Nyquist Frequency Phase Shift The figure below shows in dashed lines sinusoidal signals of the same frequency at three different phase shifts.  The signals are then sampled such that the sinusoidal frequency is exactly a half of the sampling frequency, i.e. the frequency of all the sinusoids is the Nyquist frequency.  The samples taken from this signal are represented by the circles.



From the figure, it seems that the amplitude of the digital sinusoidal signals is dependent upon the sampling rate and instant of sampling.  In fact if the sampling times coincide with the zero-crossings of the sinusoid, then no signal will be detected at all.

I had initially thought that sampling a bandlimited analog signal at the appropriate sampling frequency would enable perfect reconstruction, but this counter-example has left me stumped.  It seems that this sinusoid will generally not be reconstructed properly if digitized and then reconstructed at this rate.  Have I gone wrong in my understanding, and if so, can someone please point me in the right direction?

Cheers!
The sampling theorem states that $f_\mathrm{S} \geq 2f_\mathrm{max}$, where $f_\mathrm{S}$ and $f_\mathrm{max}$ are the sampling and maximum signal freuqency, respectively. But there's an additional condition: The equal sign only holds if the signal spectrum does not contain a dirac impulse at $f_\mathrm{S}/2$ which is clearly the case in your example. Therefore $f_\mathrm{S} &gt; 2f_\mathrm{max}$ has to be fulfilled.
A reference for this statement can be found here, for example:

If a signal contains a component at exactly B hertz, then samples spaced at exactly 1/(2B) seconds do not completely determine the signal, Shannon's statement notwithstanding. This sufficient condition can be weakened, as discussed at Sampling of non-baseband signals below.
More recent statements of the theorem are sometimes careful to exclude the equality condition; that is, the condition is if x(t) contains no frequencies higher than or equal to B; this condition is equivalent to Shannon's except when the function includes a steady sinusoidal component at exactly frequency B.

The above is an excerpt of an earlier version of the according Wikipedia article.