DSP Quest — Page Manifest

Full enumeration of every leaf section in Spectral Audio Signal Processing (SASP) by Julius O. Smith III. Each line corresponds to one HTML page in this site. The rule is: no line may be deleted until the page is built.

= page built and reviewed
[~] = page built, needs review
= not started

All pages must be bilingual (English first, then Traditional Chinese), use the 8-bit NES theme, include at least one interactive canvas where meaningful, and wrap Chinese technical terms in  for hover tooltips.

World 1 · Preface (ch01-preface/)

[~] 1.1 Acknowledgments — ch01-preface/1.1-acks.html
[~] 1.2 Book Series Overview — ch01-preface/1.2-series.html
[~] 1.3 Errata — ch01-preface/1.3-errata.html

World 2 · Introduction and Overview (ch02-introduction/)

[~] 2.1 Organization — ch02-introduction/2.1-organization.html
[~] 2.2 Overview — ch02-introduction/2.2-overview.html
[~] 2.2.1 Elementary Spectrum Analysis — ch02-introduction/2.2.1-elementary-spec.html
[~] 2.2.2 STFT & Time-Frequency Displays — ch02-introduction/2.2.2-stft-tf.html
[~] 2.2.3 Short-Time Analysis · Modification · Resynth. — ch02-introduction/2.2.3-stam.html
[~] 2.2.4 STFT Applications — ch02-introduction/2.2.4-apps.html
[~] 2.2.5 Multirate Polyphase & Wavelet Filter Banks — ch02-introduction/2.2.5-multirate.html
[~] 2.2.6 Appendices — ch02-introduction/2.2.6-appendices.html

World 3 · Fourier Transforms and Theorems (ch03-fourier-transforms/)

[~] 3.1 Discrete Time Fourier Transform — ch03-fourier-transforms/3.1-dtft.html
[~] 3.2 Fourier Transform (FT) and Inverse · Existence — ch03-fourier-transforms/3.2-ft-and-inverse.html
[~] 3.3 Linearity of the DTFT — ch03-fourier-transforms/3.3-linearity.html
[~] 3.4 Time Reversal — ch03-fourier-transforms/3.4-time-reversal.html
[~] 3.5 Symmetry of the DTFT for Real Signals — ch03-fourier-transforms/3.5-symmetry.html
[~] 3.5.1 DTFT of Real Signals — ch03-fourier-transforms/3.5.1-dtft-real.html
[~] 3.5.2 Real Even (or Odd) Signals — ch03-fourier-transforms/3.5.2-real-even-odd.html
[~] 3.6 Shift Theorem — ch03-fourier-transforms/3.6-shift.html
[~] 3.7 Convolution Theorem — ch03-fourier-transforms/3.7-convolution.html
[~] 3.8 Correlation Theorem — ch03-fourier-transforms/3.8-correlation.html
[~] 3.9 Autocorrelation — ch03-fourier-transforms/3.9-autocorrelation.html
[~] 3.10 Power Theorem (Parseval) — ch03-fourier-transforms/3.10-power.html
[~] 3.11 Stretch Operator — ch03-fourier-transforms/3.11-stretch.html
[~] 3.12 Repeat (Scaling) Operator — ch03-fourier-transforms/3.12-repeat.html
[~] 3.13 Stretch/Repeat (Scaling) Theorem — ch03-fourier-transforms/3.13-stretch-repeat.html
[~] 3.14 Downsampling and Aliasing — ch03-fourier-transforms/3.14-downsampling-aliasing.html
[~] 3.14.1 Proof of Aliasing Theorem — ch03-fourier-transforms/3.14.1-aliasing-proof.html
[~] 3.15 Differentiation Theorem Dual — ch03-fourier-transforms/3.15-diff-dual.html
[~] 3.16 Continuous-Time Fourier Theorems — ch03-fourier-transforms/3.16-ct-theorems.html
[~] 3.16.1 Scaling Theorem — ch03-fourier-transforms/3.16.1-scaling.html
[~] 3.16.2 Spectral Roll-Off — ch03-fourier-transforms/3.16.2-rolloff.html
[~] 3.17 Spectral Interpolation — ch03-fourier-transforms/3.17-spectral-interpolation.html
[~] 3.17.1 Ideal Spectral Interpolation — ch03-fourier-transforms/3.17.1-ideal-interp.html
[~] 3.17.2 Interpolating a DFT — ch03-fourier-transforms/3.17.2-interp-dft.html
[~] 3.17.3 Zero Padding in the Time Domain — ch03-fourier-transforms/3.17.3-zero-pad.html
[~] 3.17.3.1 Practical Zero Padding — ch03-fourier-transforms/3.17.3.1-practical-zp.html
[~] 3.17.3.2 Zero-Padding to Next Power of 2 — ch03-fourier-transforms/3.17.3.2-zp-pow2.html
[~] 3.17.3.3 ZP for Interpolating Spectral Displays — ch03-fourier-transforms/3.17.3.3-zp-display.html
[~] 3.17.3.4 ZP for Interpolating Spectral Peaks — ch03-fourier-transforms/3.17.3.4-zp-peaks.html
[~] 3.17.4 Zero-Phase Zero Padding — ch03-fourier-transforms/3.17.4-zero-phase-zp.html
[~] 3.17.4.1 Matlab/Octave fftshift utility — ch03-fourier-transforms/3.17.4.1-fftshift.html
[~] 3.17.4.2 Index Ranges for Zero-Phase ZP — ch03-fourier-transforms/3.17.4.2-zphase-idx.html
[~] 3.18 Summary — ch03-fourier-transforms/3.18-summary.html

