Kevin Watson, 54, of Mary Slessor Square, had sentence deferred until July 19 at Dundee Sheriff Court.
Watson admitted breaching bail on four separate occasions by approaching and contacting Stephanie Morris.
He admitted approaching Ms Morris on February 8 at Victoria Road, on February 14 at West Marketgait and Brewery Lane, and on March 8 at Peddie Street.
He also admitted attempting to contact her on February 26 by attending at her place of residence at Salvation Army, Courthouse Square, throwing stones to get her attention and shouting at her.
Watson further admitted giving false information to police by stating that he was Paul Watson, 59, of Hanover Close, with intent to pervert the course of justice, on February 8 at Victoria Road.