Adequate representation of frequency domain amplitude/magnitude of FFT of a signal I'm quite new to the subject and am having fun playing around with the FFT. What I am currently doing is trying to sample an audio signal and display its frequency spectrum at the same time. This works alright with what I am doing so far, but there are still a few missing puzzle pieces.

This is what I have implemented so far:


I get the raw audio data (i.e. my signal) and sample it with a sampling frequency of 44.1 kHz.
For each time instance of the audio file where I update the spectrum (e.g. every 1/24 th second), I grab a certain amount of samples from my sampled signal around the time instance, apply a window function to it (Hann window) and then I transform it using the fftw library.
Then I look at what I get. Since all my input data is real, I get n/2 + 1 complex values, am I correct in that assumption?
Now, I'd like to display this spectrum. I calculate the magnitude of each of the n/2 + 1 vectors using the l2-norm and try to display that.


The last part is where I'm note sure of how to proceed. First, is this magnitude I calculate called the amplitude in frequency domain or am I mixing stuff up? 
As far as I know, the amplitude of the original signal in the window I transformed is somehow spread across my spectrum (i.e. my frequency bins). 
What I am looking for is a nice mapping in order to display these frequency bins nicely (in fact...I always group a few together to get larger frequency bands). 
Here is what I am trying to do:
For my visualization, I have 12 bands and each has 15 discrete levels. So effectively what I am doing so far is trying to map the maximum of all bins in a frequency band into {0,1,...15}. 

I have just been playing around so far, trying things like logarithms and linear mappings, but none seem be giving me the results I am expecting. For example, the lower frequencies might have a very high amplitude where higher ones are comparatively low, even though the corresponding audio signal would have me expecting higher magnitudes for the higher frequency bands. 

So my main question, could this be mainly due to the fact that I am always picking the maximum? Would a mean value over all bins in a band be better?

My gut tells me thats just the tip of the iceberg. A linear transformation is, for example, difficult to adjust since I don't know what the maximum frequency magnitude is when I am calculating my spectrum on the fly.

I would appreciate it if some of you Gurus could help me learn what I am missing and, perhaps, tell me if there is anything horribly wrong with what I am doing up to the point where I want to visualize the calculated spectrum.

Cheers!
Brick
The correct way to group multiple bins together is to multiply each complex fft bin output by its complex conjugate (which gives the bin power) then add all the bin powers together and divide by the number of bins in the group. If you want to display in db (which is the conventional approach) then take 10*log10() of the result. Negative db values are normal and expected. 

Note that if your audio signal is music, it is quite normal that the spectrum falls off with frequency.

Also from your description it sounds like you are not using a 2 ^n number of points. It's best to stick with 2^n data buffer sizes to maximize the efficiency of the fft computation.  

Bob