# Generating I/Q samples from a real signal

My understanding is that if I have a real signal, it can be called as the 'I' component and its Hilbert transform can be called the 'Q' component. Due to the property of Hilbert transform, 'I' and 'Q' will have 90 degrees phase difference.

Now consider the case of a pure sine wave with constant amplitude. Let us say we sample it at 4 times its frequency, hence taking 4 samples per cycle. Consequently, each sample will have 90 degrees phase difference with respect to the previous sample. In this case, is it correct to say that "the incoming signal delayed by one sample" is the Hilbert transform, and hence the 'Q' component?

Also, now let us say we add random noise to this pure sine wave, thus making it non-periodic. Can we still say that "the incoming signal delayed by one sample" is off by 90 degrees?

I hope my question makes sense! Thanks!