Over the last decade, deep-learning methods have been gradually incorporated into conventional automatic speech recognition (ASR) frameworks to create acoustic, pronunciation, and language models. Although it led to significant improvements in ASRs' recognition accuracy, due to their hard constraints related to hardware requirements (e.g., computing power and memory usage), it is unclear if such approaches are the most computationally- and energy-efficient options for embedded ASR applications. Reservoir computing (RC) models (e.g., echo state networks (ESNs) and liquid state machines (LSMs)), on the other hand, have been proven inexpensive to train, have vastly fewer parameters, and are compatible with emergent hardware technologies. However, their performance in speech processing tasks is relatively inferior to that of the deep-learning-based models. To enhance the accuracy of the RC in ASR applications, we propose heterogeneous single and multi-layer ESNs to create non-linear transformations of the inputs that capture temporal context at different scales. To test our models, we performed a speech recognition task on the Farsdat Persian dataset. Since, to the best of our knowledge, standard RC has not yet been employed to conduct any Persian ASR tasks, we also trained conventional single-layer and deep ESNs to provide baselines for comparison. Besides, we compared the RC performance with a standard long-short-term memory (LSTM) model. Heterogeneous RC models (1) show improved performance to the standard RC models; (2) perform on par in terms of recognition accuracy with the LSTM, and (3) reduce the training time considerably.