July 14 (Reuters) - Benchmark Capital-backed Amplitude said on Wednesday it had confidentially filed paperwork for a direct listing in the United States, a month after a funding round valued the start-up at $4 billion.

Founded in 2012, Amplitude helps companies optimize their products by analyzing which features translate to better business outcomes.

Companies have bolstered their digital presence and online product offerings due to the impact of the pandemic, leading to increased demand for companies such as Amplitude.

Amplitude, which has quadrupled its valuation since May last year, said in June that revenue for fiscal 2020 jumped 50%.

The San Francisco-based firm's customers include Comcast-owned media company NBCUniversal, payments processor PayPal Holdings Ltd, fitness products maker Peloton Interactive Inc and grocery delivery firm Instacart.

Amplitude raised $9 million in a Series A funding led by Benchmark in 2015 and has since taken on investors including Sequoia Capital, Singapore's GIC and Tencent Holdings Ltd .

The start-up's co-founder and Chief Executive Officer Spenser Skates has long been a proponent of direct listings, where companies are allowed to list on the stock market without selling shares.

Cryptocurrency exchange Coinbase Global Inc and gaming platform Roblox Corp went public earlier this year through that route, which advocates argue is a better way to price shares than a traditional initial public offering. (Reporting by Niket Nishant in Bengaluru; Editing by Ramakrishnan M. and Shounak Dasgupta)