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Approximation techniques simplify sampling rate conversion with a rational ratio. The multiplierless approach, also known as zero-order polynomial interpolation, drops or repeats selected samples of the input sequence. Previous distortion analyses are based either on the time domain sample error or the frequency transform of the output sequence. Our new approach shows that any approximate conversion is equivalent to the use of a multirate finite impulse response (FIR) filter where all nonzero coefficients are identical and leads to a simplified analysis in terms of the transfer function of the underlying filter. Applications include nonuniform sampling, bandpass sampling, and digital synthesis of sinusoids.