Why does a nonlinear system cause inter-modulation?
Can someone answer or point to a link explaining why a nonlinear
  system causes harmonics.


Consider a system with a quadratic non-linearity:

$$y = Ax + \epsilon x^2$$

Let the input \$x = \alpha_1 \cos(\omega_1 t) + \alpha_2 \cos(\omega_2t)\$ be the sum of two sinusoids.

The output is thus

$$y = A[\alpha_1 \cos(\omega_1 t) + \alpha_2 \cos(\omega_2t)]+ \frac{\epsilon}{2}[\alpha^2_1 + \alpha^2_1\cos(2\omega_1t) + \alpha^2_2 + \alpha^2_2\cos(2\omega_2t)+ \alpha_1 \alpha_2 \cos(\omega_1 t + \omega_2 t) + \alpha_1 \alpha_2 \cos(\omega_1 t - \omega_2 t)]$$

Note that we have both 2nd harmonic and intermodulation distortion present.

So, the answer to your question is the well known trigonometric identity:

$$\cos(a)\cos(b) = \frac{1}{2}[\cos(a+b) + \cos(a-b)]$$

When \$a = b\$ this becomes

$$\cos(a)\cos(a) = \cos^2(a) = \frac{1}{2}[\cos(2a) + 1] $$

since \$\cos(0) = 1\$

In other words, when we multiply sinusoids, we get sinusoids with sum and difference frequencies.


  If this is true then sending a delta function through a NLTI system
  will appear to be a LTI system.


The delta "function" is a distribution so one cannot 'simply' write something like \$\delta^n(t)\$ and hope it has meaning.  From the linked Wikipedia article:


  Thus, nonlinear problems cannot be posed in general and thus not
  solved within distribution theory alone.