Temperature measurements from the HIgh Resolution Dynamics Limb Sounder (HIRDLS) instrument on the Aura satellite have exceptionally high vertical resolution and high spatial sampling. The vertical resolution, at approximately 1 km, is comparable to the resolution for temperatures derived from GPS radio occultation data, while the number of samples in the 10S-10N range is more than a factor of three higher for HIRDLS than the current GPS coverage. We exploit this high resolution and coverage to compute the spectrum of the vertical component of Eliassen-Palm (EP) flux for equatorial waves throughout the three years of HIRDLS measurements in 2005-2008. HIRDLS measures temperature from infrared emissions, so the measurements extend from cloud-tops and higher. We derive the spectrum of the vertical component of EP flux in the tropical tropopause layer and stratosphere as a function of the temperature amplitudes and observed spectral characteristics directly from HIRDLS measurements alone. The method employs an asynoptic Fourier analysis for the horizontal wavenumber and frequency spectrum, and employs a wavelet analysis for the vertical structure of the waves. No supplementary wind data is required with this method. Our results can be used to test the accuracy of reanalysis data for studies of upper tropospheric and stratospheric equatorial waves.