Can we use Tiva C series TM4C123GXL for signal processing experiment purposes?
This question is apparently out of scope. But I would like to provide you a simplest guideline so that you can by yourself decide on whether a given microprocessor would be adequate for various DSP tasks.

1- The Floating Point Capabilities:
Nowadays any processor claiming high quality DSP computation must have strong floating point hardware support. Look for its FLOPs (floating point operations) throughput. Also look for single precision (32 bits) or double precision (64 bits) FP capabilities. For most multimedia purposes (speech, music, video, image) 32 bit is more than enough. For more accurate scientific computations 64 bits is necessary. This being said, the experts can use integer capabilities of a microprocessor to implement most DSP algorithms. But that would require a lower level handling of the mpu. Depending on what kind of an algorithm you want to implement, you should first determine number of floating point operations per second and then check for the MPU if it can support that. 

2- Parallel Execution Capabilities (SIMD)
Many DSP algorithms (especially image and video prcessing types, or communication channel processing) will benefit from single instruction multiple data (SIMD) processing pipeline. It can be expensive to include in a simple MPU but if you have this capability, it's worth the money.

3- ADC / DAC capabilities are vital as you will eventually be inputting an analog signal, convert to digital, process it and cpnvert to analog before outputting. So look for for High Speed, High Accuracy ADC and DAC. Or if your application can tolerate low accuracy go with that one.  And there must be enough number of channels so that if you have multiple signals being input or output you can use that.

4- Memory: in addition to limited program code memory for several applications, data has to be buffered inside RAM. this ram can be on-chip or out of chip. First determine how much ram you will need and then look for wheter it can be on chip (very fast) or out of chip.