General:
* Copy
* Mimic
* Reproduce
* Emulate (suggests trying to equal or surpass the original)
* Mock (can have a humorous or disrespectful connotation)
* Simulate (often used for creating a realistic representation)
More specific:
* Parody (a humorous imitation)
* Counterfeit (an imitation intended to deceive)
* Fake (an imitation made to deceive)
* Echo (to repeat or reproduce a sound)
* Mirror (to reflect accurately)
The best synonym depends on the specific situation and the intended meaning.