Consider a decimated signal with a reduced frequency range due to its lower sampling rate. Insert zeros between each sample to upsample, that introduces repeated spectral replicas at intervals determined by the new Nyquist frequency. Pass the zero-inserted sequence through a lowpass filter with a cutoff frequency at the new Nyquist limit. This filter attenuates higher-frequency replicas, retaining only the original frequency components. The filtered output produces a higher sampling rate signal, maintaining the original signal's effectively and reversing the downsampling process. Take a sequence with a Fourier transform showing non-zero values from -4π/9 to +4π/9. Downsample it by two, resulting in a spectrum spanning from -8π/9 to + 8π/9. Upsample it by eight, compressing the Fourier transform to span from -π/9 to + π/9. Downsample it by nine, scaling the Fourier transform to extend from -π to +π. Combining upsampling by four and downsampling by nine gives the maximum downsampling without aliasing.