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What do you have to do to receive radio waves, not only radio broadcast, but analyze what radio waves are around me, just using a computer, and some USB devide + antenna?

I suppose getting wifi through an USB adapter is not much different than this scenario. It would be nice to have a USB RF spectrum analyzer. Or a USB cell-phone.

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The device you are looking for is part of a whole system called a Software Defined Radio, or SDR for short. There are plenty of USB devices that can act as the input to an SDR system by sampling RF for processing on a PC.

One I know a little bit about is the HackRF Jawbreaker. You can find the official site here with ample technical detail at Github. The project is entirely open source and, with a case, looks like the image below.

HackRF Jawbreaker in perspex case

Most USB devices used for SDR will allow you to plug your own antenna in. There are a number of projects looking at using DVB-T dongles to sample RF, as their chipsets lend themselves quite nicely to the task. If you can find decent software for your PC then this could be an inexpensive way of getting into SDR.

It is important to note that these USB devices are not generally "spectrum analysers" in the same sense as a dedicated benchtop spectrum analyser. Over a limited frequency bandwidth the USB devices can be persuaded to act like a spectrum analyser, for example a quote from the HackRF Kickstarter page:

The maximum bandwidth of HackRF is 20 MHz, about 10 times the bandwidth of TV tuner dongles popular for SDR.

If you are looking for a device that can sample near-DC to >1Ghz in real-time then you'll need to investigate USB/GPIB capable spectrum analysers.

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    \$\begingroup\$ Actually, no, it is not called a "software defined radio" - that would be the overall system. The peripheral is only part thereof - depending on details, an RF front end, downconverter, sampler, and possible additional digital downconverter. Also note that most "spectrum analyzers" also have a limited realtime bandwidth, and must tune their converters to perform a full spectral scan. \$\endgroup\$ – Chris Stratton Nov 20 '13 at 22:04
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    \$\begingroup\$ Both valid points, I will edit the post to accommodate your first point and leave your comment as a better explanation of the second. \$\endgroup\$ – David Nov 20 '13 at 22:08
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Software-defined radio might be what you're looking for. There are many solutions.

For simple applications (its bandwidth is limited) you can use a RTL2832-based dongle with GNU Radio or other software that supports it. This is it tuned to a local FM radio station:

enter image description here

The dongles can cheaply be found online, so if your requirements are not too demanding, you might be able to use them. I use this one that I bought on DealExtreme.

rtl-sdr.com has a wealth of information (e.g. using those dongles to do radioastronomy, receiving satellites, listening to air traffic control)...

If you have the budget (they're quite expensive), the USRP is a possible choice, too.

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