Decoding AM station from SDR into sound?

[Artlav]

In short, how do you decode AM signal from I/Q samples into sound?

In details, i made a software defined radio that uses a PC sound card as ADC.
The local oscillator on it is set to 700KHz, there is a radio station at 731KHz.
With existing software i verified that the hardware works - the station is here and i can hear it.

Now, the goal is to make my own SDR software.
I can read the I/Q signals, at 96K samples per second, into a program on a PC.
When i do FFT on them, i see the target station at 31KHz in there.

And that's where i ran out of knowledge.
There is a lot of info on the net on how to make SDR hardware, but i wasn't able to find anything on how to make SDR software.

So, i have two sets of numbers that are I/Q samples, 96000 of them per second, and a frequency of the station.

How do i get sound out of them?
Where to begin, what names to google for, what to read?

 

[Artlav]

Figured it out.
Two ways to do it, good and bad.

1. The bad. Produce the sound as beat frequency of the carrier. Sound sample = input sample (as a complex number I,Q) multiplied by sin(wt)+i*cos(wt), where w is 2*PI*Fcarrier.
This results in a sound, but the sound is quite bad.
Also, you need to pick the frequency exactly, or the sound will overlap with noise and shifted carrier.
Only advantage is - it's simple to implement.
Might be useful for some other signal type, but not quite good enough for AM audio.

2. The good. Apply a band pass filter to the target's frequency (i.e. carrier+-4KHz). Now, the sound is the complex magnitude of the input sample - the envelope of the AM signal.
This gives clear audio.
The trick is to get a good enough band-pass filter, and these are two orders of magnitude harder to implement than both the first method and the rest of the receiver program combined.
I ended up using Butterworth IIR filter, for which there is good info on http://www-users.cs.york.ac.uk/~fisher/mkfilter .

In both cases it's a good idea to apply even simple low-pass and high-pass filters to the audio, to get rid of stuff at the edges.

Things to look for and google:
-DSP, digital signal processing
-C Algorithms For Real Time DsP, by Paul Embree, a book.
-http://www.arrl.org/dsp-digital-signal-processing

Perhaps this is better moved to Math section?