Speech is our most important signal. Everything important in life is communicated with speech. Any time we want to interact with someone, the preferred method is speech. That is how humans are built (with the exception of some disabilities and such).
Consequently, any technology that we can develop to support speech communication or which takes advantage of our speaking abilities, can be very useful. For example, improving telecommunication technologies is important because that helps us connect with remote persons. Similarly, developing improved user interfaces to better support voice input, allows more intuitive interaction with devices. That is convenient for the average people, but can be life changing for children, the elderly and people with disabilities who have limited ability to interact with visual and tactile interfaces.
Speech signals are acoustic pressure waves, which vary a lot over time, yet it would be convenient to analyse the spectrum of signals, because we have an intuitive interpretation for spectral characteristics. For example, everyone knows the difference between high and low pitch, as well as between a dark and bright sound. Such features can be easily visualized with a spectrogram, where the spectral content (i.e. frequency content) is analyzed in short segments and illustrated with a heat-map.
For automated analysis of speech, the spectrogram is then also a good starting point. However, to reduce the dimensionality, we can apply perceptual compression to the mel-frequency scale, and we can apply decorrelation with the discrete cosine transform (DCT) to make the data better digestible for machine learning. This is known as the mel-frequency cepstral coefficient (MFCC) representation and it is the most commonly used feature in speech and audio recognition and classification tasks.
Application of machine learning on speech data is then straightforward. For example, a frequently appearing task is voice activity detection (VAD), where the objective is to determine whether an acoustic signal contains speech or not. We can then train a simple machine learning algorithm with MFCCs as input and the desired label (speech or non-speech) as the output. When a VAD is implemented in an efficient way, it can be very useful in reducing overall resource-consumption of a system. For example, we can let the VAD run all the time and when it detects speech, only then would we trigger a computationally expensive speech recognition engine.
Overall, speech processing is an exciting field of engineering, where signal processing and machine learning methods to solve practical, important and meaningful problems.