Theoretical performances of stationary Fourier spectrometers without mechanical scanning are compared with the performance of a scanning Fourier spectrometer. In spectrometers employing amplitude-splitting interferometers the reduction of fringe visibility, due to the extended source, can be avoided resulting in high optical throughput. In a wave-front-splitting interferometer the fringe contrast depends on the size of the source. However, the wave-front-splitting double-mirror spectrometer avoids the use of a beam splitter and forms an instrument especially suited for the detection of broad band radiation. Noise characteristics, spectral response, and resolving power of the double-mirror spectrometer are theoretically considered and measured. Due to the charge coupled device based detection the sensor characteristics affect the performance of stationary spectrometers. By background subtraction the effect of detection non-uniformity can be radically reduced increasing the signal-to-noise ratio and resolution of the spectrometer. The maximum resolving power reached in measuring the spectra of two lasers was 1600.The stationary spectrometer is applicable to a wide range of measurements ranging from recording temporally variant wide-band radiation to monitoring the wavelength of lasers.