As a major detection and identification method, cyclostationary detection (CSD) has been studied extensively for cognitive radio and other applications as well. CSD uses the cyclostationary features inherited in modulated communication signals to differentiate desired signal from other signals or noise. However, the impairments in the communication chain, like clock error or oscillator error or other errors, induces changes to the cyclostationary features. This causes a cyclic frequency mismatch in the detection. In this paper, the impact of cyclic frequency mismatch is studied mathematically in detail for the digitally modulated signals. Closed-form expressions for the discrete cyclic auto-correlations at any given number of samples are found. Furthermore, robustness of the cyclostationary detection to the cyclic frequency mismatch is found in an explicit expression. The theoretic analysis matches very well with simulations and can be used for predicting the detection performances and optimizing system parameters.