World 4 · Spectrum Analysis Windows (ch04-windows/)

[~] 4.1 The Rectangular Window — ch04-windows/4.1-rectangular.html
[~] 4.1.1 Side Lobes — ch04-windows/4.1.1-sidelobes.html
[~] 4.1.2 Summary (Rect) — ch04-windows/4.1.2-rect-summary.html
[~] 4.2 Generalized Hamming Window Family — ch04-windows/4.2-generalized-hamming.html
[~] 4.2.1 Hann (Hanning · Raised Cosine) — ch04-windows/4.2.1-hann.html
[~] 4.2.2 Matlab for the Hann Window — ch04-windows/4.2.2-matlab-hann.html
[~] 4.2.3 Hamming Window — ch04-windows/4.2.3-hamming.html
[~] 4.2.4 Matlab for the Hamming Window — ch04-windows/4.2.4-matlab-hamming.html
[~] 4.2.5 Summary of Generalized Hamming Windows — ch04-windows/4.2.5-ghamming-summary.html
[~] 4.2.6 MLT Sine Window — ch04-windows/4.2.6-mlt-sine.html
[~] 4.3 Blackman-Harris Window Family — ch04-windows/4.3-blackman-harris.html
[~] 4.3.1 Blackman Window Family — ch04-windows/4.3.1-blackman-family.html
[~] 4.3.2 Classic Blackman — ch04-windows/4.3.2-classic-blackman.html
[~] 4.3.3 Matlab for Classic Blackman — ch04-windows/4.3.3-matlab-blackman.html
[~] 4.3.4 Three-Term Blackman-Harris — ch04-windows/4.3.4-3term-bh.html
[~] 4.3.5 Frequency-Domain Blackman-Harris — ch04-windows/4.3.5-fd-bh.html
[~] 4.3.6 Power-of-Cosine Window Family — ch04-windows/4.3.6-pow-cos.html
[~] 4.4 Spectrum Analysis of an Oboe Tone — ch04-windows/4.4-oboe.html
[~] 4.4.1 Rect-Windowed Oboe — ch04-windows/4.4.1-oboe-rect.html
[~] 4.4.2 Hamming-Windowed Oboe — ch04-windows/4.4.2-oboe-hamming.html
[~] 4.4.3 Blackman-Windowed Oboe — ch04-windows/4.4.3-oboe-blackman.html
[~] 4.4.4 Conclusions (Oboe) — ch04-windows/4.4.4-oboe-conclusion.html
[~] 4.5 Bartlett (Triangular) Window — ch04-windows/4.5-bartlett.html
[~] 4.5.1 Matlab for the Bartlett Window — ch04-windows/4.5.1-matlab-bartlett.html
[~] 4.6 Poisson Window — ch04-windows/4.6-poisson.html
[~] 4.7 Hann-Poisson Window — ch04-windows/4.7-hann-poisson.html
[~] 4.7.1 Matlab for the Hann-Poisson Window — ch04-windows/4.7.1-matlab-hann-poisson.html
[~] 4.8 Slepian / DPSS Window — ch04-windows/4.8-dpss.html
[~] 4.8.1 Matlab for the DPSS Window — ch04-windows/4.8.1-matlab-dpss.html
[~] 4.9 Kaiser Window — ch04-windows/4.9-kaiser.html
[~] 4.9.1 Kaiser Window Beta Parameter — ch04-windows/4.9.1-kaiser-beta.html
[~] 4.9.2 Kaiser Windows and Transforms — ch04-windows/4.9.2-kaiser-xforms.html
[~] 4.9.3 Minimum Frequency Separation vs. Length — ch04-windows/4.9.3-kaiser-sep.html
