system
Given the following post, respond as if you're commenting on Reddit:
human
With thousands of cellphone transmissions going about, how does my cellphone pick out its signal from the spectrum it receives?

To my knowledge, the cellphone should simply receive a single spectrum that changes with time.

How exactly does a cellphone decompose that and pick out its personal signal?
gpt
The answer to this depends on what technology your phone is using and can vary dramatically.

In the case of 2G GSM (somewhat simplified): your phone is paged by the network (on a frequency/time channel that all devices listen to) informing it that the network would like to communicate. When the phone receives this page it requests network access, the network assigns it appropriate resources depending if you are making/receiving a call, SMS or something else. 

These resources effectively specify what time and what frequency a phone should use to communicate. This scheme is known as TDMA or time division multiple access and separates different users transmissions in time.

In the case of other technologies other techniques are used to differentiate users. CDMA, code division multiple access allows multiple users to transmit/receive on the same frequency at the same time and your cell phone would differentiate its signal using a code provided to the mobile by the network. This is used by the technology commonly called 'cdma' (IS-95, CDMA2000), EVDO, and UMTS. 

OFDMA is a bit more difficult to properly explain but it effectively separates a block of frequencies in time into a grid/array and the network will inform a phone what squares in this grid are allocated for its use. This scheme is used by LTE and WiMAX.

In all of the cases, there is technology built into the cellular network responsible for managing time, frequency and code-space resources and assigning these to users. All of these multiple-access schemes are fascinating and an amazing amount of technology goes into the result of pressing 'send' on your phone.