Time-frequency equivalence using chirp signals for frequency response analysis
Abstract Frequency response analysis (FRA) of systems is a well-researched area. For years, FRA has been performed using input signals, which are a series of sinusoids or a sum of sinusoids. This results in large experimentation time, particularly when the system has to be probed at lower frequencies. In this work, we describe a previously unknown time-frequency duality for linear systems when probed through chirp signals. We show that the entire frequency response can be extracted with a single chirp signal by extending the notion of instantaneous frequency to both the input and output signals. It is surprising that this powerful result had not been uncovered given that FRA has been used in multiple disciplines for more than hundred years. This result has the possibility of completely revolutionizing methods used for frequency response analysis. Simulation studies that support the main result are described. While this result is of relevance in multiple areas, we demonstrate the potential impact of this result in electrochemical impedance spectroscopy.