[~] 4.9.4 Kaiser and DPSS Compared — ch04-windows/4.9.4-kaiser-vs-dpss.html
[~] 4.10 Dolph-Chebyshev Window — ch04-windows/4.10-dolph-chebyshev.html
[~] 4.10.1 Matlab for Dolph-Chebyshev — ch04-windows/4.10.1-matlab-cheby.html
[~] 4.10.2 Example Chebyshev Windows — ch04-windows/4.10.2-cheby-examples.html
[~] 4.10.3 Chebyshev vs Hamming — ch04-windows/4.10.3-cheby-vs-hamming.html
[~] 4.10.4 Dolph-Chebyshev Window Theory — ch04-windows/4.10.4-cheby-theory.html
[~] 4.10.4.1 Chebyshev Polynomials — ch04-windows/4.10.4.1-cheby-poly.html
[~] 4.10.4.2 Dolph-Chebyshev Window Definition — ch04-windows/4.10.4.2-cheby-def.html
[~] 4.10.4.3 Main-Lobe Width — ch04-windows/4.10.4.3-cheby-mainlobe.html
[~] 4.10.4.4 Length Computation — ch04-windows/4.10.4.4-cheby-length.html
[~] 4.11 Gaussian Window and Transform — ch04-windows/4.11-gaussian.html
[~] 4.11.1 Matlab for the Gaussian Window — ch04-windows/4.11.1-matlab-gaussian.html
[~] 4.11.2 Gaussian Window and Transform (detail) — ch04-windows/4.11.2-gauss-xform.html
[~] 4.11.3 Exact Discrete Gaussian Window — ch04-windows/4.11.3-exact-discrete-gauss.html
[~] 4.12 Optimized Windows — ch04-windows/4.12-optimized.html
[~] 4.12.1 Optimal Windows for Audio Coding — ch04-windows/4.12.1-audio-coding.html
[~] 4.12.2 General Rule — ch04-windows/4.12.2-general-rule.html
[~] 4.13 Optimal Window Design by linprog — ch04-windows/4.13-linprog.html
[~] 4.13.1 Linear Programming — ch04-windows/4.13.1-lp.html
[~] 4.13.2 LP Formulation of Chebyshev Window Design — ch04-windows/4.13.2-lp-cheby.html
[~] 4.13.3 Symmetric Window Constraint — ch04-windows/4.13.3-sym-constraint.html
[~] 4.13.4 Positive Window-Sample Constraint — ch04-windows/4.13.4-pos-constraint.html
[~] 4.13.5 DC Constraint — ch04-windows/4.13.5-dc-constraint.html
[~] 4.13.6 Sidelobe Specification — ch04-windows/4.13.6-sidelobe-spec.html
[~] 4.13.7 LP Standard Form — ch04-windows/4.13.7-lp-std.html
[~] 4.13.8 Remez Exchange Algorithm — ch04-windows/4.13.8-remez.html
[~] 4.13.8.1 Convergence of Remez — ch04-windows/4.13.8.1-remez-conv.html
[~] 4.13.9 Monotonicity Constraint — ch04-windows/4.13.9-monotonic.html
[~] 4.13.10 L-Infinity Norm of Derivative Objective — ch04-windows/4.13.10-linf-deriv.html
[~] 4.13.11 L-One Norm of Derivative Objective — ch04-windows/4.13.11-l1-deriv.html
[~] 4.13.12 Summary (Windows) — ch04-windows/4.13.12-windows-summary.html

World 5 · FIR Digital Filter Design (ch05-fir-design/)

