Recent advancements in audio signal processing and pattern recognition have made bird vocalization classification a key focus in bioacoustic research. The success of automated birdsong classification largely depends on denoising and feature extraction. This paper introduces two novel methods, namely improved adaptive wavelet threshold denoising (IAwthr) and bidirectional Mel-filter bank (BiFBank), which aim to overcome the limitations of traditional methods. IAwthr achieves adaptive optimization through autocorrelation coefficient and peak-sum-ratio (PSR), overcoming the manual adjustments and incompleteness of conventional methods. BiFBank fusions FBank and inverse FBank (iFBank) to enhance feature representation. This integration addresses the shortcomings of FBank and introduces novel transformation methods and filter designs in iFBank, emphasizing the high-frequency components. The IAwthrBiFBank, a combination of IAwthr and BiFBank, creates a robust feature set that effectively denoises audio signals and is sensitive to low-frequency and high-frequency sounds. The experiments used a dataset including 16 bird species and validated the proposed method using a Random Forest (RF) classifier. The results of IAwthrBiFBank demonstrate an accuracy of 94.00%, and the other indicators, including the F1-score, are higher than 93.00%, outperforming all other tested features. Overall, this proposed method effectively reduces audio noise, captures birdsong characteristics comprehensively, and enhances classification performance.