2.5 Summary

Before closing this section, let’s repeat the two main points in this section:

  1. The highest frequency observed in digital data is the Nyquist frequency given by fN = 1/2Dt (or 1/2Dx); signals with frequencies above fN end up being aliased (folded) into lower frequencies.

  2. The frequencies resolved in finite-length, digital time domain data of length T are 0, 1/T, 2/T, …, 1/2Dt (or 0, 1/Lx, 2/Lx,…, 1/2Dx for space domain data of length Lx).

These points are so fundamental, so important, in digital recording that we will repeat them "in other words":

These points are so fundamental, so important, in digital recording that we will repeat them "in other words"…

  1. The sampling interval Dt (or Dx) determines the highest frequency recorded, 1/2Dt (or 1/2Dx) and the degree of aliasing at all recorded frequencies.

  2. The length of data recorded (T or Lx) determines the lowest frequency recorded, (1/T or 1/Lx) which is also the frequency resolution Df or Dfx in digital spectra.

We have characterized the two operations leading to these conclusions as multiplications in the time or space domains by Dirac combs or boxcar functions, respectively. These descriptions will allow very nice proofs of the conclusions above once we have a little more mathematical machinery. You'll see; we promise.