In recent work we have demonstrated that key features of wall turbulence can be captured by an input-output relationship between nonlinear forcing and velocity response, where the transfer function, constructed in wavenumber-frequency space, is named the resolvent. A basis for the wall-normal direction can be obtained by singular value decomposition of the resolvent, where the singular functions (or resolvent modes) represent the most amplified velocity response to the “most dangerous” input forcing. As such, a low-rank approximation can be obtained by retaining a limited number of singular functions; recognizable statistical and structural features of wall turbulence can be identified in even the rank-1 approximation, in which only the principal singular functions are investigated.