## Inverse Transform Sampling method on FPGA

Started by 11 months ago●3 replies●latest reply 11 months ago●36 viewsHi,

I am working on **pseudo random number generation topic**. To be precise, ** Inverse Transform Sampling method** , i.e., a method for generating sample numbers at random from any probability distribution given its cumulative distribution function.

The problem that the inverse transform sampling method solves is as follows:

- Let X be a random variable whose distribution can be described by the cumulative distributive function Fx.

- I want to generate values of X which are distributed according to this distribution.

The exact reference of what I would like to implement on FPGA is : https://en.wikipedia.org/wiki/Inverse_transform_sa...

**Questions:**

- What would be the mathematical challenges? I mean challenges in context of **natural log** and then data types like **integer**, **fixed** and **floating points**.

- What should be the right approach? I mean the starting point.

I am looking for some example codes (if any) and helping literature that would help me to understand the granularity of implementation on FPGA.

Looking forward to suggestions. Thanks a lot !

Hi,

Here are my initial thoughts

1) You can precompute your chosen CDF and insert it in a look up table. This will reduce a lot of run time computations.

2) You then generate runtime initial random numbers say from shift registers with feedback taps and assume they are in the range 0-1 e.g a 16 bit shift register will generate numbers between 1 and 2^16 then you can assume the ratio as the generated number relative to 2^16

3) use the generated numbers to address the look up table. The content will be your inverse sample.

thanks :-)

Kaz it was a helpful reply... I have posted another question on the forum. Can you also please help me in that question. Here is the link: https://www.fpgarelated.com/thread/10860/