A modern FPGA is an excellent way to go. If you already understand Verilog and digital design, then grab some free FPGA development software such as Xilinx ISE WebPACK or Al.tera Qu.artus II Web Edition, and start experimenting with simple digital designs to learn the software tools and HDL simulator. An easy way to test your designs is to buy a small FPGA development kit from Xilinx or Al.tera, they start around $150 US.
Also explore the math and signal processing modules included with the FPGA development software. The Xilinx software includes all sorts of math transforms, digital filters, and other handy cores that you can drop into your Verilog project. Many are free, some are demo versions. The Xilinx web site has lots of application notes for signal processing projects and FPGA design techniques. Al.tera probably has similar resources. As deepu_s_s suggested, OpenCores is a good free resource too.
The free software supports only small FPGAs. If you have a large project, you may need to use a big FPGA and buy the full software.
MATLAB is an excellent tool for designing your signal processing algorithms. You can also get optional MATLAB modules that generate HDL code for digital filters and Simulink. If you really enjoy MATLAB, also check out Xilinx "System Generator for DSP", and similar DSP-related tools from Al.tera, Synplicity, and other vendors. These tools help you generate HDL code for signal processing projects. The results may less efficient than carefully hand-written HDL code, but you might finish your project a lot sooner.