DSP/dsPIC Getting Started
Well, I will not comment on the DSP capabilities of an ARM Cortex A (Application) or M (Microcontroller), only focus on how to start with DSPIC. The DSPIC family is well stablished product and excellent for medium DSP applications. I’ve designed several successful products based on it. Also, It is an opportunity to try something different. Microchip has several application notes, mainly in power electronics and control systems. Some features useful for signal processing: 

RISC / Harvard;
Barrel Shifter;
Executes 8 operations in 1 instruction;
Fixed point math manages overflow and rounding;
Zero cycle looping;
40-bit accumulators for high-precision results;
Up to 70 MIPS performance;
ADCs with multiple sample and holds;
Peripheral Trigger Generator (PTG) for scheduling complex, high-speed peripheral operations;
Sophisticated PWMs with app specific modes);

Another major advantage when using  Microchip products  is that it provides libraries, for example, complete TCP/IP stack (not a non optimized and minimal lwIP), USB, DSP, motor control, graphical LCD, and so on.  Finally, as Microchip produces a multitude of analog and digital sensors can be easier to integrate with the PIC/DSPIC MCUs. Note: Microchip recently acquired Atmel company.
MikroEletronika  has invested in DSPIC. See the book on:

learn.mikroe.com/ebooks/dspicprogrammingc/

There is a lot of C and assembly code in Microchip web site and Internet. Also, read the DSPIC User's Manual.

It is true that the appearance of 32-bit processors with DSP capacity has diminished interest in dsPICs (16 bits), but do not let yourself be carried away by the "experts." Build your own conclusions. If you are interested, stay on studying about them. Success with your  band-pass filter!