For a basic introduction to digital sampling, Nyquist, and the basics of superheterodyne receivers watch theses three videos:
Sound By Numbers: The Rise of Digital Sound
Nyquist-Shannon; The Backbone of Digital Sound
The Superheterodyne Radio: No really, that's its name
SDR Refs:
DEF CON 26 WIRELESS VILLAGE - Balint Seeber - SDR Basics Class
What’s Your IQ – About Quadrature Signals… - For a while I didn't understand I-Q and the connection to Signals and Systems
I recommend playing with GQRX (Linux) or SDRSharp (Windows) with the RX side of SDR. This will get you quickly familiar with basic like modulation (amplitude, frequency, phase, filter width). gain, and the knowledge of how much RF there is. Please take some time to also research the legal ramifications.
I like to think about it like the IR LED in common TV remotes. The LED emits a high frequency EM wave which has modulated data that can be received within range and decoded. The frequency of light is much higher than RF and has limited range but it works similarly.
Cool bands to check out:
80-110 MHz - Wideband FM
110-130 MHz - Air Traffic Control and aviation, HNL channels
130 and beyond is ham radio territory and marine traffic, local repeaters here
410-440 MHz - ISM band, you can often hear data traffic here
460-470 MHz - FRS/GMRS band. These are used for walkie-talkies and you can often hear voice traffic in the the daytime, sometimes it must be decoded. The most fun.
910-930 MHz ISM band, radios and other things
2.4 and 5GHz - Wi-Fi and cordless phones, with phones be aware of the wiretapping regulations and tap only your equipment
Many more ideas and a list of allocations is in this graphic.
Cool projects I've done and can give feedback on:
Digital Voice decoding (DMR, P25 Emergency Services, trunked decoding)
NOAA Weather Fax satellite image download
433 MHz Sunsetter Awning control by Arduino - Reverse engineering using FCC database, $2 433 MHz RF Receiver and Transmitter, and PC audio input of the remote control.
Cordless Phone Security Exposed With HackRF SDR - I've tired this with a HackRF and it works...
If we take a look at the HackRF blocks you can see it is a heterodyne receiver, with a baseband intermediate between 2.3-2.7 GHz. 20 MHz and 8 bit DAC is what we are recording.
We are focusing on the consumer L1 GPS band on 1575.42 MHz. GPS works by sending a satellite location and precise time, using four satellites a receiver will resolve the four dimensions to two solutions, one of which is a location on Earth. The signal uses a high frequency code word modulated with a low frequency data stream. The resulting sum of all signals is received because all satellites transmit on the same frequency. The receiver must synchronize with signal clock and apply the known code words to received signal to filter each satellite's original data. This is a form of CDMA.
Our main point of interest are navigation messages. This contains the time, unit health, ephemeris (satellite orbit), and almanac (GPS system data; allows for cold boot of receiver). The ephemeris is what goes out of date and is used to calculate the orbits.
Most receivers use a NMEA string to send the GPS information. We should also be aware of GNSS vs. GPS hardware, what GLONAS and Galileo are too. Other possible hangups we might encounter are A-GPS and WAAS which is now built into some receivers.