This paper presents the development of Quantum Fourier transform (QFT) education tools in the object-oriented Java-DSP (J-DSP) simulation environment. More specifically, QFT and Inverse QFT (IQFT) user-friendly J-DSP functions are developed to expose undergraduate students to quantum computing. These functions provide opportunities to examine QFT resolution, precision (qubits), and the effects of quantum measurement noise. In our study, we also describe a laboratory exercise on QFT-based speech analysis-synthesis which has been deployed in our senior-level DSP class and in our NSF workforce development programs. The software and the laboratory exercise are evaluated using formative and summative assessments.