In this article, a new synthesis method for generalized multi-band filters has been proposed. Different from the traditional frequency transformation method, which transforms a low-pass prototype into a multi-band filter, multiple low-pass prototypes have been transformed into a multi-band filter. This study introduces the idea of transforming more than two lowpass prototypes into a filter, called multi-prototype transformation. It divides the multi-band filter to be synthesized into different segments each of which corresponds to a low-pass prototype. After frequency transformation, these segments are combined together to get the final transfer function. The multi-band filter synthesized by this method can have different orders, bandwidths or return losses in different passbands. Prescribed transmission zeros can also be realized. The return loss adjustment, segment boundary estimation and equal-ripple realization of this method are further explained in theory. To verify this method, an asymmetric quad-band filter is synthesized as an example and a symmetric triple-band filter is synthesized, designed, fabricated and measured. The obtained results show good agreement with the simulation. 1 | INTRODUCTION Wireless communication has various applications, such as global positioning systems, bluetooth, wireless local-area networks and so on. In recent decades, there is a trend to integrate these applications into a single system [1], called the multi-band communication system. This system needs multiband filters to incorporate the multiple passbands within a single filter structure. The main advantages of using multiband filters are saving mass and volume and simplifying the circuit. To design multi-band filters, two methods are usually used: (1) using multi-mode resonators [2] and (2) filter synthesis method [3]. Many multi-mode resonators have been used to design multi-band filters. Pal et al. [4] made a review of different types of multi-mode resonators, including stepped-impedance resonators [5], stub-loaded resonators [6], ring-loaded resonators [7] and fractal-shape resonators [8], for the design of multiband filters. In Ref. [9], a novel multi-mode square ring loaded resonator is proposed to design a tri-band balanced bandpass filter. Multi-band filters realized by multi-mode resonators can have a compact size, according to Ref. [10,11]. However, their design process is not general. Different multi-mode resonators have different design processes and a multi-mode resonator is not applicable for all filters. The filter synthesis method has an important role in multi-band filter design [12]. It is more flexible and simple since it can be realized through the topologies and technologies commonly used in single-band filter design. Many research studies have been done on the synthesis of multiband filters. The frequency transformation method has wide applications. In Ref. [13-15], a dual-band filter was realized by a quadratic transformation equation. An asymmetrical dual-band bandpass filter was synthesized by mod...