Table 4 Computational effort for the identification of a ESA-HM with a PB-FNLMS algorithm
From: Significance-aware filtering for nonlinear acoustic echo cancellation
Computed quantity | Equation | Multiplicity | Required operations | |||||
|---|---|---|---|---|---|---|---|---|
FFT | CMUL | CADD | RMUL | RADD | RDIV | |||
Preprocessed input | (30) | \(p=0,\dots,\frac {N}{2}-1\) | 0 | 0 | 0 | (B−1)N/2 | (B−1)N/2 | 0 |
HM submodel (forward) | Table 2,B=1 | 2P+3 | 2P N N | N N(2P−1) | 6N N | \(\frac {N}{2}+3N_{\mathrm {N}}\) | N N | |
Inversion submodel | Table 2,B=1 | 2P+3 | 2P N N | N N(2P−1) | 6N N | \(\frac {N}{2}+3N_{\mathrm {N}}\) | N N | |
Time-domain HGM | Table 1,L=L SA | \(\frac {N}{2}\) | 0 | 0 | 0 | \(2B(L_{\text {SA}}+1)\frac {N}{2}\) | \(2B(L_{\text {SA}}+1)\frac {N}{2}+\frac {N}{2}\) | \(B\frac {N}{2}\) |
submodel | ||||||||
Kernel correlation | (46) | ∀b | 0 | 0 | 0 | B L SA | B(L SA−1) | 0 |
Instantaneous weights | (45) | ∀b>1 | 0 | 0 | 0 | 0 | 0 | B−1 |
Smoothing weights | (47) | ∀b>1 | 0 | 0 | 0 | 2(B−1) | B−1 | 0 |
Accumulated: | 4P+6 | 4P N N | N N(4P−1) | \(\begin {aligned} 2B+12N_{\mathrm {N}}+\\\frac {N(B-1)}{2}+BL_{\text {SA}}+\\ BN(L_{\text {SA}}+1)-2 \end {aligned}\) | \(\begin {aligned} N+6N_{\mathrm {N}}+\\BL_{\text {SA}}+\frac {3BN}{2}+\\BL_{\text {SA}} N-1 \end {aligned}\) | \(\begin {aligned} B+\\2N_{\mathrm {N}}+\\\frac {BN}{2}-1 \end {aligned}\) | ||
Total: \(\left (8P+12\right)N\log _{2}N+16P+\frac {N}{2}+\left (2L_{\text {SA}}+\frac {7N}{2}+2L_{\text {SA}} N+3\right)B+10PN-10\) FLOPs | ||||||||