Can anyone provide an insight to select a filter structure out of multi-stage and single stage FIR filter?(it will be great help if references are also provided) Let's say I have to make 50 tap filter. So, is it better to design it using two cascaded filters each with 25 tap then 50 tap single filter only or both are same ? Thank you.
First, two cascaded 24th-order (25-tap) filter will yield a 48th-order filter which is not identical to a 49th-order (50 tap). However, as I assume that this isn't really the answer you are looking for, but rather the difference between multi-stage and single stage.
Assuming infinite precision arithmetic they are the same. In practice, multi-stage filters have lower coefficient sensitivity, so using two (or more) filters would (statistically) allow shorter coefficients word lengths. However, multi-stage filters also require intermediate quantization, so for a complete comparison one should also consider that. And, as obvious from the first paragraph, multi-stage require more multiplications for a given filter order. I would say that unless you run into problems with coefficient quantization you should go with a single stage.
Another use case where multi-stage is relevant is when implementing interpolation and decimation. By using more than one stage some of the filtering can be performed at a lower sample rate and the total arithmetic complexity is reduced.