Can anyone suggest any microcontroller based development board (like arduino,rashberry pi etc.) that can be useful for implementing real-time processing of speech processing systems (such as application related to speech enhancement)?
I will tend to agree with Djamel Teguig. You need a more powerful processor than an Arduino to do anything worthwhile with speech in real time. A DSP is clearly adequate, although it doesn't need to be a floating-point one, as long as you are careful with the data collection.
There are some Arduino libraries for voice commands available (uSpeech), but only for limited set of commands and without use of FFT or complex mathematics.
For better recognition and by more complex algorithms I agree to use DSP`s.
Freescale e.g. also offers a DSP suitable for voice recognition from the 56800 family.
The BeagleBoard-xM has an ARM processor and a C64+ DSP core and should be more than enough for speech enhancement applications. Developing for this board is not straightforward, though.