In theory, all applications done for Signal Processing can be performed using VLSI, and all approaches used by VLSI field can contribute with SP field. Thus, it is a very deep and fruitful area.
Almost all the applications of signal processing can be done using VLSI system design. While choosing the circuit one must take care of frequency of operation of the system while designing VLSI circuits.
VLSI is the basic building block of SP domain. More precisely An optimal signal proessing application is always developed using VLSI techniqus. Please try searching SCIENCE DIRECT and IEEE EXPLORER for the same.
Any signal processing like audio, video and control based application integrated with VLSI domain. It may be FPGA implementation or ASIC implementation.
In VLSI design, timing analysis play major role and need to consider power consumption.