The processing power and storage capacity of portable devices have improved considerably over the past decade. This has motivated the implementation of sophisticated audio and other signal processing algorithms on such mobile devices. Of particular interest in this thesis is audio/speech processing based on perceptual criteria. Specifically, estimation of parameters from human auditory models, such as auditory patterns and loudness, involves computationally intensive operations which can strain device resources. Hence, strategies for implementing computationally efficient human auditory models for loudness estimation have been studied in this thesis. Existing algorithms for reducing computations in auditory pattern and loudness estimation have been examined and improved algorithms have been proposed to overcome limitations of these methods. In addition, real-time applications such as perceptual loudness estimation and loudness equalization using auditory models have also been implemented. A software implementation of loudness estimation on iOS devices is also reported in this thesis. In addition to the loudness estimation algorithms and software, in this thesis project we also created new illustrations of speech and audio processing concepts for research and education. As a result, a new suite of speech/audio DSP functions was developed and integrated as part of the award-winning educational iOS App 'iJDSP." These functions are described in detail in this thesis. Several enhancements in the architecture of the application have also been introduced for providing the supporting framework for speech/audio processing. Frame-by-frame processing and visualization functionalities have been developed to facilitate speech/audio processing. In addition, facilities for easy sound recording, processing and audio rendering have also been developed to provide students, practitioners and researchers with an enriched DSP simulation tool. Simulations and assessments have been also developed for use in classes and training of practitioners and students.