I dont work with Ubuntu on my BeagleBoard so i am not quite sure which alsa packages you need but i guess that you will need to install alsa-base and alsa-utils
sudo apt-get install alsa-base alsa-utils
check whether there is the alsa device with
and you should get something like
**** List of PLAYBACK Hardware Devices ****
card 0: omap3beagle [omap3beagle], device 0: TWL4030 twl4030-0 
Subdevice #0: subdevice #
now you can test alsa with
aplay -vv someFile.wav
If there is no sound maybe some channels are muted or the level is very low and you can adjust it with
A simple FIR filter should be able to be implemented in an ALSA application on the ARM only. Maybe also the NEON Data Engine could be interesting for you as it would gain performance and avoid the IPC between the ARM and the DSP.
An easy way to use the DSP on the BeagleBoard is to use the C6EZ tools (http://processors.wiki.ti.com/index.php/C6EZ_Tools) which are included in the DVSDK from TI (http://processors.wiki.ti.com/index.php/DVSDK_4.x_FAQ). In the DVSDK you find several examples of how to work with the various frameworks.
The package manager in Angstrom has support for several TI packages but i don´t know about ubuntu.
I could send you a paper (BSc) which i wrote about that topic, but it is also my first experience and for sure not perfect.