How do I apply the Nyquist criterion on the following spectrum to see if it satisfies the criterion or not? I am trying to find out if the pulse in the figure satisfies the Nyquist criterion for a modulation interval T. I'm used to the Nyqusit frequency, but I cannot grasp what the Nyquist criterion is about.
The Nyquist criterion for avoiding intersymbol interference (ISI) requires the pulse to have zeros at multiples of the symbol interval $T$, such that symbols do not interfere with each other. The time domain requirement is

$$h(t)=\begin{cases}1,&amp;t=0\\0,&amp;t=nT\end{cases}\tag{1}$$

In the frequency domain, criterion $(1)$ can be formulated as

$$\sum_{k=-\infty}^{\infty}H\left(f-\frac{k}{T}\right)=T\tag{2}$$

where $H(f)$ is the Fourier transform of $h(t)$. I.e., the shifted spectra (shifted by the symbol rate) must add up to a constant.

I leave it up to you to decide whether or not the given pulse satisfies $(1)$ and $(2)$.

I suggest you go through your lectures notes because it would be surprising if the Nyquist criterion has never been mentioned and you get an exercise like this.