The mathematical operation of correlation is a very simple concept, yet has a very rich history of application in a variety of engineering fields. It is essentially nothing but a technique to measure if and to what degree two signals match each other. Since this is a very basic and universal task in a wide variety of fields such as signal processing, communications, computer vision etc., it has been an important tool. The field of pattern recognition often deals with the task of analyzing signals or useful information from signals and classifying them into classes. Very often, these classes are predetermined, and examples (templates) are available for comparison. This task naturally lends itself to the application of correlation as a tool to accomplish this goal. Thus the field of Correlation Pattern Recognition has developed over the past few decades as an important area of research. From the signal processing point of view, correlation is nothing but a filtering operation. Thus there has been a great deal of work in using concepts from filter theory to develop Correlation Filters for pattern recognition. While considerable work has been to done to develop linear correlation filters over the years, especially in the field of Automatic Target Recognition, a lot of attention has recently been paid to the development of Quadratic Correlation Filters (QCF). QCFs offer the advantages of linear filters while optimizing a bank of these simultaneously to offer much improved performance. This dissertation develops efficient QCFs that offer significant savings in storage requirements and computational complexity over existing designs. Firstly, an adaptive algorithm is presented that is able to modify the QCF coefficients as new data is observed. Secondly, a transform domain implementation of the QCF is presented that has the benefits of lower computational complexity and computational requirements while retaining excellent recognition accuracy. Finally, a two dimensional QCF is presented that holds the potential to further save on storage and computations. The techniques are developed based on the recently proposed Rayleigh Quotient Quadratic Correlation Filter (RQQCF) and simulation results are provided on synthetic and real datasets.