Question

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

Solution:

Given data:

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

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

a) baud refers to the speed at which the knowledge is transferred through the modem. This transfer is measured at a stationary location. Hence, the method is continuous in space. Also, the transfer is measured at intervals of 60s. Hence, the knowledge is discretized in time-domain.

b) the amount of individuals refers to the space dimension here. Since the amount of individuals can't be continuous, this information is discretized. the knowledge 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 among the 2 values, it's discrete in space. This state is being reported at the top of every 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 thus is continuous in time.