[~] 5.1 Ideal Lowpass Filter — ch05-fir-design/5.1-ideal-lp.html
[~] 5.2 Lowpass Filter Design Specifications — ch05-fir-design/5.2-lp-specs.html
[~] 5.2.1 Ideal Lowpass Filter Revisited — ch05-fir-design/5.2.1-ideal-lp2.html
[~] 5.3 Least-Squares FIR Design — ch05-fir-design/5.3-ls.html
[~] 5.3.1 Examples (LS) — ch05-fir-design/5.3.1-ls-examples.html
[~] 5.4 Frequency-Sampling FIR Design — ch05-fir-design/5.4-freq-samp.html
[~] 5.5 Window Method for FIR Design — ch05-fir-design/5.5-window-method.html
[~] 5.5.1 Matlab Support for the Window Method — ch05-fir-design/5.5.1-matlab-window.html
[~] 5.5.2 Bandpass Filter Design Example — ch05-fir-design/5.5.2-bp-example.html
[~] 5.5.2.1 Under the Hood of kaiserord — ch05-fir-design/5.5.2.1-kaiserord.html
[~] 5.5.2.2 Comparison to Optimal Chebyshev FIR BP — ch05-fir-design/5.5.2.2-vs-cheby.html
[~] 5.6 Hilbert Transform Design Example — ch05-fir-design/5.6-hilbert.html
[~] 5.6.1 Hilbert Transform Theory — ch05-fir-design/5.6.1-hilbert-theory.html
[~] 5.6.1.1 Hilbert Transform (definition) — ch05-fir-design/5.6.1.1-hilbert-def.html
[~] 5.6.2 Preparing the Desired Impulse Response — ch05-fir-design/5.6.2-desired-ir.html
[~] 5.6.2.1 Matlab, Continued — ch05-fir-design/5.6.2.1-matlab-cont.html
[~] 5.6.2.2 Kaiser Window (in Hilbert design) — ch05-fir-design/5.6.2.2-kaiser-in-hilbert.html
[~] 5.6.2.3 Hilbert Transformer by Window Method — ch05-fir-design/5.6.2.3-hilbert-window.html
[~] 5.6.3 More General FIR Filter Design — ch05-fir-design/5.6.3-general-fir.html
[~] 5.6.4 Comparison to Optimal Chebyshev FIR — ch05-fir-design/5.6.4-vs-optimal.html
[~] 5.6.5 Conclusions (Hilbert) — ch05-fir-design/5.6.5-hilbert-conclusion.html
[~] 5.7 Generalized Window Method — ch05-fir-design/5.7-generalized-window.html
[~] 5.8 Minimum-Phase Filter Design — ch05-fir-design/5.8-min-phase.html
[~] 5.9 Minimum-Phase and Causal Cepstra — ch05-fir-design/5.9-min-phase-cepstra.html
[~] 5.10 Optimal FIR Digital Filter Design — ch05-fir-design/5.10-optimal-fir.html
[~] 5.10.1 Lp Norms — ch05-fir-design/5.10.1-lp-norms.html
[~] 5.10.1.1 Special Cases (Lp) — ch05-fir-design/5.10.1.1-lp-special.html
[~] 5.10.1.2 Filter Design using Lp Norms — ch05-fir-design/5.10.1.2-lp-design.html
[~] 5.10.2 Optimal Chebyshev FIR Filters — ch05-fir-design/5.10.2-optimal-cheby.html
[~] 5.10.3 Least-Squares Linear-Phase FIR Design — ch05-fir-design/5.10.3-ls-linphase.html
[~] 5.10.3.1 Geometric Interp. of Least Squares — ch05-fir-design/5.10.3.1-ls-geom.html
[~] 5.10.3.2 Matlab Support for LS FIR — ch05-fir-design/5.10.3.2-ls-matlab.html
[~] 5.10.4 Chebyshev FIR Design via LP — ch05-fir-design/5.10.4-cheby-lp.html
[~] 5.10.5 More General Real FIR Filters — ch05-fir-design/5.10.5-general-real.html
[~] 5.10.6 Nonlinear-Phase FIR Filter Design — ch05-fir-design/5.10.6-nonlin-phase.html
[~] 5.10.6.1 Problem Formulation — ch05-fir-design/5.10.6.1-nlp-problem.html
[~] 5.10.7 Matlab for General FIR Filter Design — ch05-fir-design/5.10.7-matlab-general.html
[~] 5.10.8 Second-Order Cone Problems — ch05-fir-design/5.10.8-socp.html
[~] 5.10.8.1 Resources — ch05-fir-design/5.10.8.1-socp-resources.html
[~] 5.10.9 Nonlinear Optimization in Matlab — ch05-fir-design/5.10.9-nonlin-opt.html

World 6 · Spectrum Analysis of Sinusoids (ch06-sinusoids/)

