Sampling and Digitization

Fourier Analysis · Axiom Academy

INTRO Sampling and Digitization Discover how we convert the continuous world into digital information. Step 1: From Analog to Digital Every digital device must convert continuous signals into discrete numbers. Let's see this transformation in action. Adjust the sampling rate and watch how it affects our ability to capture the signal. Step 3: What Gets Lost, What Gets Saved? Compare different sampling rates to understand information preservation. Understanding the mathematical relationship between sampling interval and sample rate. The time between consecutive samples. If we sample every 0.1 seconds, then Ts = 0.1 s. The number of samples taken per second, measured in Hertz (Hz). This is the reciprocal of the sampling interval. The Big Picture: Why Sampling Rate Matters The critical importance of choosing the right sample rate. If you sample too slowly, you miss critical features of the signal. A 2 Hz sine wave sampled at 3 Hz will not be accurately represented. This is called aliasing. The Nyquist theorem tells us we need to sample at least twice the highest frequency in our signal. For a 2 Hz signal, sample at 4 Hz or higher. Sampling faster than necessary creates huge data files and requires more processing power. Engineers balance quality with efficiency.

This is the written version of the interactive lesson above. See the full Fourier Analysis course.