In this paper we investigate the problem of voice communications across heterogeneous telephony systems on dual-mode (WiFi and GSM) mobile devices. Since GSM is a circuit-switched telephony system, existing solutions that are based on packet-switched network protocols cannot be used. We show in this paper that an enabling technology for seamless voice communications across circuit-switched and packet-switched telephony systems is the support of digital signal processing (DSP) techniques during handoffs. To substantiate our argument, we start with a framework based on the Session Initiation Protocol (SIP) for vertical handoffs on dual-mode mobile devices. We then identify the key obstacle in achieving seamless handoffs across circuit-switched and packet-switched systems, and explain why DSP support is necessary in this context. We propose a solution that incorporates time alignment and time scaling algorithms during handoffs for supporting seamless voice communications across heterogeneous telephony systems. We conduct testbed experiments using a GSM-WiFi dual-mode notebook and evaluate the quality of speech when the call is migrated from WiFi to GSM networks. Evaluation results show that such a cross-disciplinary solution involving signal processing and networking can effectively support seamless voice communications across heterogeneous telephony systems.