting a part of an input signal into various discrete electrical values for purposes of storage, processing and/or display. The extent of every sampled point is similar to the input signal’s amplitude at the exact time the signal is sampled.

Sampling is just like taking snapshots. A single snapshot represents a particular point in time on the waveform. To reconstruct the input signal, the snapshots can be organized in their respective order in time.

There are several sampling methods, namely, real-time sampling and equivalent-time sampling.

Suitable for signals with frequency range less than half the maximum sample rate of the oscilloscope, real-time sampling allows the oscilloscope to capture more than enough points in a single “sweep” of the waveform to form an accurate picture. It is the only way a digital oscilloscope can capture quick, single-shot, transient signals.

This sampling method provides the greatest challenge for digital oscilloscopes due to the sample rate required to accurately digitize high-frequency transient events. Occurring only once, these transient events must be sampled in similar time frame that they occur, with high-frequency components “folding-down” into lower frequency if the sample rate is not fast enough. Real-time sampling is also complicated by the high-speed memory needed to store the digitized waveform.

Real-time sampling with interpolation occurs when discrete samples of the signal are taken by the digital oscilloscope. Users will find it hard to visualize the signal, which is represented by dots, since there are only a few dots representing the signal’s high-frequency portions. To help users visualize the signals, digital oscilloscopes normally feature interpolation display modes. This mode connects the dots to provide an accurate display of the signal sampled for a few times.

In real-time sampling with interpolation, the oscilloscope gathers a few sample points of the signal in one pass in real-time and utilizes interpolation to fill in the gaps. A kind of process technique, interpolation is utilized to estimate the appearance of the waveform based on a few points.

Connecting sample points with straight lines, linear interpolation is restricted to reconstructing straight-edged signals. The more flexible sin x/x interpolation connects curves with sample points. A mathematical process used to calculate the points to fill in the period among the real samples, sin x/x interpolation lends itself to irregular and curved signal shapes that are more common than pulses and square waves. Thus, sin x/x is the preferred method for applications with sample rate three to five times the system bandwidth.

Meanwhile, equivalent-time sampling is used when measuring high-frequency signals that cannot be collected by the oscilloscope in a single sweep. It is also utilized to accurately acquire signals whose frequency is more than half of the oscilloscope’s sample rate.

Taking advantage of the fact that most man-made and naturally occurring events are repetitive, equivalent-time digitizers (samplers) forms a picture of repetitive signal by acquiring a bit of information from every repetition. The waveform gradually builds up like a series of lights, illuminating one-by-one. This enables the oscilloscope to capture signals with frequency components higher than the sample rate of the oscilloscope.

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