# How to describe frequency spectrum with samples?

I posted this same question in math, but nobody is answering, so I thought I'd give a try here too...

To me the question is pretty straightforward, but nevertheless I have to explain its background in order to actually receive the answers I need.

I have to describe portions of the entire current (I'm talking about the telecommunications field - but keep in mind that my method should be "future-developements-resistant" - ) frequency spectrum by selecting samples of it. Those samples should be near enough to guarantee that antennas operating in its boundaries do change their properties/radiation diagrams only a little bit for each sample (provided that these antennas are optimized to work inside the described boundaries). Viceversa, the samples should be far enough to make sure that the behavior of an antenna does change, since I do need representative data of a portion of the spectrum.

• Now, how would I statistically select those samples?

As you may know, some frequency bands are separated by a gap to ensure that uplink and downlink can be distinguished and make no interference. So if I wanted to describe a portion of spectrum with some samples...

• How much "space" would I have to consider if I had to decide whether to treat uplink and downlink as two distinct portions of spectrum (viceversa: how much "space" will allow me to treat uplink+downlink as a single portion?)

Please notice that at the end I would have to use statistics again in order to provide to an end-user a single evaluation of parameters (parameter = average +/- tolerance), so...

• How "big" should a portion of spectrum be, in order to be able to correctly describe it without having a huge tolerance and an average with low probability?

There are also portions of spectrum that are nowadays defined, which are really small in comparison to the majority.

• How would I treat "small" portions of spectrum (e.g. : there is the need to give parameters that describe a 1 MHz band)
• Why do you expect the samples you take to change the behavior of an antenna? Commented Jul 15, 2015 at 14:36
• Please read a bit about signal processing, sampling theory, Nyquist-Kotelnikov sampling law and rephrase your question. Try to read a bit about the Nyquist-Kotelnikov sampling theorem first. Commented Jul 27, 2015 at 12:42
• @Photon because higher frequencies imply higher directivity, therefore smaller half-power-beamwidth etc. Commented Jul 29, 2015 at 4:33
• @kurtovic I think you didn't get the question: it's not about SIGNAL sampling, it's about "how do I describe an antenna in a frequency spectrum". Commented Jul 29, 2015 at 4:35
• @Noldor130884 - Are you asking about the effective length/area of an antenna as a function of frequency/wavenumber, i.e., the complex transfer function of the antenna? Commented Sep 3, 2015 at 22:03