A method and apparatus are disclosed for converting a signal between the analog and digital domains using frequency interleaving. The disclosed frequency interleaving techniques can be similarly applied to convert analog signals to the digital domain or vice-versa. An analog-to-digital converter decomposes the input broadband signal into N frequency bands that are separately sampled (quantized) before a Fourier transform is applied to convert the signal into the digital domain. Each of the frequency bands can be sampled in the corresponding narrow passband using narrow-band converters, such as passband Sigma-Delta converters, or can be returned to baseband prior to sampling. The various analog samples are then converted to the digital domain using an inverse Fourier transform, or another combining technique. Both sampling and analog-to-digital conversion can be performed at a speed that is N times slower than the input frequency. The disclosed frequency interleaving technique decomposes the input signal into frequency bands that are digitized separately at a slower rate. A disclosed calibration scheme corrects for phase and gain mismatches.