Mel-frequency Cepstral Coefficients (MFCC), Linear Predictive Coding (LPC), Linear Predictive Cepstral Coefficients(LPCC), Temporal Discrete Cosine Transform (TDCT), Deep Neural Networks all can be used for speech based emotion recognition.
As a development software package LibROSA can be used. LibROSA is a python package for music and audio analysis. Using LibROSA speech based features can be extracted to be used in machine learning pipeline.
The following links may be helpful :
Thesis Emotion Aware Artificial Intelligence for Cognitive Systems
You can try Watson Tone Analyzer for voice emotion recognition. You can find more information about it at the following link: https://www.ibm.com/watson/services/tone-analyzer/