1. A method comprising: training an source hidden Markov model (HMM) based speech features generator implemented by one or more processors of a system using speech signals of a source speaker, wherein the source HMM based speech features generator comprises a configuration of source HMM state models, each of the source HMM state models having a set of generator-model functions; extracting speech features from speech signals of a target speaker to generate a target set of target-speaker vectors; for each given source HMM state model of the configuration, determining a particular target-speaker vector from among the target set that most closely matches parameters of the set of generator-model functions of the given source HMM; determining a fundamental frequency (F0) transform that speech-adapts F0 statistics of the source HMM based speech features generator to match F0 statistics of the speech of the target speaker; constructing a converted HMM based speech features generator implemented by one or more processors of the system to be the same as the source HMM based speech features generator, but wherein the parameters of the set of generator-model functions of each source HMM state model of the converted HMM based speech features generator are replaced with the determined particular most closely matching target-speaker vector from among the target set; and speech-adapting F0 statistics of the converted HMM based speech features generator using the F0 transform to thereby produce a speech-adapted converted HMM based speech features generator.