Intermodulation

Intermodulation is caused by Non-linear behaviour of the Signal Processing being used. The Theoretical outcome of these non-linearities can be Calculate d by conducting a Volterra Series of the characteristic, while the usual Approximation of those non-linearities is obtained by conducting a Taylor Series . Intermodulation is rarely desirable in radio, as it essentially creates Spurious Emission s, which can create minor to severe Interference to other operations on the resulting frequency. Intermodulation may be desirable in Audio if the intent is to create specific Sound Effect s; for instance, intermodulation is the basis of the Power Chord technique in rock music. CAUSES OF INTERMODULATION By definition, a linear system cannot produce intermodulation. If the input of a linear system is a signal of a single frequency, then the output is a signal of the same frequency; only the Amplitude and Phase can differ from the input signal. However, non-linear systems generate Harmonic s, meaning that if the input of a non-linear system is a signal of a single frequency, $~f_a$ , then the output is a signal which includes a number of integer multiples of the input frequency; (i.e some of $~ f_a, 2f_a, 3f_a, 4f_a, \ldots$ ). Intermodulation occurs when the input to a non-linear system is composed of two or more frequencies. Consider, an input signal that contains three frequency components at $~f_a$ , $~ f_b$ , and $~f_c$ ; which may be expressed as : $\ x(t) = M_a \sin(2 \pi f_a t + \phi_a) + M_b \sin(2 \pi f_b t + \phi_b) + M_c \sin(2 \pi f_c t + \phi_c)$ where the $\ M$ and $\ \phi$ are the amplitudes and phases of the three components, respectively. We obtain our output signal, $\ y(t)$ , by passing our input through a non-linear function: : $\ y(t) = G\left(x(t) ight)\,$ $\ y(t)$ will contain the three frequencies of the input signal, $~f_a$ , $~ f_b$ , and $~f_c$ (which are known as the ''fundamental'' frequencies), as well as a number of Linear Combinations of the fundamental frequencies, each of the form : $\ k_af_a + k_bf_b + k_cf_c$ where $~k_a$ , $~ k_b$ , and $~k_c$ are arbitrary integers which can assume positive or negative values. These are the intermodulation products (or '''IMPs'''). In general, each of these frequency components will have a different amplitude and phase, which depends on the specific non-linear function being used, and also on the amplitudes and phases of the original input components. More generally, given an input signal containing an arbitrary number $N$ of frequency components $f_a, f_b, \ldots, f_N$ , the output signal will contain a number of frequency components, each of which may be described by : $k_a f_a + k_b f_b + \cdots + k_N f_N,\,$ where the coefficients $k_a, k_b, \ldots, k_N$ are arbitrary integer values. Intermodulation order The ''order'' $\ O$ of a given intermodulation product is the sum of the absolute values of the coefficients,
	For Example, In Our Original Example Above, Third-order Intermodulation Products (IMPs) Occur Where <math>\ k A+k B+k C	3</math>:

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Intermodulation