[~] 6.1 Spectrum of a Sinusoid — ch06-sinusoids/6.1-spec-sinusoid.html
[~] 6.2 Spectrum of Sampled Complex Sinusoid — ch06-sinusoids/6.2-spec-sampled-complex.html
[~] 6.3 Spectrum of a Windowed Sinusoid — ch06-sinusoids/6.3-windowed-sinusoid.html
[~] 6.4 Effect of Windowing — ch06-sinusoids/6.4-effect-of-windowing.html
[~] 6.4.1 Frequency Resolution — ch06-sinusoids/6.4.1-freq-resolution.html
[~] 6.4.1.1 Two Cosines ("In-Phase") — ch06-sinusoids/6.4.1.1-two-cosines.html
[~] 6.4.1.2 Sine + Cosine (Phase Quadrature) — ch06-sinusoids/6.4.1.2-sine-cos-quad.html
[~] 6.5 Resolving Sinusoids — ch06-sinusoids/6.5-resolving.html
[~] 6.5.1 Other Definitions of Main-Lobe Width — ch06-sinusoids/6.5.1-mainlobe-defs.html
[~] 6.5.2 Simple Sufficient Condition for Peak Res. — ch06-sinusoids/6.5.2-peak-resolution.html
[~] 6.5.3 Periodic Signals — ch06-sinusoids/6.5.3-periodic.html
[~] 6.5.4 Tighter Bounds for Min Window Length — ch06-sinusoids/6.5.4-tighter-bounds.html
[~] 6.5.5 Summary — ch06-sinusoids/6.5.5-resolve-summary.html
[~] 6.6 Sinusoidal Peak Interpolation — ch06-sinusoids/6.6-peak-interp.html
[~] 6.6.1 Quadratic Interpolation of Spectral Peaks — ch06-sinusoids/6.6.1-quadratic-interp.html
[~] 6.6.1.1 Phase Interpolation at a Peak — ch06-sinusoids/6.6.1.1-phase-interp.html
[~] 6.6.1.2 Matlab for Parabolic Peak Interp. — ch06-sinusoids/6.6.1.2-matlab-qint.html
[~] 6.6.2 Bias of Parabolic Peak Interpolation — ch06-sinusoids/6.6.2-parabolic-bias.html
[~] 6.7 Optimal Peak-Finding in the Spectrum — ch06-sinusoids/6.7-optimal-peak.html
[~] 6.7.1 Min Zero-Padding for High-Freq Peaks — ch06-sinusoids/6.7.1-min-zp-high.html
[~] 6.7.2 Min Zero-Padding for Low-Freq Peaks — ch06-sinusoids/6.7.2-min-zp-low.html
[~] 6.7.3 Matlab for Min ZP Factors — ch06-sinusoids/6.7.3-matlab-zp.html
[~] 6.7.4 Least-Squares Sinusoidal Param Estimation — ch06-sinusoids/6.7.4-ls-param.html
[~] 6.7.4.1 Sinusoidal Amplitude Estimation — ch06-sinusoids/6.7.4.1-amp-est.html
[~] 6.7.4.2 Sinusoidal Amplitude & Phase Estimation — ch06-sinusoids/6.7.4.2-amp-phase-est.html
[~] 6.7.4.3 Sinusoidal Frequency Estimation — ch06-sinusoids/6.7.4.3-freq-est.html
[~] 6.7.5 Maximum Likelihood Sinusoid Estimation — ch06-sinusoids/6.7.5-mle.html
[~] 6.7.6 Likelihood Function — ch06-sinusoids/6.7.6-likelihood.html
[~] 6.7.6.1 Multiple Sinusoids in AWGN — ch06-sinusoids/6.7.6.1-mult-sin-awgn.html
[~] 6.7.6.2 Non-White Noise — ch06-sinusoids/6.7.6.2-nonwhite-noise.html
[~] 6.7.7 Generality of ML Least Squares — ch06-sinusoids/6.7.7-general-mle-ls.html

World 7 · Spectrum Analysis of Noise (ch07-noise/)

