Latest Zynq based boards can perform very fast calculations .... see  website on Zynq boards

Your first question is not easy to answer, since it is not well posed. There are too many solutions characterized by the embedded processor, amount of memory, the software implementation, and so on. Comparing two solutions is not easy - you cannot only look at the speed. The fastest solutions may also be the most expensive ones and dissipate most power. 

Your second solution is a little more easy to answer. Beagleboard is a platform where the embedded processor has both a DSP and a microprocessor inside. When compared to a microcontroller, the Beagleboard will typically be faster even if you just look at the clock speeds of the processors. At the same time, you must also look at the cost and power aspects. For example, an MSP430 launchpad is perhaps a low-cost and a low-power solution, but may not be suited for real-time image processing. 

In summary, you have to evaluate solutions for a given problem and constraints. Sorry to disappoint you - there are no easy answers!!

It is depends on your computation complexity of the application

As the others stated, your question has not a simple answer. However, if you want hard numbers to compare, I suggest having a look at the Coremark Benchmark for embedded microprocessors: https://www.eembc.org/coremark/

Hello All,

Thanks everybody for sharing your views. Indeed, the processor speed (CLOCK) alone cannot be criterion to select or choose a particular hardware platform. It is the execution time of your algo. that should govern the speed selection. So, ultimately it is your code. I have had an interesting situation while working with 32-bit DSP. A code written in C (at that time) was consuming 14k-word of memory thereby taking longer time to execute. However, when the same requirement was implemented in pure Assembly, the size drastically reduced to 7-8kwords of memory and thereby delivering the expected execution time.

I would invite others view also in this regard - Most of the code now a days is written in C or C++ yet we embed some assembly routines/modules for time critical applications.

 Now a days when we have 32-bit ARM or other similar processors/controllers with 1GHz clock speed and higher RAM, the individual device or the hardware platform is not a big issue. So in my opinion consider giving a look at how you are writing your code!

May be Ravi (@ TI) can shed some light in this regard.

Thanks!

An old and always-useful article about what you posted concerning the "fast vs. real-time" dichotomy, is this from Jack Stankovic.

Regards,

Leo

I think that the fastest embedded platform is application specific circuit (ASIC). As the acronym tells us, it is design specifically to fulfil some function which make very fast. However, since it is specific, it cannot be used for other functions. Hence, field-programmable-gate-arrays (FPGA) are the second choice. They can contain both hardware and software as well as be reprogrammed at run-time, which makes them very flexible and rather fast.