Program phase analysis has many applications in computer architecture design and optimization. Recently, there has been a growing interest in employing wavelets as a tool for phase analysis. Nevertheless, the examined scope of workload characteristics and the explored benefits due to wavelet-based analysis are quite limited. This work further extends prior research by applying wavelets analysis to abundant types of program execution statistics and quantifying the benefits of wavelet analysis in terms of accuracy, scalability and robustness in phase classification. Experimental results on SPEC CPU 2000 benchmarks show that compared with methods that work in the time domain, wavelet domain phase analysis achieves higher accuracy and exhibits superior scalability and robustness. We examine and contrast the effectiveness of applying wavelets to a wide range of runtime workload execution characteristics. We find that wavelet transform significantly reduces temporal dependence in the sampled workload statistics and therefore simple models which are insufficient in the time domain become quite accurate in the wavelet domain. More attractively, we show that different types of workload execution characteristics in wavelet domain can be assembled together to further improve phase classification accuracy. For long-running, complex and real-world workloads, a scalable phase analysis technique is essential to capture the manifested large-scale program behavior. In this study, we show that such scalability can be achieved by applying wavelet analysis of high dimension sampled workload statistics to alleviate the counter overflow problem which can negatively affect phase classification accuracy. By exploiting the wavelet denoising capability, we show in this paper that phase classification can be performed robustly under program execution variability. To our knowledge, this work presents the first effort on using wavelets to improve scalability and robustness in phase analysis.