Minimum bandwidth signals with some specified waveform parameters

For each of four separate conditions placed on a waveform (amplitudes at certain epochs, and slopes at those epochs) constraints on the corresponding spectra are obtained for a system of any bandwidth. Waveforms which satisfy certain combinations of amplitude and slope constraints, within a minimum bandwidth, are shown to have unique spectra. The method confirms that Nyquist's first and second conditions are satisfied by the raised-cosine frequency spectrum, and spectra are obtained for other waveform conditions. The new results are of interest in practical systems where constraints are placed on intersymbol interference and telegraph distortion or in theoretical systems are design targets.