500 MHz is no longer very high.  I believe the Xilinx Virtex 7 or UltraScale will handle it.  Each chip has 2880 digital signal processing slices, and usually with signal processing you can expand the signal chain easily with as many chips as you need.  The clock rate of these 20nm devices should allow a multiply-accumulate operation to be done far faster than 500 MHz.  The older Virtex 6 would handle that rate.  My last project did Lidar real time coordinate conversion and re-gridding at 200 MHz in a Virtex 5 without taxing it at all.  I was able to use full floating point at that rate (see paper linked below).

http://www.xilinx.com/products/silicon-devices/fpga/virtex-ultrascale.html

http://mc1soft.com/papers/2011_PhaseCoherentPipeline.pdf

500 MHz is no longer very high.  I believe the Xilinx Virtex 7 or UltraScale will handle it.  Each chip has 2880 digital signal processing slices, and usually with signal processing you can expand the signal chain easily with as many chips as you need.  The clock rate of these 20nm devices should allow a multiply-accumulate operation to be done far faster than 500 MHz.  The older Virtex 6 would handle that rate.  My last project did Lidar real time coordinate conversion and re-gridding at 200 MHz in a Virtex 5 without taxing it at all.  I was able to use full floating point at that rate (see paper linked below).

http://www.xilinx.com/products/silicon-devices/fpga/virtex-ultrascale.html

http://mc1soft.com/papers/2011_PhaseCoherentPipeline.pdf

Dear Bimlendra,

               I have attached few files. I will suggest you to go through these files to get a detailed solution of your concern. Please feel free to ask any doubts.

Regards,

A.Kar

You are saying 500 G/s samples per second?  From what source?  By the way, what planet are you from?  I know it is not Earth, as we do not have that technology.

Re: "If The ALMA can observe at wavelengths in the range 3 mm to 400 μm (84 to 720 GHz). Then why I can't make a system to generate 500GHz?"

Usually what people really mean when they say they want to make a 500 MHz signal processing system (your original question, which you can edit by the way), is that they want to make a digital signal processing system which accepts samples at 500 Gs/s (giga samples per second).  Now we understand that is not what you meant to ask.

Before moving on, let me introduce for anyone who might be a novice, that if the question is to process signals having 500 MHz bandwidth (regardless of their absolute frequency, which might be higher), then applying the Nyquist criteria we'd need at least 2x500= 1 Gs/s of signal processing. 

If there is a known signal modulated on a very high frequency, like 500 GHz, then the usual procedure is to run the signal through an analog mixer to down convert it to the lowest possible frequency for processing.  Some filtering generally must be applied to prevent aliasing. 

My field is signal processing, not radio astronomy, so I cannot address this part of the requirement at all, and truthfully have no interest in looking into it.  But you should research this part and state your minimum rate requirement for samples per second of real time processing.  (You can also record the data and process it slower, but at those speeds you might have trouble even recording it.  At Nyquist rates you'd fill up a terabyte every second even with just 8 bit samples.)

Something must convert the signal to digital form.  This is the first limitation.  Most signal processing needs at least 8 bit samples.  The fastest converter I saw as a remarkably fast 56 Gs/s, but it can't really resolve frequencies that high.  It is listed as able to resolve frequencies only up to 15 GHz.

http://www.fujitsu.com/us/Images/56G_ADC_FactSheet.pdf

The Xilinx part I mentioned in the original post might get you a "few Gs/s".  You can talk with a Xilinx rep and ask its limitations.  To go faster, you'd need specialized hardware, an ASIC, a very complex one, fabbed in the latest process, maybe Intel's new 7nm.  This is probably way out of your budget. 

By breaking your signal into blocks, which is natural if you are doing FFTs, you can use parallel processing and achieve any throughput rate in real time that you want.  But you still must capture the signal and convert to digital, and I am not familiar with technology that can do that faster than 10 to 15 Gs/s, though it might exist.  I'm pretty sure that on Earth it does not exist at 500 or 1000 Gs/s.  That signal will have to be mixed down.  Any signal can be observed or generated, right up to cosmic rays (using particle accelerators), but the computation implied by digital signal processing is not practical currently above a few tens of Gs/s.  I'm thinking you only meant to ask how to receive and process 500 GHz signals via analog means, which is not my field.

Try CASPER boards from UC Berkeley Signal Processing Group, UniBoard From JIVE. If you're looking to build something on your own, selecting the appropriate ADC is important. You get lot of ADCs upto 2GHz sampling at 8 bit resolution. You can digitize your 500 MHz, do your signal processing on an FPGA (latest xilinx ones are capable of Signal Processing upto 750 MHz) and bring out the data through PCIe or 10G or 40G ethernet which the FPGAs support.