[~] 7.1 Introduction to Noise — ch07-noise/7.1-intro.html
[~] 7.1.1 Why Analyze Noise? — ch07-noise/7.1.1-why.html
[~] 7.1.2 What is Noise? — ch07-noise/7.1.2-what.html
[~] 7.2 Spectral Characteristics of Noise — ch07-noise/7.2-spec-chars.html
[~] 7.3 White Noise — ch07-noise/7.3-white.html
[~] 7.3.1 Testing for White Noise — ch07-noise/7.3.1-testing-white.html
[~] 7.4 Sample Autocorrelation — ch07-noise/7.4-sample-autocorr.html
[~] 7.5 Sample Power Spectral Density — ch07-noise/7.5-sample-psd.html
[~] 7.6 Biased Sample Autocorrelation — ch07-noise/7.6-biased-autocorr.html
[~] 7.7 Smoothed Power Spectral Density — ch07-noise/7.7-smoothed-psd.html
[~] 7.8 Cyclic Autocorrelation — ch07-noise/7.8-cyclic-autocorr.html
[~] 7.9 Practical Bottom Line — ch07-noise/7.9-bottom-line.html
[~] 7.10 Why an Impulse is Not White Noise — ch07-noise/7.10-impulse-vs-white.html
[~] 7.11 The Periodogram — ch07-noise/7.11-periodogram.html
[~] 7.11.1 Matlab for the Periodogram — ch07-noise/7.11.1-matlab-periodogram.html
[~] 7.12 Welch's Method — ch07-noise/7.12-welch.html
[~] 7.12.1 Welch Autocorrelation Estimate — ch07-noise/7.12.1-welch-autocorr.html
[~] 7.12.2 Resolution versus Stability — ch07-noise/7.12.2-res-vs-stab.html
[~] 7.13 Welch's Method with Windows — ch07-noise/7.13-welch-windows.html
[~] 7.13.1 Matlab for Welch's Method — ch07-noise/7.13.1-matlab-welch.html
[~] 7.14 Filtered White Noise — ch07-noise/7.14-filtered-white.html
[~] 7.14.1 Example: FIR-Filtered White Noise — ch07-noise/7.14.1-fir-white.html
[~] 7.14.2 Example: Synthesis of 1/F (Pink) Noise — ch07-noise/7.14.2-pink.html
[~] 7.14.3 Example: Pink Noise Analysis — ch07-noise/7.14.3-pink-analysis.html
[~] 7.15 Processing Gain — ch07-noise/7.15-processing-gain.html
[~] 7.16 The Panning Problem — ch07-noise/7.16-panning.html

World 8 · Time-Frequency Displays (ch08-time-frequency/)

[~] 8.1 Short-Time Fourier Transform — ch08-time-frequency/8.1-stft.html
[~] 8.1.1 Mathematical Definition of the STFT — ch08-time-frequency/8.1.1-stft-math.html
[~] 8.1.2 Practical Computation of the STFT — ch08-time-frequency/8.1.2-stft-practical.html
[~] 8.1.3 Summary of STFT Computation Using FFTs — ch08-time-frequency/8.1.3-stft-fft-summary.html
[~] 8.1.4 Two Dual Interpretations of the STFT — ch08-time-frequency/8.1.4-stft-duals.html
[~] 8.1.5 STFT as a Time-Frequency Distribution — ch08-time-frequency/8.1.5-stft-tfd.html
[~] 8.1.6 STFT in Matlab — ch08-time-frequency/8.1.6-stft-matlab.html
[~] 8.1.6.1 Notes — ch08-time-frequency/8.1.6.1-notes.html
[~] 8.2 Classic Spectrograms — ch08-time-frequency/8.2-spectrograms.html
[~] 8.2.1 Spectrogram of Speech — ch08-time-frequency/8.2.1-speech-spec.html
[~] 8.3 Audio Spectrograms — ch08-time-frequency/8.3-audio-spec.html
[~] 8.3.1 Auditory Filter Banks — ch08-time-frequency/8.3.1-aud-fb.html
[~] 8.3.2 Loudness Spectrogram — ch08-time-frequency/8.3.2-loudness.html
[~] 8.3.2.1 A Note on Hop Size — ch08-time-frequency/8.3.2.1-hop.html
[~] 8.3.3 Examples — ch08-time-frequency/8.3.3-examples.html
[~] 8.3.3.1 Multiresolution STFT — ch08-time-frequency/8.3.3.1-mrstft.html
[~] 8.3.3.2 Excitation Pattern — ch08-time-frequency/8.3.3.2-excitation.html
[~] 8.3.3.3 Nonuniform Spectral Resampling — ch08-time-frequency/8.3.3.3-nonuniform.html
[~] 8.3.3.4 Auditory Filter Shapes — ch08-time-frequency/8.3.3.4-aud-shapes.html
[~] 8.3.3.5 Specific Loudness — ch08-time-frequency/8.3.3.5-specific-loud.html
[~] 8.3.3.6 Spectrograms Compared — ch08-time-frequency/8.3.3.6-spec-compared.html
[~] 8.3.3.7 Instant / Short-Term / Long-Term Loudness — ch08-time-frequency/8.3.3.7-loud-timescales.html
[~] 8.4 Summary (Ch 8) — ch08-time-frequency/8.4-summary.html

