Phase-modulating the signal using a Brownian random walk signal in a lithium niobate phase modulator utilizing a mirror approach is a workable way to adjust the linewidth without sacrificing the output wavelength and power stability. White noise and bounded-random walk noise were combined and fed into the modulator to address the issue of low-frequency components being lost as a result of the mirror method's artificial reflections, which leaves the linewidth's center unmodulated. Furthermore, it is now possible to create a bounded-random walk signal using field-programmable gate array (FPGA) boards instead of the more conventional Arbitrary Waveform Generator (AWG). This gets beyond the preloaded memory of AWG and enables real-time signal synthesis depending on algorithms. In this work, we present an FPGA-based technique for producing low-frequency white noise by tuning the sampling rate of the Digital-to-Analog Converter, which improves the modulation at the linewidth's center and increases the linewidth. Moreover, to obtain better measurement of signal with low-frequancy, a spectial method for spectrum analysis for modulating signal which achieved high resolution has been proposed.This work has been submitted to the conference of CLEO-PR 2024.