... in^4.1

$n^k$ is the value contained in row $n$ and column $k$ in matrix $\mathbf{N}$

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... expansion^4.2

This transform is also commonly referred to as the principal component or Hotelling-transform. Hotelling was the first to derive the transformation of discrete variables into uncorrelated coefficients. He referred to it as the ``method of principal components". The analogous transformation for transforming continuous data was discovered by Karhunen and Loève [GW92].

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... zero-pad^5.1

Zero-padding to 1024 samples is done for all spectra throughout the thesis, if not stated otherwise. With decreasing $N$, the frequency resolution comes larger but the basic trend remains the same.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.