As we have seen musical instruments and the human voice have several dominant resonances or modes of vibration. These modes correspond to individual sinusoidal oscillations of different frequencies which are superimposed in the time waveform. They are unique to each instrument and voice. Often it is difficult to identify these modes merely by viewing the time waveform. In such cases, it is common to perform a spectral analysis of the time waveform.
This figure shows the spectral representation of a single sinusoid. Note the spectral representation has two parts - an amplitude part and a phase part. All the information about the sinusoid (its amplitude, frequency, and phase) is represented in these two plots.
This figure shows the spectral representation of a sinusoid of different amplitude, frequency, and phase. What do you suppose the time waveform would look like if we were to combine these two modes of vibration? What do you suppose the spectral representation would be?
