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Sampling rate conversion (SRC) is usually performed in the time domain by using the operations of up-sampling, filtering, and down-sampling. However, it is also possible to perform the SRC in the frequency domain by formulating the desired spectrum from the spectrum of an input signal. This article shows how to perform SRC for both integer and fractional-rate conversion by manipulating the discrete Fourier transform (DFT), implemented using the fast Fourier transform (FFT), of a time-domain signal. The analysis on error performance and the required computational complexities show that by using the FFT, for both short and long input sequences, improvements in conversion accuracy is achieved at reduced computational costs.