This paper presents a method of constructing Parseval frames from any collection of complex envelopes. The resulting Enveloped Sinusoid Parseval (ESP) frames can represent a wide variety of signal types as specified by their physical morphology. Since the ESP frame retains its Parseval property even when generated from a variety of envelopes, it is compatible with large scale and iterative optimization algorithms. The ESP construction provides an analysis and synthesis transform pair that can be tuned according to the characteristics of the signal to which it is applied. This work provides examples of ESP frame generation for both synthetic and experimentally measured signals. Furthermore, the frame's compatibility with distributed sparse optimization frameworks is demonstrated. Numerical experiments on acoustics data reveal that the flexibility of this method allows it to be simultaneously competitive with a signal agnostic short-time Fourier Transform in time-frequency processing and also with Prony's Method for time-constant parameter estimation, surpassing the shortcomings of each individual technique.