is yields (A.16) Using (A.16) and (A.3), we can now compute the norm of the operator H for any given set of input signals Si. For instance, for Si = L2([0,00[), i.e. the set of all square integrable functions, it is readily shown that For other sets of input signals, the corresponding operator norm can be computed in a similar manner. CONCLUSIONS A.4 Conclusions This appendix has discussed the theory on HTM norms and their computation. HTM norms are a basic tool in comparing whether HTMs represent LPTV systems that show similar behavior. This is especially useful when trying to simplify a given HTM. Appendix B The Sherman-Morisson-Woodbury formula he Shermann-Morisson-Woodbury formula [Gol96] is used to invert matrices struc- tered as A + UVT, with A E RNXN and U,V E RNXM. . It goes as (B.1) The Shermann-Morisson-Woodbury formula is especially useful when A-Superscript(1) computed at low cost (e.g. when A is diagonal, orthonormal or upper/lower trian- gular) and both U and V are of low rank, i.e. M << N. As a special case for M = 1, we (B.2) 1+vTA-1u This is also known as the Sherman-Morisson formula. Appendix C HTM elements of the linear downconversion mixer his appendix lists the full expressions for the HTM elements H0,1(s), Ho,o(s) and H0,2 (s) of the linear downconversion mixer topology discussed in section 4.3.7 of chapter 4. The expressions are presented for the SymbolicHTM algorithm performing computations up to first order in (the dummy variable) . In these expressions (C.1) Go,o(s) Hi(s)(A1(s)(sm2,0+sCc)+Yfb(s)) (C.2) Gk,o(s) Yo(s+jkwo) Furthermore, gm,k are the Fourier coefficients of the time-varying transconductance of the second OTA stage, as specified in (4.88), and the Vn1,k are the Fourier coefficients corresponding to the time-varying operating point Vn1 (t) in equation (4.87). The wanted signal transfer is described by BVoscGo,o(s) L(s)Yfb(s) L(s)Y(s+jwo) L(s)Yb(s+2jwo) (C.3) L(s)L(s+jwo)Yfb(s+jw0) L(s)Yo(s)L(s+jwo)Yfb(s+jwo) L(s)Yfb(s)L(s+jwo)Yfb(s+jw) C. HTM ELEMENTS OF THE LINEAR DOWNCONVERS