An Elementary Introduction to the Discrete Fourier Transform 1.1 ComplexNumbers 1.3 Analyzing the Series 1.5 Filtering a Signal 1.6 How Often Does One Sample? 1.7 Notes and References 1.2 Trigonometric Interpolation 1.4 Fourier Frequency Versus Time Frequency 2 Some Mathematical and Computational Preliminaries 2.1 Computing the Twiddle Factors 2.2.1 Real floating-point operation (FLOP) count 2.2.2 Special considerations in computing the FFT 2.3 Expressing Complex Multiply-Adds in Terms of Real Multiply-Adds 2.4 Solving Recurrences to Determine an Unknown Function 2.2 Multiplying Two Complex Numbers II Sequential FFT Algorithms 3 The Divide-and-Conquer Paradigm and Two Basic FFT Algorithms 3.1 Radix-2 Decimation-In-Time (DIT) FFT 3.1.1 Analyzing the arithmetic cost 3.2 Radix-2 Decimation-In-Frequency (DIF) FFT 3.2.1 Analyzing the arithmetic cost 3.3 Notes and References

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