In many practical applications such as power systems, it is often required to realize a digital filter that passes the fundamental component and cancels the DC and harmonic components. This paper presents a new framework for designing band-pass FIR digital filters that meet this requirement. Under a constraint on the tap number and the fundamental frequency, the proposed method describes the desired filter coefficients in a simple sinusoidal function. The proposed filters have an advantage that the phase shift of the fundamental component in the input signal can be freely controlled by a parameter in the filter coefficients. In addition, we prove that the magnitude responses of the proposed filters become unity at the fundamental frequency, and zero at the DC and harmonic frequencies. Furthermore, we also show that the proposed filters are the special case of the well-known Wiener filter for enhancement of a sinusoid in white noise.