The line is blurring between today's very capable MCUs and what is a true DSP.

Basically, someone says they want a DSP because they are doing lots of "signal processing stuff" but truth is that they often don't need a full-on DSP for basic signal processing. Only when it gets more advanced then this will they need a real dedicated DSP, and here's why:

a DSP has an accumulator that is designed around multiply-accumulate, because filters are mostly a continuous application of high-order polynomials. The accumulator has guard bits, so that it doesn't lose precision, and the final result can be truncated without much loss of precision. A DSP operating in real-time is more efficient with a Harvard architecture (but it's not needed for non-realtime signal processing, so MCUs do ok here). DSP's have fractional number representation internally, and you can operate on fractional numbers directly, and the registers and instruction set understand fractional numbers, -1.0 < Rx < 1.0. This is because a filter's coefficients are already fractional numbers and the results will also be fractional numbers as it accumulates. DSPs can do parallel fetch while calculating a result.. and DSPs can often do all of this in just a few specialized instructions.

Now, the ARM Cortex-M4 has some DSP extensions, such as a single cycle MAC. This may make it operate faster doing some "DSPish" things, but it may fall short if you want to do DSP in real time on the incoming datastream from your multichannel measurement system.

Finally, a DSP makes programming a filter so easy

the basic FIR filter is

Which is just a series of multiply and accumate, and can often be done in just a few instructions on a DSP, which might take several instructions on a non-DSP. The DSP can parallel fetch the next x value and the b coefficient while calculating and accumulating y[n]

So.. just some food for thought, to help you decide if you need a real DSP or if a modern MCU with DSP extensions will be good enough for your needs.