how much of DSP (digital signal processing) is related VLSI? Although,this question may not be very much related to the topic of discussion, but i just wanted to know how much of DSP (digital signal processing) is used in VLSI. Like in the industry or for the sake of knowledge, which all topics share common between the two Domains?
PS:I know this may be off topic, but still thought that I could get answers from knowledegeable people on this platform.
First, an example: designing FIR filters pops to mind, or for that matter any signal processing module. The FIR filter is a nice example, since it can easily be implemented in VLSI even at the lowest abstraction level - physical mask level (in Cadence for example). 

If we recall an example of the FIR filter design:


We can see that we only need to design:


Delay
Multiplier
Adder


elements, which are quite easy to implement in VLSI, either at the high level (VHDL, Verilog), or lower level (Cadence, Magic IC, etc.). 

So now we have a mixed problem - the DSP part is designing the FIR filter, which can be designed in various ways, and dealing with the transfer function/frequency response. The VLSI part is actually implementing the filter - creating the layout which can be printed on a real integrated circuit. 





In general, the two fields are connected, but in industry usually one deals in only a single layer of abstraction. Either one deals with circuits/elements as black boxes, without caring so much about the physical implementation, or conversely focuses on the optimal design of a component, which would later be produced and used in projects where DSP is employed.