Notes on Digital Signal Processing: Practical Recipes for Design, Analysis and Implementation

Note 6. Natural Sampling

In natural sampling, an analog signal is gated in such a way that the resulting signal consists of pulses with time-varying amplitudes that follow the contours of the original waveform as shown in Figure 6.1. In this example, the original signal is a sinusoid with a period of T_x, and the sampled signal has a sampling interval of T, and a sample width of τ. Natural sampling is mathematically equivalent to multiplying the original signal with a train of unit-amplitude rectangular sampling pulses. Therefore, the spectrum of a naturally sampled signal can be determined by convolving the original signal’s spectrum with the spectrum of the train of sampling pulses.

Figure 6.1. In natural samping, the amplitudes of the sample ...