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This Excel spreadsheet is intended as a teaching aid.
It shows the waveforms created by adding various combinations of harmonics
with various phase relationships.
The spreadsheet has two windows: one into which the
level and phase of each harmonic is entered, and one that shows the resulting
waveform. The waveform always shows two complete cycles (periods)
and is scaled to fit the height of the window. As a result of this
scaling, the absolute values of the numbers entered for the levels of
the harmonic components are unimportant; it is only the ratio between
harmonics that matters. The level of each harmonic is entered into
row two of the spreadsheet, and the phase of each harmonic (in degrees)
is entered into row three.
Row four of the spreadsheet allows the polarity of the
waveform to be inverted (set to "POS" or "NEG"), for
a given phase shift (in degrees) to be added to every harmonic, or for
the phase of the complete waveform to be shifted (by adding a phase shift
to each harmonic proportional to the harmonic number). It also allows
a DC offset to be added.
The spreadsheet handles the first twenty harmonics only.
For frequencies above around 1kHz, therefore, it gives an approximation
of what the ear hears (because the twentieth harmonic of 1kHz is 20kHz
which is outside of the range of human hearing).
Further down the spreadsheet are sets of harmonic and
phase data for sawtooth waves, square waves, and triangle waves.
These waveforms may be displayed by copying data from the appropriate
rows and pasting it over rows 2 and 3. The illustrations show the
resulting square wave (above) and triangle wave (below) displays.
A sawtooth wave contains every harmonic, and the amount
of harmonic number n is given by 1/n. A square
wave has the same harmonic proportions as the sawtooth wave but contains
only odd harmonics.
A triangle wave also contains only odd harmonics, but
the amount of harmonic number n is given by 1/(n^2).
In addition, for the wave to look triangular, the phase of every other
harmonic present (numbers 3, 7, 11, 15, and so on) must be shifted by
© 2014, 100dB sound