Is that real!? https://www.cooking-hacks.com/documentation/tutorials/extreme-range-lora-sx1272-module-shield-arduino-raspberry-pi-intel-galileo/I have no application for this but it is pretty cool. I can see this being good for a DIY security for a large business. A large business should probably pay a security business to handle that though... "The Hydrophones- Arduino UNO will be mounted on a Aerial vehicle whose purpose is to float on water, capture sound of underwater mammals and transmit them to the base station. Transmission part is easy as I have tried it with other sensors and it works fine" That sounds exciting. Why do you want to use FFT to record mammals underwater?
I can see how having a large range would be useful for that application. What mammals are you interested in monitoring? This sounds like a fun project. Where is your group located? I was having a hard time getting usable results from the FFT library your using. My application is for lights and music. I switched over from the UNO to the Teensy 3.2 and the FFT library that Mr. Stoffregen wrote. It is much better I think you will be happy with the results. Plus if your looking to strap this on a drone that floats it will save more space. His audio shield has a mic input so you wont have to worry about an opamp circuit for your hydromic.
Perhaps you should use both Teensy and Uno, connected together by serial (pin 1 on Uno to pin 0 on Teensy, and pin 1 on Uno to pin 0 on Teensy). On Teensy, you'd use Serial1 for those pins, and on Uno there's only one Serial.Maybe you could program Teensy to simply send the FFT data to Uno? The FFT example already sends data to USB serial. Maybe you could just use that, with Serial changed to Serial1, so it transmits the data to your Uno?All 512 points sent 88 times per second might be more data (and a higher baud rate needed) than Uno can handle. But if you don't care about higher frequencies, you could just send the lower bins. Then instead of the extremely difficult task of FFT on Uno, you'd only have to write code on Uno to receive the data Teensy sends.You're still going to have to do significant programming on the Uno side, and maybe a small amount on the Teensy side to edit the code to send less data and maybe adapt the format for something you can more easily parse on the Uno side. If you're not skilled with programming, you might need to find someone to help with that coding (and no, I'm not going to do it for you, even if you buy a Teensy, not even if you buy a lot of Teensys)But at least Teensy and the audio shield can make the FFT part fairly simple.