It is useful to maintain the same shape while the frequency parameter is varied.
2.
As such, the nucleotide GTR requires 6 substitution rate parameters and 4 equilibrium base frequency parameters.
3.
Since the 4 frequency parameters must sum to 1, there are only 3 free frequency parameters.
4.
Since the 4 frequency parameters must sum to 1, there are only 3 free frequency parameters.
5.
To adapt the system to different propagation conditions, the number of tones and the bandwidth can be changed and the time and frequency parameters are proportionally scaled.
6.
In addition to classical FFT-based methods used for the calculation of frequency parameters, a more appropriate PSD estimation method is the Lomb Scargle ( LS ) periodogram.
7.
Therefore, GTR ( for four characters, as is often the case in phylogenetics ) requires 6 substitution rate parameters, as well as 4 equilibrium base frequency parameters.
8.
The inverse operation is usually accomplished by replacing instances of the frequency parameter, \ textstyle f, with \ textstyle f / f _ s or \ textstyle f \ cdot T.
9.
In probability theory, the Fourier transform of the probability distribution of a real-valued random variable " X " is called the characteristic function of that variable, and can be defined as the expected value of " e " " i tX ", as a function of the real variable " t " ( the frequency parameter of the Fourier transform ).
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