#### Topic: Strange graph results

I'm learining Graph by implementing the Convolution and Cross-Correlation functions, as per Wikipedia.

I've used custom functions for this as follows:

```
Duration = 1
a(x) = if( x < 0, 0, x < Duration, 1, x > Duration, 0) # _-_ function
b(x) = if( x < 0, 0, x < Duration, 1 - ( x / Duration), 0) # _\_ function
Convolution(t) = integrate( a(dT) * b( t - dT ), dT ,-INF,INF)
crossCorrelation(t) = integrate( conj( a ( dT ) ) * b( dT + t ), dT,-INF,INF)
autoCorrelationA(t) = integrate( conj( a ( dT ) ) * a( dT + t ), dT,-INF,INF)
autoCorrelationB(t) = integrate( conj( b ( dT ) ) * b( dT + t ), dT,-INF,INF)
```

The resulting graphs look a bit strange. Compare the images attached; When duration is one, compared to when it's two. There are missing portions of the plots, and some results are truncated (eg @ approx -1.55 and 3.55 the curves suddenly return 0 values.

A follow-on question concerning the actual calculation:

Whilst the Convolution and Autocorrelation plots have the right shape, it seems their amplitudes are not correct.

The Cross-Correlation plot is calculated as the mirror (wrt Y axis) of what it should be.

Is there something wrong with how I've defined the functions?

Can someone help me understand what's going on?

Cheers,

Nap