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# Selective Listening: Drown Out the Noise- FICA Assumptions

Summary: An overview of the conditions that must be met in order for fastICA to work successfully.

## FICA Assumptions

The fastICA algorithm is founded upon several important assumptions:

1. The sources are all independent random variables: i.e. P(AB)= P(A)P(B)
2. The sum of signals into a microphone is linear.
3. The signal energy is finite
4. The mathematical model is represented as y=Hx where y is the observed mixed signal, H is the square mixing matrix, and x is the source. It is important to note, as will be discussed later, that this assumption states that the mixing matrix is multiplicative with the source.
5. All signals are recorded simultaneously, analogous to the Cocktail Party problem.
6. The number of sources and the number of microphones is equal. The fastICA will find as many independent component sources as there are microphones, which input the mixed signals.

All of these assumptions must be met in order for the fastICA algorithm to successfully isolate the independent sources from one another.

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