  We propose the development of an instrument by the Martin & Puplett-type
Fourier Transform Spectrometer to applying the aperture synthesis technique in
millimeter and submillimeter waves. We call this equipment the Multi-Fourier
Transform interferometer (MuFT). MuFT performs a wide band imaging,
spectroscopy and polarimetry in millimeter and submillimeter wavelengths. We
describe the fundamentals of MuFT, and give an example of one potential
implementation. Full description of the observables by MuFT are provided. A
physical explanation of the observability of the complex visibility by MuFT is
given. Fundamental restrictions on observations with MuFT, eg. limits on
spectral and spatial resolutions and field-of-view, are discussed. The
advantages of MuFT are also summarized.
