Methods for Computing Instantaneous Characteristics Using Hilbert Transform and Estimating Signal Symbol Rate Using Wavelet Transform

In this paper, we can utilize Hilbert transform to compute instantaneous characteristics of signals, while also employing wavelet transform to estimate signal symbol rate. Hilbert transform is a widely used method in signal processing that extracts instantaneous features such as signal phase and amplitude. This can be implemented in MATLAB using the hilbert() function which returns the analytic signal, from which instantaneous amplitude can be obtained via abs() function and instantaneous phase through angle() function. Wavelet transform serves as another common signal processing technique that helps estimate symbol rate, which represents the information transmission rate carried by the signal. The wavelet transform approach typically involves applying continuous wavelet transform (CWT) using functions like cwt() in MATLAB to detect symbol transitions in digital communications. By analyzing the scale information from wavelet coefficients, one can identify periodic patterns corresponding to symbol rate. Therefore, when researching and analyzing signals, we can combine both Hilbert transform and wavelet transform methods to achieve more comprehensive and accurate results through complementary time-frequency analysis techniques.