Idealizing the radio-frequency (RF) modulating ultrashort electron pulse as a δ time function, we analysize theoretica1ly the coherent synchrotron radiation emitted by the high bunched electron beam and its frequency properties in a reetangular waveguide. We find two new performances: (1 ) when the resonance frequency fs is just equal to integral times of radio frequency fRF which is applied to modulate electron beam, the coherent synchortron radiation field pattern appears "pure" waveguide eigenmode; (2) the coherent synchrotron radiation power at low resonance frequency is higher than that of at high resonance frequency. In addition, we predict the condition for single mode transverse operation in a waveguide FEL.