Which freeware analysis software most closely resembles the functionality of Matlab DSP toolbox
Try SciPy/NumPy and Matplotlib if you're into Python.  It doesn't have all of the functionality of the Matlab toolboxes but lots of the basic functionality.  

I actually doubt you'll find a complete freeware replacement for the DSP toolbox.   The toolboxes are the hard part and where Mathworks puts most of its effort.  The general functionality is easier to find for free.