Orthogonality of the Fourier Transform Kernel

To state the orthogonality of harmonically related sinusoids in words Any two harmonically related sines (or cosines), when multiplied by each other and integrated (summed) over the fundamental interval, yield a zero result if the sinusoids are not of the same harmonic frequency. Further, any harmonically related sine, when multiplied by any harmonically related cosine and integrated over the fundamental interval, always yields zero. 

Orthogonality means that we can extract the individual sinusoidal Fourier terms off(n) by multiplying each, one at a time, and obtain the projection of each sinusoidal component off(n) individually. 

---