It can be used for design analog applications. The thesis attached, shows the design of a complete link including both analog and digital circuits via FPGA.
I believe there are two answers to your question: from one side, FPGA with analog features (e.g. ADCs and DACs, maybe conditioning amps...) are available and are being developed, even though their analog features cannot be considered as flexible as their digital counterpart. Regarding these devices, you may find it useful to see the following discussion:
On the other hand, a big challenge could be to implement analog functions taking advantage just of a "purely digital" FPGA, i.e. describing and sysnthesizing analog functionalities in terms of conventional digital gates possibly using an hardware description language (HDL). In some cases this approach is feasible, even if the performance are in general not so good as in a true analog implementation. This is an open research topic.
The answer depends on exactly what kind of analog functions you need. The thesis included by https://www.researchgate.net/profile/El_Sayed_El-Rabaie is interesting but it does not exactly represent a true analog design. At its ultimate output is a serializer, which converts PLL based pulse trains to a frequency modulated high-frequency output. For things like analog filters using digital logic one would need to revisit digital filtering techniques where different windows are applied.
What do you mean by "ABILITY TO DESIGN ANALOG CIRCUITS "? Ability to build analog or mixed-mode system by means of connecting blocks like ADC/DAC/OPAMP? Maybe this will help:
Direct answer is not!, but you can creat the concept of amplification by digital multipliers. Also sometimes some digital devices have built in ADC and DACs but you should check on them! Generally ADC and DAC are like the gates from analog to digital word. Then this question is like can these gates be inside castles that you get in the castle without passing through the gates!
Hi, you can use FPGA to simulate the function of an analog amplifier, but still it's not the same as an analog amplifier and won't have some of its advantages such as speed. You may want to think about what's the advantage of doing this if it's a practical development. Factors like simplicity, price and speed need to be considered.
There are some programmable analog arrays in the market (FPPA), they are not very large or complex circuits and are limited to 2 Mhz Bandwidth, but are field programmable and can process analog signals using switch capacitors techniques.
Anadigm is the company I know that initially developed such circuits and have a product on the market. They also have a development kit to test the circuits.
I don't know if this is the kind of application you need but you can look at them and decide.
If you don't have A&D features on the FPGA board. You have to make the simulation of the simulation code for A/D and D/A conversion befor and after the computation algorithm.