Transformada Z en sistemas de telecomunicaciones: revisión y aplicaciones

Abstract

Introduction: The paper explores the various applications of the Z-Transform in Telecommunications, focusing on modulation, demodulation, and DTMF with the Goertzel Algorithm. Problem: There is a need to deepen the specific applications of the Z-Transform in the engineering field, particularly in telecommunications. Objective: To analyze the applications of the Z-Transform in engineering found in recent research on implementing Goertzel's Algorithm in DTMF systems. Methodology: A bibliographic study was carried out on the applications of the Z-Transform in the engineering field. Applications were categorized in control and automation, biomedical processing and telecommunications with DTMF, a simulation of the Goertzel Algorithm in MATLAB was performed and compared with FFT. Results: Several applications of the Z-Transform were found and with the simulation the efficiency of the Goertzel Algorithm in terms of efficiency for detecting DTMF tones was proved. Conclusion: The Goertzel Algorithm is presented as a good application of the Z-Transform in telecommunications and is an efficient alternative to the FFT for the detection of DTMF tones. Originality: The study combines the literature review on the Z-Transform and the Goertzel Algorithm with a comparative analysis of their efficiency in DTMF. Limitations: The simulation is limited to an example with few frequencies for the Goertzel Algorithm. Separate studies are required to evaluate performance in more complex situations.