  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. ESP frames are constructed by applying
time-shifted enveloping functions to the discrete Fourier Transform basis, and
in this way are similar to the short-time Fourier Transform.
  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, and efficient
implementation details are provided. Numerical experiments on acoustics data
reveal that the flexibility of this method allows it to be simultaneously
competitive with the STFT in time-frequency processing and also with Prony's
Method for time-constant parameter estimation, surpassing the shortcomings of
each individual technique.
