How to detect patterns in an FFT output?
It depends.

First you need to break the problem in steps:


If you can make a static analysis, than there is a chance. Meaning, if you can record a snapshot of the howl, and than spend some time processing it.
If you need to process it (almost) real time, than I am almost sure the Arduino is way too slow for that. In the next steps will be clear why, and otherwise you can use the next steps to get some idea how to do the analysis.
Assume you can do a snapshot of the sound, than you have to store it. The Arduino has only 2 KB of SRAM which is way too small. I assume you want a decent frequency (let's say 40 KHz) of mono (1 channel) samples, which is 40 KB of memory.
You need to record this (probably any sound sensor will be fast enough), and store it to some device, either external SRAM (fastest, most expensive), external EEPROM (somewhere in the middle) or SD card (might be slow). EEPROM/SD cannot be written 'forever' so if you want to process a sample every second, you might run in trouble.
Than you need to run your algorithm over the static data. I do not know this algorithm, if you have to iterate many times, forget about using SD, use SRAM or EEPROM. 
Otherwise, read a few blocks (typically 2 or 3, to get 1 or 1.5 KB) and process it. I hope you can store the result also in the Arduino, otherwise write it (if you write much, probably SRAM is the only well feasible solution).


As you can see, you have to break your problem into smaller pieces, and check how the algorithm works (does it need a lot of data, or a snapshot), can it be processed in pieces, or does it need to iterate over the entire sample data a lot, are there intermediate results need to be stored etc.

Note there might be other solutions:


If you need more speed, try an Arduino Due
If you need more (internal) SRAM, try a Mega (8 KB) or Due (48 KB)