Description: 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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