The 19-year-old was interviewed by Oprah Winfrey - along with other members of the singer's family - for a special programme broadcast on the OWN network. Houston opened up about her past drug use on an episode of The Oprah Winfrey Show in 2009.
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Brown explained that her mother's influence, as well as the support of her family, was keeping her going, saying: "I'm doing as good as I possibly can at this point. I'm just trying to keep going.
"I can hear her voice telling me to keep moving. 'Baby, I gotcha'. She's always with me. I can always feel her with me."
Brown also paid tribute to her mother, adding: "No-one knows what an amazing spirit she was. She wasn't only a mother, she was a best friend. She was a sister, a comforter.
"Of course, we had our arguments, we had everything, but at the end of the day, that was still my mother, my confidante, my everything... Everything people are saying about her - all that negativity - it's garbage. That's not my mother."
She also expressed a wish to "carry on the legacy" of Houston, telling Winfrey that she wanted to try "some acting [and] some dancing" in addition to singing.
"It's a lot of pressure, but she prepared me for it," Brown explained.
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Watch a clip of Whitney Houston's 2009 interview with Oprah Winfrey below (US users only):