Recent developments in power semiconductor devices have made High Voltage Direct Current (HVDC) transmission systems the most crucial technology for future power systems. Today several HVDC projects have been commissioned around the world. The primary concern for such an advanced HVDC grid is to follow standard grid codes to maintain the safety and stability of the electrical equipment during transient and dynamic circumstances. Although the HVDC system has been recognized as the most prominent technology to transmit electric power, some issues must be addressed, such as selective and quick detection of faults. For selective fault detection, it is essential to look into the several fault detection strategies that fortify the HVDC system with time-frequency signal processing techniques. This research uses a time frequency-based method to identify the different HVDC transmission line faults. The most suitable mother wavelet for various transient states is selected by analyzing fault voltage and current signals based on variance, standard deviation, and range parameters. An experimental setup of a thyristor-based HVDC transmission system has been developed in the MATLAB/Simulink environment, and multiple fault scenarios have been analyzed. The simulation outcomes reveal that the most effective mother wavelet for detecting DC line, symmetrical and unsymmetrical faults occurs at the 6th level of fault signal decomposition. By examining current and voltage signals, our work has determined the best mother wavelet for various faults. Using more than one mother wavelet to detect faults is more reliable than using a single mother wavelet to detect all faults. Additionally, it has been noted that each fault's voltage and current signals have two distinct mother wavelets.