- Factoring a Polynomial
- The Quadratic Formula
- Complex Roots
- Fundamental Theorem of Algebra
- Complex Basics
- The Complex Plane
- More Notation and Terminology
- Elementary Relationships
- Euler's Identity
- De Moivre's Theorem
- Conclusion
- Complex_Number Problems
- Euler's Identity
- Positive Integer Exponents
- Properties of Exponents
- The Exponent Zero
- Negative Exponents
- Rational Exponents
- Real Exponents
- A First Look at Taylor Series
- Imaginary Exponents
- Derivatives of f(x) = a to the power x
- Back to e
- e^(j theta)
- Back to Mth Roots
- Roots of Unity
- Direct Proof of De Moivre's Theorem
- Euler_Identity Problems
- Sinusoids
- Exponentials
- Complex Sinusoids
- Circular Motion
- Projection of Circular Motion
- Positive and Negative Frequencies
- Plotting Complex Sinusoids versus Frequency
- Sinusoidal Amplitude Modulation (AM)
- Sinusoidal Frequency Modulation (FM)
- Analytic Signals and Hilbert Transform Filters
- Generalized Complex Sinusoids
- Sampled Sinusoids
- Powers of z
- Phasors and Carriers
- Importance of Generalized Complex Sinusoids
- Comparing Analog and Digital Complex Planes
- Sinusoid Problems
- The DFT
- Signals as Vectors
- Vector Addition
- Vector Subtraction
- Scalar Multiplication
- Linear Combination of Vectors
- Linear Vector Space
- Signal Metrics
- The Inner Product
- Signal Reconstruction from Projections
- Signal Projection Problems
- Geometric Series
- Orthogonality of Sinusoids
- Orthogonality of the DFT Sinusoids
- Norm of the DFT Sinusoids
- An Orthonormal Sinusoidal Set
- The Discrete Fourier Transform (DFT)
- Frequencies in the ``Cracks''
- Spectral Bin Numbers
- Fourier Series Special Case
- Normalized DFT
- The Length 2 DFT
- Matrix Formulation of the DFT
- DFT Problems
- The DFT and its Inverse Restated
- Signal Operators
- Even and Odd Functions
- Fourier Theorems
- Linearity
- Conjugation and Reversal
- Symmetry
- Shift Theorem
- Convolution Theorem
- Dual of the Convolution Theorem
- Correlation Theorem
- Power Theorem
- Rayleigh Energy Theorem (Parseval's Theorem)
- Stretch Theorem (Repeat Theorem)
- Downsampling Theorem (Aliasing Theorem)
- Zero Padding Theorem (Spectral Interpolation)
- Interpolation Theorems
- DFT Theorems Problems
- Why a DFT is usually called an FFT in practice
- Spectrum Analysis of a Sinusoid
- Spectrograms
- Filters and Convolution
- Correlation Analysis
- Power Spectral Density
- Coherence Function
- Recommended Further Reading
- Mixed-Radix Cooley-Tukey FFT
- Prime Factor Algorithm (PFA)
- Rader's FFT Algorithm for Prime Lengths
- Bluestein's FFT Algorithm
- Fast Transforms in Audio DSP
- Related Transforms
- FFT Software
- Introduction to Sampling
- Aliasing of Sampled Signals
- Sampling Theorem
- Geometric Sequence Frequencies
- Informal Derivation of Taylor Series
- Taylor Series with Remainder
- Formal Statement of Taylor's Theorem
- Weierstrass Approximation Theorem
- Points of Infinite Flatness
- Differentiability of Audio Signals
- Complex Numbers in Matlab and Octave
- Factoring Polynomials in Matlab
- Geometric Signal Theory
- The DFT
- Spectrogram Computation
