Hardware-Efficient Parallel FIR Filter Structure Based on Modified Cook-Toom Algorithm

Design of low complexity parallel polyphase finite impulse response filter using coefficient symmetry

“…From Tables 2 and 3, it is clear that the proposed structure always requires less number of delay elements $$(\mathcal{D})$$ and adders $$(\mathcal{A})$$ for different combinations of N and M . For instance, when M = 3, N = 578 proposed structure requires $$\mathcal{D}=579$$ and $$\mathcal{M}=867$$ while existing structures [8–14] need more number of $$\mathcal{M}$$, $$\mathcal{A}$$, and $$\mathcal{D}$$. Comprehensively, for M = 2 and M = 3, the proposed structure has better performance than refs.…”

“…[2, 3] as well as recent work reported in refs. [8–14] in terms of number of multipliers $$(i.e.\mathcal{M})$$, adders $$(i.e.\mathcal{A})$$ and delay elements $$(i.e.\mathcal{D})$$, the required number of $$\mathcal{D}$$ and $$\mathcal{A}$$ are almost same as traditional structures. The count of multipliers, adders and delay‐elements involved in the proposed structure can be calculated using following equations.…”

“…Moreover, we have also estimated the values of $$\mathcal{M}$$, $$\mathcal{A}$$, and $$\mathcal{D}$$ for the proposed structure, and the structures of refs. [8–14] with M = 2, 3 and different values of N as summarised in Tables 2 and 3. Table 2 shows the comparison of even filter‐length structures with proposed approach.…”

“…As per Table 2, our approach is using same value of $$\mathcal{M}$$ as of refs. [8–11] for M = 2, whereas the proposed structure requires lower number of $$\mathcal{M}$$ for M = 3. Besides, it can be seen in Table 3 that the proposed approach requires lower number of multipliers for M = 2 and M = 3 as well.…”

“…In all the FFA based parallel FIR structures of refs. [8–14], there is a requirement to precalculate the modified coefficients values based on symmetry which needed extra adders. From Tables 2 and 3, it is clear that the proposed structure always requires less number of delay elements $$(\mathcal{D})$$ and adders $$(\mathcal{A})$$ for different combinations of N and M .…”