Is this statement contradicting with the band-limiting theorem? The following sentences are from the footnote of page 240 in R.C. Gonzalez's Digital Image Processing (3rd): 


  An important special case is when a function that extends from -Inf to
  +Inf is band-limited and periodic. In this case, the function can be truncated and still be band-limited, provided that the truncation
  encompass- es exactly an integral number of periods. A single
  truncated period (and thus the function) can be repre- sented by a set
  of discrete samples satisfying the sampling theorem, taken over the
  truncated interval.


Isn't these contradicting to the band-limiting theorem that a bandlimited signal cannot be also timelimited?
there is some choice of words i would do differently.  

yes truncating the infinite bandlimited function makes it time-limited and then band-unlimited.  but truncating it to an integer number of periods still allows one to fully describe it with discrete samples.  

a periodic function can be described with a Fourier series.  the Fourier coefficients will virtually entirely describe the periodic function.

a bandlimited and periodic function can be completely described with a finite set of Fourier coefficients.  also a bandlimited and periodic function can be completely described by sampling a single period with a sufficient number of samples that are spaced closer in time than $\frac{1}{2B}$ where $B$ is the bandlimit.