World 9 · Overlap-Add STFT Processing (ch09-ola-stft/)

[~] 9.1 Convolution of Short Signals — ch09-ola-stft/9.1-conv-short.html
[~] 9.1.1 Cyclic FFT Convolution — ch09-ola-stft/9.1.1-cyclic.html
[~] 9.1.2 Acyclic FFT Convolution — ch09-ola-stft/9.1.2-acyclic.html
[~] 9.1.2.1 Acyclic Convolution in Matlab — ch09-ola-stft/9.1.2.1-matlab-acyclic.html
[~] 9.1.2.2 Pictorial View of Acyclic Convolution — ch09-ola-stft/9.1.2.2-pictorial.html
[~] 9.1.3 Acyclic FFT Convolution in Matlab — ch09-ola-stft/9.1.3-acyclic-matlab.html
[~] 9.1.4 FFT versus Direct Convolution — ch09-ola-stft/9.1.4-fft-vs-direct.html
[~] 9.1.4.1 Audio FIR Filters — ch09-ola-stft/9.1.4.1-audio-fir.html
[~] 9.1.4.2 Example 1: LP Filtering by FFT Conv — ch09-ola-stft/9.1.4.2-fft-lp.html
[~] 9.1.4.3 Example 2: Time Domain Aliasing — ch09-ola-stft/9.1.4.3-td-aliasing.html
[~] 9.2 Convolving with Long Signals — ch09-ola-stft/9.2-conv-long.html
[~] 9.2.1 Overlap-Add Decomposition — ch09-ola-stft/9.2.1-ola-decomp.html
[~] 9.2.2 COLA Examples — ch09-ola-stft/9.2.2-cola-examples.html
[~] 9.2.3 STFT of COLA Decomposition — ch09-ola-stft/9.2.3-stft-cola.html
[~] 9.2.4 Acyclic Convolution — ch09-ola-stft/9.2.4-acyclic2.html
[~] 9.2.5 Example of Overlap-Add Convolution — ch09-ola-stft/9.2.5-ola-example.html
[~] 9.2.6 Summary of OLA FFT Processing — ch09-ola-stft/9.2.6-ola-summary.html
[~] 9.3 Dual of Constant Overlap-Add — ch09-ola-stft/9.3-cola-dual.html
[~] 9.3.1 Poisson Summation Formula — ch09-ola-stft/9.3.1-psf.html
[~] 9.3.2 Frequency-Domain COLA Constraints — ch09-ola-stft/9.3.2-fd-cola.html
[~] 9.3.2.1 Strong COLA — ch09-ola-stft/9.3.2.1-strong-cola.html
[~] 9.3.3 PSF Dual and Graphical Equalizers — ch09-ola-stft/9.3.3-psf-dual-eq.html
[~] 9.3.4 PSF and Weighted Overlap Add — ch09-ola-stft/9.3.4-psf-wola.html
[~] 9.3.5 Example COLA Windows for WOLA — ch09-ola-stft/9.3.5-cola-wola-examples.html
[~] 9.4 Overlap-Save Method — ch09-ola-stft/9.4-overlap-save.html
[~] 9.5 Time-Varying OLA Modifications — ch09-ola-stft/9.5-tv-ola.html
[~] 9.5.1 Time-Varying STFT Modifications — ch09-ola-stft/9.5.1-tv-stft.html
[~] 9.5.2 Length L FIR Frame Filters — ch09-ola-stft/9.5.2-frame-filters.html
[~] 9.6 Weighted Overlap Add — ch09-ola-stft/9.6-wola.html
[~] 9.6.1 WOLA Processing Steps — ch09-ola-stft/9.6.1-wola-steps.html
[~] 9.6.1.1 Choice of WOLA Window — ch09-ola-stft/9.6.1.1-wola-window.html
[~] 9.7 Review of Zero Padding — ch09-ola-stft/9.7-review-zp.html

World 10 · Filter Bank View of the STFT (ch10-filter-bank-stft/)

