1. In a food processor, process the apricots until well-pureed.
2. Place in a medium bowl and add the pistachios; mix well. Divide the mixture in half. Roll each half into a log about 7 inches long. Cover and chill for at least 2 hours, or until firm.
3. Place the splenda in a shallow dish; coat the apricot logs with the sugar, turning to coat all sides. Cut into 1/4-inch slices and serve, or store in an airtight container until ready to serve.