Distinction between polynomial phase signals with constant amplitude and random amplitude

In this paper we propose to distinguish between constant amplitude polynomial phase signals and the ones having random amplitude. We study four possibilities for the modulating process. We show that the distinction of this kind of signals is not always possible when using the polynomial phase transform. In fact, in some applications, we show that we cannot estimate the phase of the signal with this transform. In order to solve this problem, we introduce a new transform which allows us to estimate this phase in these particular situations. The obtained transform is referred to as the modified polynomial phase transform.