7. Sampling Theory#
In this chapter we seek a deeper understanding of the theory behind digital audio sampling, and its practical consequences. Back in Chapter 1, we converted analog sound to digital audio in the time domain, through sampling and quantization. Since then we have gained crucial context about the frequency domain: in Chapter 5 we developed the Fourier transform, and in Chapter 6 we uncovered the negative frequencies that lurk behind every positive one.
Armed with these tools, we can now study sampling from the perspective of the frequency domain. Our goal is to understand the theory of sampling well enough to make principled choices about how to sample for a given audio application. Along the way we will answer three questions:
What, if anything, do we lose when we sample a sound?
Can we sample in a way that permits perfect reconstruction of the original sound?
What sample rates and bit depths should we actually use?