Observer-based discrete Gabor transform
Bence Ország, László Sujbert · 2022 IEEE International Instrumentation and Measurement Technology Conference (I2MTC) · 2022
Time-frequency representations are frequently used in signal processing applications. This paper presents a framework for recursive implementation of biorthogonal nonstationary discrete Gabor transforms. These transforms can achieve a nonuniform frequency resolution unlike the well known Fourier transform. Typically they are realized with finite impulse response filters. This paper shows an observer-based recursive implementation of these transforms based on Hostetter’s approach. In addition it reviews the construction of generalized Gabor frames and the conditions of their invertibility in detail. The design of the observer’s parameters are discussed and multiple examples are given to illustrate the properties and capabilities of both the design process and the observer.