Integrated microwave photonic filters are becoming increasingly important for signal processing within advanced wireless and cellular networks. Filters with narrow transmission passbands mandate long time delays, which are difficult to accommodate within photonic circuits. Long delays may be obtained through slow moving acoustic waves instead. Input radio-frequency information can be converted from one optical carrier to another via surface acoustic waves and filtered in the process. However, the transfer functions of previously reported devices consisted of multiple periodic passbands, and the selection of a single transmission band was not possible. In this work, we demonstrate surface acoustic wave, silicon-photonic filters of microwave frequency with a single transmission passband. The filter response consists of up to 32 tap coefficients, and the transmission bandwidth is only 7 MHz. The results extend the capabilities of integrated microwave photonics in the standard silicon-on-insulator platform.