I'm trying to find a PDF of Y where Y is a funtion x, and x is normally distributed with variance other than 1. For example..$$\mu = 0$$ $$\sigma^2 = 3$$
$$Y = \sum_{t=0}^9 |x(t)|^2 $$
I've found that if variance equals 1 then the Chi Squared PDF with k=9 can be used, but that doesn't seem to work for the more general case. I'm stumped, is there a good way for me to solve this.
There are so many typos in your post (should $t$ be $i$? should the sum be from $i=1$ to $i=9$?), so I will try to answer the question I think you are trying to ask.
If $X_i$ follows the normal distribution with mean $0$ and variance $\sigma^2$, then it can be written as $\sigma Z_i$ where $Z_i$ is standard normal.
If $X_1,\ldots, X_9$ are independently drawn from $N(0, \sigma^2)$, then $$Y := \sum_{i=1}^9 X_i^2 = \sigma^2 \sum_{i=1}^9 Z_i^2 = \sigma^2 W$$ where $W $ is a $\chi^2$ random variable with $9$ degrees of freedom.
If you want to deal with cases where $X_i \sim N(\mu, \sigma^2)$ with $\mu \ne 0$, then you will probably need to go to the full general case of a non-central chi-squared distribution.