INTRODUCTION The goal of this document is to outline the deliverable products and performance requirements for the ZTF Data Systems. This is to ensure that ZTF can achieve the science goals described in the ZTF Science Requirements Document. The requirements listed below apply lessons learned from PTF and iPTF to specify what should be possible with ZTF. In this document we will try to review the current status, precision and accuracy, of the PTF pipeline, and suggest ways to improve it. We also provide the list of required pipeline steps, meta data and data products to be stored. Some of this requirements may have implications to hardware apparatus (e.g., flat field screen?), and some to computing requirements and data storage. The primary science goals for ZTF, as outlined in the science requirements document, are listed below: 1. Discovery of Fast, Young, and Rare Transients at near real time; 2. Searches for Electromagnetic Counterparts to Gravitational Wave Sources; 3. Producing high precision light curves for all sources; 4. Asteroid and streaks Discovery.

INTRODUCTION Consider the following system of signals: $$ S = \{ (a_j, x_j) \}, \quad j = 1, \ldots , N $$ where aj are signal amplitudes and xj are signal positions. {aj} and {xj} may be represent by real or complex numbers. Define the Prony map as a map {(aj, xj)} ↦ {mk} of the following form: $$ m_k = ^N a_j x_j^k. $$ Numbers {mk} are moments of the system, equation is the Prony equation system. There is a special case of the Prony system: $$ S_t = \{ (a_j, \mu_j) \}; \quad m_k = ^N a_j e^{-2\pi i \mu_j k \delta} $$ where δ ∈ ℝ+ is a parameter. We say that it is the trigonometric Prony map. If |xj|=1, we can reduce general Prony map to the trigonometric case by xj = e−2πiμjδ. In the practical application, we usually know only moments of a source system and we want to reconstruct original amplitudes and positions of signals. This means that we should build the inverse Prony map. Unfortunately, measurements of moments frequently include some noise. A feature of the inverse Prony map is the following: even small noise can produce a significant reconstruction error. Therefore, it is very important to understand geometry of the Prony map and the inverse Prony map. In this technical report, we consider some examples of the direct and inverse Prony map and build corresponding plots. You can also view the source code on the R language for each plot. See also: , , , , , , , , , , , , , , , , , , , , , , , , , , .