whenever we start working on Discrete Cosine Transform(DCT), Loeffler algorithm a key role. Furthur if we approach hardware implementation of this algorithm, we find methods based on Distributed Arithmetic and Shift-and-Add. Both of these method stress on multiplierless circuits. In both cases multiplication is either performed by shift and adding or using a ROM which stores the look-up tables.
The point I am asking here is why everyone is neglecting multipliers replacing them by adders,shift registers in circuits. We can make a N-bit multiplier using adders and registers. Can someone highlight the negative impact of using multipliers?