There are all sorts of things that can be considered DSP. Certainly, if you want to process a measured signal without constraints of how fast, you don't need to worry about how a computer works. But in some applications, you actually need to design a computing system that fits the application in order to get the problem solved in real time.
I've repeatedly been surprised about how ideas from one field unexpectedly turn out to be useful in another field. I was once confronted with a VLSI chip reliability problem, where a possibly leaky integrated circuit could absorb a contaminant and corrode, and where a screening technology for spotting leaks was inadequate, and I found myself using antenna array beam forming theory to improve the performance of the screening technology.
If you plan to sit behind a computer all day, and write MATLAB/Simulink algorithms, probably not as much a need for computer architecture. But if you ever envision yourself in a DSP firmware role, definitely computer architecture could be handy. Really, any target where DSP or firmware runs is essentially a computer - possibly more barebones than the ones we normally interact with for non-work pursuits, but still the same - a core processor, memory support, IO devices, etc. But as mentioned by others, analog knowledge can be just as essential. Working with hardware engineers, my understanding of the analog before the digital, including analog gain and scaling, analog anti-alias filters, has been essential to the big picture of any DSP firmware project. VLSI? could be handy, particularly if wanting to head into FPGA or ASIC development.
Ideally, you could take courses in all 3 areas ;)
The short answer is yes. Knowing architecture will allow you to pick out the right device for any particular application. To paraphrase Sun Tzu: If you understand the problem, and you understand the processor, you will never fail to make a project work.
But do you NEED to know for every problem you work on? Probably not. Sometimes you will be thrown into a project and things are already fixed, and it's "just software" that will change. It will still help to understand what the compiler is doing. And if you know the architecture, you can do things in assembler more easily.
Everything is analog at the bottom. Knowing how transistors work, and how they make flip-flops which makes registers which makes processors and being able to keep track of it all will help you solve strange problems. Knowing both software and hardware has helped me a lot. I would say take the architecture class - and keep programming and pay attention to the analog side - all at the same time! It's fun :-)
My undergraduate was computer engineering. But I did take DSP and VSLI as well as EMAG. I was working then in geophysics so got pulled into an analog instrumentation. It's an analog world.
My master's was in EE with a concentration in digital comm.
Digital Comm DSP means interfacing and dealing with RF and the flaws in radio transceivers. The instrumentation work was a good starting point.
For doing ASIC work the COMP E background was very handy. Note that high speed DSP is often done in hardware using FPGAs or ASICs.
So my vote would be yes to all of it. Note that the Degree is just a starting point. As a practicing engineer you continue to learn.
Sorry but I disagree. I have over 25 years FPGA DSP work experience. Never needed to know about computer architecture of my PCs. Just basic file issues, documentation, license setup for tool management. Unless I use fpga to build a processor...Never ever used spreadsheet DSP but matlab/octave for testing. You can be pilot and need not know about how a plane is built. Or you can build a plane but never need to fly it.