Exercise
[1, p. 14 exercise 1.1] asks to prove that
is a monotonically increasing function over the interval
![0<x<1](https://lysario.de/wp-content/cache/tex_aa135e67321926f181d788c1a35afdf2.png)
. Furthermore it asks to show that due to the monotonicity of the peaks of the spectral estimate shown in
[1, Figure 1.2b] that they must also be present in the spectral estimate of
[1, Figure 1.2a].
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