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Table 1 Duality relations between STN and FTN multicarrier communication

From: FTN multicarrier transmission based on tight Gabor frames

System STN FTN
Frequency spacing \(\tilde {F}_{0} ~=~1/T_{0}\) \(F_{0} = 1/\tilde {T_{0}}\)
Time spacing \(\tilde {T}_{0} ~=~1/F_{0}\) \(T_{0}~=~1/\tilde {F_{0}}\)
Density \(\tilde {\rho } ~=~1/(\tilde {F}_{0} \tilde {T}_{0})~=~F_{0} T_{0}~<~1\) \(\rho ~=~1/(F_{0} T_{0})~=~ \tilde {F}_{0} \tilde {T}_{0} ~>~1\)
Interference mitigation PR with biorthogonal frames Dual frames
Noise reduction PR with orthogonal frames Tight frames with A g = 1
Transmission generator \(\tilde {g} ~=~ {g/\sqrt {\tilde {\rho }}} ~=~ \sqrt {\rho }\ g\) \(g ~=~ {\tilde {{g}}/\sqrt {\rho }} ~=~ \sqrt {\tilde {\rho }}\ \tilde {{g}}\)
Reception generator \(\tilde {\check {g}} ~=~ {\check {g}/\sqrt {\tilde {\rho }}} ~=~ \sqrt {\rho }\ \check {g}\) \(\check {g} ~=~ {\tilde {{\check {g}}}/\sqrt {\rho }} ~=~ \sqrt {\tilde {\rho }}\ \tilde {{\check {g}}}\)