Hi,
You could use Matlab, and in that case no hardware is needed. There is also open source software that is Matlab-like. I forget what it is called.
Many DSP books use Matlab for their examples. I think most people create and prove their algorithms on software like Matlab, or using C code on
a Windows or Unix machine, before implementing in a hardware platform.
If you want to try it on hardware, digital signal processing can be done using microcontrollers, FPGAs, CPLDs or on actual DSP devices. After all,
DSP is essentially an exercise in math, and all these devices are good at that. In that case, probably best to get a development platform for
the device of interest.