A transient image is the optical impulse response of a scene, which also visualizes the propagation of light during an ultra-short time interval. In contrast to the transient image sampling in the time domain using an ultrafast system, we propose the theory of the transient image sampling in the frequency domain using a multifrequency time-of-flight (ToF) camera. Our Fourier analysis reveals the Fourier relationship between transient images and the data from a ToF camera, and identifies the causes of the systematic error, i.e. the modulation signal of a ToF camera being non-sinusoidal, frequency-varying, and of limited frequency range. Based on the analysis we propose a novel framework of frequency-domain transient imaging. By removing the systematic error our technique achieves high quality reconstruction results. More importantly, our technique significantly reduces the computational cost of ToF camera based transient image reconstruction, especially lowers down the memory usage, such that it is feasible for the reconstruction of transient images at extremely high temporal resolutions, for example 10 picoseconds per frame. The effectiveness of frequency-domain transient imaging is tested on synthesized data, real data from the web, and real data acquired by our prototype camera.