Intermodular distortion (IMD)
Intermodular / intermodulation distortion
Intermodular or intermodulation distortion (IMD) is a form of distortion that introduces spurious signal components with frequencies that were not present in the original signal, based on the sum and difference products of the original frequencies. The introduced frequencies are often not related harmonically to the original frequencies, so the resultant newly generated frequencies are immediately perceived by human hearing as being non-musical; they generally sound annoying. Any system in the sound reproduction chain that is nonlinear - including signal processing - may introduce IMD to the output, but one of the most prominent physical sources are loudspeakers (and other pistone sound sources).
If a high and a low frequency note is played on a loudspeaker simultaneously, the effect can be heard most easily. A driver covering the entire audible frequency spectrum has a higher IMD than a multiple array of loudspeakers, each assigned to handle specific frequency ranges. Some high fidelity loudspeakers and headphones produce inaudibly low IMD. Also, when broadband signals are present, the IMD may be inaudible due to Masking effects of human hearing.
Any nonlinear physical source producing harmonic distortion also produces intermodulation distortion when there are more than one note is present. For example when there is a signal with two frequencies <math>f_a</math> and <math>f_b</math> driven through a system with a response <math>H(t)</math> which is a nonlinear function, such as a squaring circuit for example, the resulting output will contain the original (fundamental) frequencies and other frequencies as well that are some multiples of the originals: <math>k_1 \cdot f_a</math> and <math>k_2 \cdot f_b</math>. The order of distortion is the absolute sum of the multipliers.
The Doppler effect is most commonly experienced when one hears a motor vehicle equipped with a siren or horn -- the pitch of the siren or horn drops noticeably as the speeding vehicle passes the listener. Doppler distortion in a loudspeaker sounds to the human ear as a warbling effect, usually of the higher of two frequencies generated in the same loudspeaker driver. A linear cause of this distortion is the Doppler distortion which occurs when two tones of largely different frequency are radiated from the same membrane. It is a linear form of distortion since its magnitude is independent of the amplitude of the higher frequency tone and the distortion increases linearly with the amplitude of the lower frequency tone. When the cone moves forward in the speaker due to the slow motion of low frequency sound, the pitch of the higher frequency component is raised and it is dropped when the speaker moves backward  which is a kind of phase modulation distortion that causes:
- Intermodulation distortion
- Amplitude modulation
- Phase shift
The maximum phase shift due to this effect occurs when the cone has a zero velocity at is maximum excursion while the maximum frequency shift occurs when the cone at its zero excursion but maximum velocity.