# What is the relationship between angular frequency and normalized angular frequency

This is a slide from my lecture notes:

My professor used the following words " We denote digital frequencies with capital letters and analogue frequencies with lower case letters"

The problem I have is $$\Omega=\omega T_s$$

Wherever I am looking it is actually the other way round i.e.

$$\omega = \Omega T_S$$

For example here

Is my proffesor wrong?

• I think it can be however you want to define it; as long as it is clearly defined it is not wrong. Commented Jan 13, 2019 at 20:09

Again there is no wrong or right here. In the Alan Oppenheim's Discrete-Time Signal Processing book, the notation is as follows:

• when there are only continuous-time signals we use $$\omega$$ for radians per second frequency.
• when there are only discrete-time signals we use $$\omega$$ for radians per sample frequency
• when both types of signals are present, (as in sampling), we use $$\Omega$$ for the continuous-time radians per second frequency, and $$\omega$$ for the discrete-time radians per sample frequency.

Furthermore the relationship between the two frequencies because of sampling normalization is:

$$\Omega = \frac{\omega}{T_s}$$

or equivalently

$$\omega = \Omega ~ T_s$$

However, your instructor seems to prefer the opposite notation for frequencies. That's why most literature seems to be reciprocal of your instructor's.