Waves
IEEE 802.2 LLC review

The previous section discussed how complex analog and digital waves can be built out of sine waves. Another way to look at the connection between analog and digital is to see how an analog wave can be converted into discrete digits that represent the analog wave.

In the interactive activity, click on Draw Wave and a sine wave will be drawn. The goal is to completely represent this wave, and its continually varying voltages, by a set of discrete values. This process is referred to as analog-to-digital (A to D) conversion. Conversely, a similar process operates in the opposite direction, converting D to A.

The A to D process is completed through the following steps:

  1. Analog wave amplitudes are sampled at specific instances in time.
  2. Each sample is assigned a discrete value.
  3. Each discrete value is converted to a stream of bits.

Before an analog wave can be sampled, it must be determined at what points the analog wave must be measured. The process of measuring the analog wave only at certain time intervals is referred to as sampling. A related decision is how many samples should be taken. Click on Take Samples in the activity and note the result. Then, slide the Set # of Samples bar to the right and click on Take Samples again. Now, slide the bar all the way to the right and again click Take Samples. It is easy to see that as more samples are taken, the wave is better represented.

Notice that the values shown do not consist of equally balanced positive and negative values, as is usual for a sine wave. This is because the values have been normalized, which means that a continuous range of positive numbers from zero to the maximum exists. Normalization of values is frequently done in mathematics, to make it easier to work with, and understand, what the values represent. Although the actual voltages have not changed, the scale representing the voltages has been shifted.

It would seem that taking more samples is the way to achieve an accurate representation of the signal. However, the more samples that are taken, the more bits that will need to be sent. Fortunately, there is a point beyond which additional samples will not be useful. Based on a formula called the sampling theorem, sampling at any rate equal to or greater than twice the frequency of the wave will allow reconstruction of the wave without error. Therefore, a sampling rate more than twice the frequency of the wave will not increase the accuracy.

Use the activity to set different values for the number of samples. Click on Read Sampled Values each time, to see the bit stream that would be transmitted for each sample.

As stated earlier, this process can be reversed. The bit stream can be decoded, by using the approximate analog values. This process occurs whenever someone plays a musical compact disk (CD). The music is encoded as bits in the plastic of the CD. These bits undergo a digital to analog (D to A) conversion, are processed by more electronics, and become the music that people hear.


Interactive Media Activity

Interactive Activity: Analog to Digital Conversion

In this activity, the student will take samples of an analog signal and turn it into digital form.