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The reliability of cervical cytology for the detection of premalignant and malignant disease is dependent on proper sampling of the transformation zone. The use of a cervical brush to collect enough endocervical cells is more effective, than the use of the conventional cotton swab.
Riemann sums and counting measure are used to motivate an intuitive derivation of the discrete Fourier transform. Poisson summation is then used to obtain an error estimate for the DFT with respect to the continuous Fourier transform on the circle. This paper fulfills a term-paper requirement for Bill Faris’ spring 2006 Real Analysis course (Math 523B).