Progress has been made in the development and application of mechanism-based pharmacodynamic models for describing the drug-specific and physiological factors influencing the time course of responses to the diverse actions of drugs. However, the biological variability in biosignals and the complexity of pharmacological systems often complicate or preclude the direct application of traditional structural and nonstructural models. Mathematical transforms may be used to provide measures of drug effects, identify structural and temporal patterns, and visualize multidimensional data from analyses of biomedical signals and images. Fast Fourier transform (FFT) and wavelet analyses are two methodologies that have proven to be useful in this context. FFT converts a signal from the time domain to the frequency domain, whereas wavelet transforms colocalize in both domains and may be utilized effectively for nonstationary signals. Nonstationary drug effects are common but have not been well analyzed and characterized by other methods. In this review, we discuss specific applications of these transforms in pharmacodynamics and their potential role in ascertaining the dynamics of spatiotemporal properties of complex pharmacological systems.Quantitative pharmacology involves the characterization of drug effects within and across scales of organization by means of integrating drug-specific properties and those reflective of physiological processes and control systems. A major goal is to identify specific factors that influence the time course of pharmacological effects; however, biosignals emanating from complex physiological systems often exhibit temporal variability. As opposed to simply errors in measurement assay, time-series analysis has revealed that such highly variable data are a product of nonlinear dynamical systems that can be described by chaos theory (Tallarida, 1990;van Rossum and de Bie, 1991; Dokoumetzidis et al., 2001;Goldberger et al., 2002). Traditional pharmacodynamic models are unable to recognize such complex and variable information.High-frequency measurement of drug effects allows development of concepts of pharmacodynamic systems analysis and drug effects based on integrated signaling networks. There are many challenges to this approach; however, recognition of the basic tenets of the complexity, robustness, emergent properties, and intrinsic noise of biological signaling networks provide insight for their analysis (Weng et al., 1999;Aderem, 2005). Current approaches attempting to characterize such interactions in mechanistic terms include deterministic systems such as ordinary differential equations (e.g., chemical kinetics and compartmental models) and partial differential equations (e.g., reaction-diffusion models), stochastic systems (frequently used for species existing in small numbers), and hybrid systems that combine deterministic and stochastic components (Eungdamrong and Iyengar, 2004).