- 2.1 Implicit Sampling Techniques
- 2.2 Explicit Sampling Techniques
- Reference
This chapter is from the book
This chapter is from the book
This chapter is from the book
2.2 Explicit Sampling Techniques
Unlike implict sampling, in which samples are triggered by some aspect of signal behavior, in explicit sampling, signal values are measured at specified times without regard to the signal's behavior. Consider the continuous-time sinusoidal signal and its two-sided magnitude spectrum depicted in Figure 2.1. There are three explicit sampling techniques—natural sampling, instantaneous sampling, and ideal sampling—that can be used to sample such a signal. The results produced by these techniques, and the corresponding impacts on the signal's spectrum are compared in Key Concept 2.1.
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Figure 2.1 Continuous-time sinusoid and its two-sided magnitude spectrum
Ideal Sampling
As depicted in Key Concept 2.1, zero-width samples take on instantaneous values of the analog signal. Neglecting quantization and timing errors, the sequence of values produced by an analog-to-digital converter can be modeled as the output of an ideal sampling process. Ideal sampling is discussed further in Note 3.
Natural Sampling
Nonzero-width samples have time-varying amplitudes that follow the contours of the analog signal, as shown in Key Concept 2.1. Commutator systems for time-division multiplexing of telegraph signals, first proposed in 1848, used an approximation to natural sampling. The sample pulses were created by gating a signal with rotating mechanical contacts. This multiplexing technique was subsequently applied to telephone signals in 1891. It was the application of natural sampling to telephony that first led to consideration of just how rapidly a continuous-time signal needed to be sampled in order to preserve fidelity and ensure the ability to reconstruct exactly the original, unsampled signal. Natural sampling is explored further in Note 6.
Instantaneous Sampling
In instantaneous sampling, nonzero-width samples each have a constant amplitude that corresponds to the instantaneous value of the analog signal at the beginning of the sample. The sample values are held constant long enough to create flat-topped sample pulses. The output of a digital-to-analog converter (DAC) can be modeled as the output of an instantaneous sampling process, often as the limiting case in which the sample width equals the sampling interval. As discussed in Note 7, the results of the instantaneous sampling model play a key role in the specification of the analog filter used to smooth the DAC output.
Key Concept 2.1. Explicit Sampling Techniques
Ideal Sampling
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Instantaneous Sampling
Natural Sampling
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