  The construction of finite tight Gabor frames plays an important role in many
applications. These applications include significant ones in signal and image
processing. We explore when constant amplitude zero autocorrelation (CAZAC)
sequences can be used to generate tight Gabor frames. The main theorem uses
Janssen's representation and the zeros of the discrete periodic ambiguity
function to give necessary and sufficient conditions for determining whether
any Gabor frame is tight. The relevance of the theorem depends significantly on
the construction of examples. These examples are necessarily intricate, and to
a large extent, depend on CAZAC sequences. Finally, we present an alternative
method for determining whether a Gabor system yields a tight frame. This
alternative method does not prove tightness using the main theorem, but instead
uses the Gram matrix of the Gabor system.
