Advantages of the Rotation Translation Operation Before Doing FT Smoothing
Upon closer inspection, this doesn't even seem to be a rotation:

$R_n$ being the output sample corresponding to the input sample $A_n$, we can understand their equation


  $$R_n = A_n - \Delta_n \tag1$$


as the statement that we add sequence $(-\Delta_n)_{n=1,\ldots,k}$ to the input signal $a$ and get the output signal $r$. I'll call that sequence $s$, $S_n := -\Delta_n$. 

Let's look at this not on the individual sample level, but from a signal level:

$$r = a + s\tag{*}\label{additive}$$

From $\eqref{additive}$ we can see that this is just adding another signal to the input signal.

Let's have a closer look at $S$, as they claim it compensates spectral components present in $R$:

\begin{align}
s_n &amp;= \underbrace{-A_1}_{\text{const.}} - \frac{\overbrace{(A_k - A_1)}^{\text{const.}}(n-1)}{\underbrace{k-1}_{\text{const.}}}&amp;
\text{eq. (2) from paper}\\
&amp;= -A_1 + \frac{A_1-A_k}{k-1}(n-1)\\
&amp;=\underbrace{\frac{A_1-A_k}{k-1}}_{c_1}n -\underbrace{\left(\frac{A_1-A_k}{k-1}+A_1
\right)}_{-c_2}\\
&amp;=c_1n+c_2
\end{align}

That is... underwhelming. The magical rotation is just an addition with a ramp of slope $\frac{A_1-A_k}{k-1}$. So let's look at the FFT of that:

\begin{align}\DeclareMathOperator{\dft}{\mathrm{DFT}_k}
\dft\{s\}[l] &amp;= \dft\{c_1n\}[l] + \dft\{-c_2\}[l]\\
&amp;= \begin{cases}
-kc_2+c_1\displaystyle \frac{k(k-1)}{2},&amp;\quad l=0\\
-c_1\displaystyle\frac{k}{1-e^{-j2\pi l/k}},&amp;\quad l\in[1,k-1]
\end{cases} \label{matt}\tag{;}\\
\end{align}

Eq. $\eqref{matt}$ follows according to Matt. 

I see absolute no sense in these operation – it  actively introduces an error term, that will skew an estimate the original exponential decay signal model, to the signal – without that actually being there.

So, that "pseudoration" actually fakes an exponential decay  component that depends less on the actual exponential decay of the signal than on the observation length $k$. That transform is bad and you shouldn't use it.



Generally, applying a rectangular window in frequency domain – which seems to be what they're aiming for – is simply a bad idea for circular convolution reasons. 
We've got a pretty good answer explaining why that's the case. The fact that this isn't bad here is that there's little signal at the end of the observation anyway – but I don't see how folding that over your beginning actually improves the data! It just makes it look smoother.