Distortion Introduced by Sampling

Back to: Sampling & Reconstruction

In general, sampling introduces three types of distortion due to:

• Signal bandwidth
• Quantization
• Digital-to-analog converter (DAC) interpolation

Distortion Due to Signal Bandwidth

In Lesson 2, we learned that perfect reconstruction without distortion is theoretically possible for band-limited signals. However, in the real world, no signal is truly band-limited. If nothing else, there is always thermal noise.

If the sample rate, 𝖥_s, is not at least the Nyquist rate, then aliasing occurs (see Figure 1.10.) Typically, engineers prevent aliasing by band-limiting the signal with a low-pass filter (often called an anti-aliasing filter). However, any kind of filtering—no matter how useful—changes the signal and introduces distortion.

Distortion Due to Quantization

Quantization is the mapping from a continuous waveform to a discrete quantity. Quantization forces continuous signals with an infinite number of possible values to be represented as discrete-value sequences with a finite number of possible values.

For example, a signal in the range of ±1 volt has an infinite number of possible values; however, when sampled by an 8 bit ADC, it is forced to be one of 28 = 256 possible values (see Figure 1.11.) The difference between the ideal value and the discrete value is, by definition, distortion.

Distortion due to DAC Interpolation

A digital-to-analog converter (DAC) must convert a sequence of discrete values back to a continuous voltage or current waveform. From a theoretical standpoint, this waveform is ideally a sequence of weighted “infinitely high and infinitely narrow” pulses called Dirac delta functions.

However, real-world systems can’t support infinite voltage levels, so we must settle for more mundane solutions. In practice, engineers often implement simple “sample-and-hold” circuitry or, more generally, Lagrange interpolation (see Figure 1.12.)

Sample-and-hold is simple because it can be implemented with D-flip-flops. However, its operation is equivalent to convolution with a rectangle function. As such, it introduces distortion in both the time and frequency domains.