Question

2. Classify each of the following processes as discrete-time or continuous-time, and discrete-space
or continuous-space.
(a) The baud rate of a modem, recorded every 60 s
(b) The number of people logged into Facebook throughout the day
(c) The operational state, denoted 1 or 0, of a certain machine recorded at the end of each hour
(d) The noise (in dB) in an audio signal measured throughout transmission

Answer 1

A process that assumes spaced and distinct values in time is called a discrete-time process. Similarly, a process that assumes spaced and distinct values in space is called a discrete-space process.

A continuous-space process assumes continuous or near-continuous values in space. Similarly, a continuous-time process assumes continuous values in the time domain.

a) Baud rate refers to the rate at which the information is transferred through the modem. This transfer is measured at a stationary location. Hence, the process is continuous in space. Also, the transfer is measured at intervals of 60s. Hence, the information is discretized in time-domain.

b) The number of people refers to the space dimension here. Since the number of people cannot be continuous, this information is discretized. The information is obtained throughout the day. Thus, time is continuous here.

c) The operational state is being recorded as either 0 or 1. The operational state forms the space domain. And since it can assume one of the two values, it is discrete in space. This state is being reported at the end of each hour. Thus, time is discretized.

d) The noise in dB refers to the space domain here. The dB varies continuously and hence this process is continuous in space. The noise is measured throughout the transmission and therefore is continuous in time.