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An acoustic model is created by taking audio recordings of speech, and their text transcriptions, and using software to create statistical representations of the sounds that make up each word. It is used by a speech recognition engine to recognize speech.
Speech recognition engines require two types of files to recognize speech. They require an acoustic model, which is created by taking audio recordings of speech and their transcriptions (taken from a speech corpus), and 'compiling' them into a statistical representations of the sounds that make up each word (through a process called 'training'). They also require a language model or grammar file. A language model is a file containing the probabilities of sequences of words. A grammar is a much smaller file containing sets of predefined combinations of words. Language models are used for dictation applications, whereas grammars are used in desktop command and control or telephony interactive voice response (IVR) type applications.
Speech audio characteristics 
Audio can be encoded at different sampling rates (i.e. samples per second – the most common being: 8, 16, 32, 44.1, 48, and 96 kHz), and different bits per sample (the most common being: 8-bits, 16-bits or 32-bits). Speech recognition engines work best if the acoustic model they use was trained with speech audio which was recorded at the same sampling rate/bits per sample as the speech being recognized.
Telephony-based speech recognition 
The limiting factor for telephony based speech recognition is the bandwidth at which speech can be transmitted. For example, a standard land-line telephone only has a bandwidth of 64 kbit/s at a sampling rate of 8 kHz and 8-bits per sample (8000 samples per second * 8-bits per sample = 64000 bit/s). Therefore, for telephony based speech recognition, acoustic models should be trained with 8 kHz/8-bit speech audio files.
In the case of Voice over IP, the codec determines the sampling rate/bits per sample of speech transmission. Codecs with a higher sampling rate/bits per sample for speech transmission (which improve the sound quality) necessitate acoustic models trained with audio data that matches that sampling rate/bits per sample.
Desktop-based speech recognition 
For speech recognition on a standard desktop PC, the limiting factor is the sound card. Most sound cards today can record at sampling rates of between 16 kHz-48 kHz of audio, with bit rates of 8 to 16-bits per sample, and playback at up to 96 kHz.
As a general rule, a speech recognition engine works better with acoustic models trained with speech audio data recorded at higher sampling rates/bits per sample. But using audio with too high a sampling rate/bits per sample can slow the recognition engine down. A compromise is needed. Thus for desktop speech recognition, the current standard is acoustic models trained with speech audio data recorded at sampling rates of 16 kHz/16bits per sample.