Question

Time ----> frequency domain:: (please correct me if i have this idea wrong).

When describing a quantity (say voltage (V) ) in the time domain we can write the value in terms of a certain position (usually fixed) and a certain time, This value corresponds to describing a complicated object (a wave) in a simple space.

In the FREQUENCY domain we describe the value for V in the opposite sense ( a simple object a vector in a complicated space). My question here is why is it called only frequency domain when it corresponds to three coordinates ?

Answer 1

time is inversely proportional to time.

Answer 2

A time domain description does indeed describe how the magnitude of a quantity (let's say an electrical signal in some wire) changes over time (and sometimes on the position as well).

A frequency domain description does not describe the signal over time, but it indicates which frequencies are present in the signal and 'how much and in what way' they are present. Which is why it is called the frequency domain.

In short: in the time-domain, you vary the time and you see what happens with the signal (the time would be on the x-axis in a plot). In the frequency-domain, you vary the frequency and you see what happens (the frequency would be on the x-axis).

If you consider a signal with just one frequency, you'd have a time-domain description like: \[A \sin (\omega t + \phi) + d\]
Think about how you could map these four variables (not including time) to the frequency domain in terms of frequency, magnitude and phase? That should help you understand the relation between the three frequency-domain variable a bit better.