Table 2 Notation for different reshaping filter lengths and the corresponding matrices
Variable | Denotes |
|---|---|
\(L^{\mathrm {t}}_{g} = \left \lceil {\frac {L_{h}-1}{M-1}} \right \rceil \) | Reshaping filter length conventionally used in acoustic multi-channel equalization techniques |
\(\mathbf {W}_{\mathrm {t}}\hat {\mathbf {H}}_{\mathrm {t}}\) | Matrix when using the reshaping filter length \(L^{\mathrm {t}}_{g}\) |
pt=L h +Lgt−1 | Number of rows in \(\mathbf {W}_{\mathrm {t}}\hat {\mathbf {H}}_{\mathrm {t}}\) |
qt=MLgt≥pt | Number of columns in \(\mathbf {W}_{\mathrm {t}}\hat {\mathbf {H}}_{\mathrm {t}}\) |
rt≤pt | Rank of \(\mathbf {W}_{\mathrm {t}}\hat {\mathbf {H}}_{\mathrm {t}}\) |
Lgs<Lgt | Reshaping filter length smaller than \(L^{\mathrm {t}}_{g}\) |
\(\mathbf {W}_{\mathrm {s}}\hat {\mathbf {H}}_{\mathrm {s}}\) | Matrix when using the reshaping filter length \(L^{\mathrm {s}}_{g}\) |
ps=L h +Lgs−1 | Number of rows in \(\mathbf {W}_{\mathrm {s}}\hat {\mathbf {H}}_{\mathrm {s}}\) |
qs=MLgs<ps | Number of columns in \(\mathbf {W}_{\mathrm {s}}\hat {\mathbf {H}}_{\mathrm {s}}\) |
rs=qs | Rank of \(\mathbf {W}_{\mathrm {s}}\hat {\mathbf {H}}_{\mathrm {s}}\) |