A quantitative, property-based approach to protein sequence analysis is presented, grounded in Fourier analysis and signal-processing methodologies. The resulting tools are applied to four protein structure families. We demonstrate the existence of architecture-specific, large amplitude periodicities in amino acid properties encoded in the sequences of proteins. These signals, whose statistical significance we establish, occur at well-defined wavenumbers, but are expressed in different physical properties in the various proteins which fold to a common architecture. This result explains the long-known convergence of unrelated sequences to a common fold. It is further suggested that these results provide a physical basis for the experimental observation that unrelated sequences that adopt similar architectures fold with similar rates.