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Higher-order integrated wavetable synthesis (HOIWS) is an efficient technique to reduce aliasing in wavetable and sampling synthesis. A periodic audio signal is integrated repeatedly before it is stored in a wavetable. During playback, the pitch of the audio signal can be changed using interpolation techniques and the resulting signal is differentiated as many times as the wavetable has been integrated. Previous discrete-time integrators approximate ideal integration, which leads to magnitude and phase errors. This paper proposes an ideal integration method, which is applied in the frequency domain with the help of the FFT. Its remarkable advantage is that both the magnitude and the phase errors are completely avoided in the special case of periodic signals. The proposed ideal integrator shows a superior performance over previous digital integration methods. It improves the sound quality of the HOIWS algorithm and helps it to maintain the original waveform after interpolation and differentiation stages.