For the waveform with sharp peaks which cannot be expressed explicitly as a function of the independent variable, the usual graphical methods of Fourier analysis are of little help since the accuracy of results is limited to the first few harmonics only, even if a large number of intervals/ordinates are used. This paper presents a new method for harmonic analysis of such waveforms, which are frequently encountered in various engineering analyses. Unequal, discrete intervals can be chosen on the waveform and the analysis can be performed using limited data. Even then the higher order terms can be obtained with much better accuracy.