Analogue and digital signals

A signal carries information about a quantity. An analogue signal can vary continuously, taking any value within a range. This allows it to represent a continuously changing physical quantity.

Sensors produce signals corresponding to the quantities they measure. For example, a microphone can produce an analogue signal that changes with sound, while temperature and light sensors can produce analogue signals that change with temperature and light level.

Digital signals and bits

A digital signal represents information using separate, or discrete, values rather than a continuous range. In a binary digital signal, each piece of information called a bit has one of two values: $$0$$ or $$1$$. These values are commonly transmitted using two distinguishable voltage levels.

A byte consists of eight bits. For example, $$00001010$$ is a byte.

Binary numbers from 1 to 10

Binary numbers use only the digits $$0$$ and $$1$$. Each position has a value twice that of the position to its right: starting from the right, the position values are $$1$$, $$2$$, $$4$$ and $$8$$. For example, $$1010_2$$ has a $$1$$ in the $$8$$ and $$2$$ positions, so it represents $$10$$ in ordinary decimal notation.

The decimal numbers from $$1$$ to $$10$$ are represented in binary as follows:

• $$1 \rightarrow 1$$; $$2 \rightarrow 10$$; $$3 \rightarrow 11$$; $$4 \rightarrow 100$$; $$5 \rightarrow 101$$
• $$6 \rightarrow 110$$; $$7 \rightarrow 111$$; $$8 \rightarrow 1000$$; $$9 \rightarrow 1001$$; $$10 \rightarrow 1010$$

Pulse code modulation

Pulse code modulation (PCM) converts a continuously varying analogue signal into a sequence of binary digits. It does this by measuring the signal at regular intervals, approximating each measurement using an available level, and encoding that level in binary.

Sampling and quantisation

In sampling, the signal’s amplitude is measured at regular time intervals. For an audio signal, the resulting samples represent how its amplitude changes over time.

Each measured amplitude is then quantised: it is assigned to one of a set of discrete amplitude levels, generally the nearest one. If the measured amplitude lies between two available levels, the assigned level is an approximation of the measurement. The difference between them is called the quantisation error.

Binary encoding and transmission

Each quantised level is represented by a binary code. For example, if four levels are labelled in order by the codes $$00$$, $$01$$, $$10$$ and $$11$$, a sample assigned to the third level is encoded as $$10$$.

The codes for successive samples form a sequence of bits. These bits can be transmitted using two distinguishable voltage levels: one representing $$0$$ and the other representing $$1$$.

Digital sampling quality

A changing analogue signal can be recorded digitally by measuring its amplitude at regular intervals. Each measurement is a sample. The quality of the digital representation depends on how often samples are taken and how precisely each amplitude is recorded.

Sampling rate

The sampling rate is the number of samples taken per second, measured in hertz (Hz). A higher sampling rate means shorter intervals between measurements, so faster changes in the analogue signal can be represented more accurately.

If the sampling rate is too low, important changes may occur between samples and be missed. When the signal is reconstructed from those samples, its shape can therefore be distorted.

Bits per sample

Each sampled amplitude must be recorded using one of a limited set of values called quantisation levels. The number of bits used for each sample determines how many levels are available. With $$n$$ bits per sample, there are $$2^n$$ possible codes. For example, three bits provide eight possible codes.

The sampled amplitude may fall between two available levels, so it must be approximated by a level. The difference between the actual amplitude and the recorded level is a quantisation error. More bits provide more levels and finer amplitude steps, generally reducing this error.

Quality and data demands

Increasing the sampling rate produces more samples for the same duration. Increasing the number of bits per sample makes each sample larger. Either change therefore produces more data, increasing the storage required and the data rate needed for transmission.

Digital sampling makes data convenient to store, process and reproduce. Its limitations are the approximations introduced by sampling and quantisation, together with the greater storage and transmission demands of higher-quality data.

Noise and digital signal recovery

A signal carries information from a transmitter to a receiver. During communication, an unwanted disturbance can be added to it. This disturbance is called noise. Noise changes the received signal, making the information it carries less reliable.

In an analogue signal, information is represented by continuously varying signal values. Noise changes those values, and the receiver may not be able to distinguish the unwanted change from the original variation in the signal.

Recovering a binary digital signal

A binary digital signal uses two intended levels to represent the bits 0 and 1. The receiver compares each received pulse with a decision threshold: a pulse on one side of the threshold is read as 0, while a pulse on the other side is read as 1.

Noise can alter a pulse's level without preventing the receiver from identifying its bit. If the pulse remains on the correct side of the threshold, the receiver makes the correct decision and can regenerate the signal at the intended level. By doing this for each pulse, it can recover the original binary data from a noisy signal.

Digital communication is not immune to noise. If a disturbance moves a pulse across the threshold, the receiver makes an incorrect bit decision. It may then regenerate a clean-looking signal containing the wrong bit.