I have been assigned responsibility as Lab instructor of DSP at undergrad Level and so i have to equip my lab,please recommend which processors should i purchase for hardware implementation of dsp concepts
This really depends on what the contents of your class is and what the labs are supposed to achieve. "DSP" spends a huge variety all the way from basic math (z-transform, difference equations) to DSP Hardware design (chip design, interfaces, Harvard architecture, memory layouts, instruction sets, etc.).
If you just do math, filters, algorithm design, etc. Matlab, Octave or Python are popular choices. If you want get hands on with real hardware, a Raspberry Pi can work well. If you want exposure to dedicated DSP chips, you probably would want an eval board from a specific manufacturer such as Analog Devices or Texas Instruments.
For an undergrad DSP lab, there's absolutely no benefit in complicating what hardware your students need to learn: Let them do DSP on a completely normal PC.
There's plenty of offline processing and real-time capable DSP platforms for PCs. I'd personally recommend getting a bunch of Linux PCs, and having Python3 with scipy/numpy/matplotlib on them for basic algorithms exploration on that.
For advanced topics, like doing live signal processing on audio coming from a microphone or from an internet stream, or doing software defined radio with real SDR hardware, I'd go for GNU Radio, which comes with a lot of useful building blocks, and can be easily extended using Python and C++.¹
¹ Disclaimer: I'm involved with the GNU Radio project, but I do, and I know several educators, use it in DSP/communications engineering labs. Say "hello" on the mailing list.