**Jan
Van Den Dobbelsteen** **COSMIC
VOLUME # 51**

INTERMODULATION

2012

SleepWellStudio The Netherlands

Intermodulation or intermodulation distortion (IMD) is the amplitude modulation
of signals containing two or more different frequencies in a system with nonlinearities.
The intermodulation between each frequency component will form additional signals
at frequencies that are not just at harmonic frequencies (integer multiples)
of either, but also at the sum and difference frequencies of the original frequencies
and at multiples of those sum and difference frequencies.

Intermodulation is caused by non-linear behaviour of the signal processing being
used. The theoretical outcome of these non-linearities can be calculated by
generating a Volterra series of the characteristic, while the usual approximation
of those non-linearities is obtained by generating a Taylor series.

Intermodulation is rarely desirable in radio or audio processing, as it creates
unwanted spurious emissions, often in the form of sidebands. For radio transmissions
this increases the occupied bandwidth, leading to adjacent channel interference,
which can reduce audio clarity or increase spectrum usage. It should not be
confused with harmonic distortion (which does have widespread use[dubious –
discuss] in audio effects processing), nor with intentional modulation (such
as a frequency mixer in superheterodyne receivers) where signals to be modulated
are presented to an intentional nonlinear element (multiplied) (see non-linear
mixers such as mixer diodes and even single-transistor oscillator-mixer circuits).
In audio, the intermodulation products are nonharmonically related to the input
frequencies and therefore "off-key" with respect to the common Western
musical scale.

In analog recording, wow and flutter are forms of intermodulation distortion
caused by speed variations in the medium (usually tape). When the flutter rate
is above a certain point, typically about 20Hz, the modulation products impressed
into the musical signal no longer present as an audibly obvious flutter, yet
continue to interfere with the signal as extraneous frequency modulation, and
the resulting sideband products manifest as distortion. This distortion results
in a thicker, grainier texture due to the excess non-musical sum and difference
components riding above and below the harmonic content of the material.

Intermodulation order.

The order O of a given intermodulation product is the sum of the absolute values
of the coefficients,

O = \left|k_a\right| + \left|k_b\right| + \cdots + \left|k_N\right|,

For example, in our original example above, third-order intermodulation products
(IMPs) occur where \ |k_a|+|k_b|+|k_c| = 3:

(f_a + f_b - f_c), (f_a + f_c - f_b), (f_b + f_c - f_a)

(2f_a - f_b), (2f_a - f_c), (2f_b - f_a), (2f_b - f_c), (2f_c - f_a), (2f_c
- f_b)

In many radio and audio applications, odd-order IMPs are of most interest, as
they fall within the vicinity of the original frequency components, and may
therefore interfere with the desired behaviour.

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