As the seed-injected lasers widely used in Brillouin Lidar area are too expensive and huge, the algorithm for a broadband Brillouin signal should be developed, which could accelerate the application of compact and economic diode lasers. A variation of Thomae's function was found during the signal processing of broadband Brillouin lidar, and the property of this function-reaching minimum value at the Brillouin frequency shift was used to recover the original signal spectrum and the corresponding frequency shift from a 1:1 superposition of pump light and Brillouin light spectra. Experiments using test data show nearly 100% accuracies for ideal cases; but for non-ideal cases, only when the noise level is less than -30 dB and the ratio of pump light to Brillouin light is less than 1.05 can this algorithm obtain accurate result.