[~] 10.1 Dual Views of the STFT — ch10-filter-bank-stft/10.1-dual-views.html
[~] 10.1.1 Overlap-Add View of the STFT — ch10-filter-bank-stft/10.1.1-ola-view.html
[~] 10.1.2 Filter Bank View of the STFT — ch10-filter-bank-stft/10.1.2-fb-view.html
[~] 10.1.3 FBS and Perfect Reconstruction — ch10-filter-bank-stft/10.1.3-fbs-pr.html
[~] 10.2 STFT Filter Bank — ch10-filter-bank-stft/10.2-stft-fb.html
[~] 10.2.1 Computational Examples in Matlab — ch10-filter-bank-stft/10.2.1-matlab-examples.html
[~] 10.3 The DFT Filter Bank — ch10-filter-bank-stft/10.3-dft-fb.html
[~] 10.3.1 The Running-Sum Lowpass Filter — ch10-filter-bank-stft/10.3.1-running-sum.html
[~] 10.3.2 Modulation by a Complex Sinusoid — ch10-filter-bank-stft/10.3.2-mod-complex.html
[~] 10.3.3 Making a BP from a LP — ch10-filter-bank-stft/10.3.3-lp-to-bp.html
[~] 10.3.4 Uniform Running-Sum Filter Banks — ch10-filter-bank-stft/10.3.4-uniform-rs.html
[~] 10.3.4.1 System Diagram of the Running-Sum FB — ch10-filter-bank-stft/10.3.4.1-rs-diagram.html
[~] 10.3.4.2 DFT Filter Bank — ch10-filter-bank-stft/10.3.4.2-dft-fb-detail.html
[~] 10.3.4.3 Inverse DFT and the DFT-FB Sum — ch10-filter-bank-stft/10.3.4.3-idft-fb.html
[~] 10.4 FBS Window Constraints for R=1 — ch10-filter-bank-stft/10.4-fbs-r1.html
[~] 10.5 Nyquist(N) Windows — ch10-filter-bank-stft/10.5-nyquist-n.html
[~] 10.6 Duality of COLA and Nyquist Conditions — ch10-filter-bank-stft/10.6-cola-nyquist-duality.html
[~] 10.6.1 Specific Windows — ch10-filter-bank-stft/10.6.1-specific-windows.html
[~] 10.6.2 Nyquist Property on the Unit Circle — ch10-filter-bank-stft/10.6.2-nyquist-unit.html
[~] 10.7 Portnoff Windows — ch10-filter-bank-stft/10.7-portnoff.html
[~] 10.8 Downsampled STFT Filter Banks — ch10-filter-bank-stft/10.8-downsampled.html
[~] 10.8.1 Downsampled STFT Filter Bank — ch10-filter-bank-stft/10.8.1-ds-stft-fb.html
[~] 10.8.1.1 Filter Bank Reconstruction — ch10-filter-bank-stft/10.8.1.1-fb-recon.html
[~] 10.8.2 Downsampling with Anti-Aliasing — ch10-filter-bank-stft/10.8.2-ds-anti-aliasing.html
[~] 10.8.2.1 Properly Anti-Aliasing Window Transforms — ch10-filter-bank-stft/10.8.2.1-window-anti-aliasing.html
[~] 10.8.2.2 Hop Sizes for WOLA — ch10-filter-bank-stft/10.8.2.2-wola-hop.html
[~] 10.8.3 Constant-Overlap-Add (COLA) Cases — ch10-filter-bank-stft/10.8.3-cola-cases.html
[~] 10.8.3.1 Hamming Overlap-Add Example — ch10-filter-bank-stft/10.8.3.1-hamming-ola.html
[~] 10.8.3.2 Periodic-Hamming OLA from PSF — ch10-filter-bank-stft/10.8.3.2-periodic-hamming.html
[~] 10.8.3.3 Kaiser Overlap-Add Example — ch10-filter-bank-stft/10.8.3.3-kaiser-ola.html
[~] 10.9 STFT with Modifications — ch10-filter-bank-stft/10.9-stft-mods.html
[~] 10.9.1 FBS Fixed Modifications — ch10-filter-bank-stft/10.9.1-fbs-fixed.html
[~] 10.9.2 Time-Varying Modifications in FBS — ch10-filter-bank-stft/10.9.2-fbs-tv.html
[~] 10.9.2.1 Points to Note — ch10-filter-bank-stft/10.9.2.1-notes.html
[~] 10.10 STFT Summary and Conclusions — ch10-filter-bank-stft/10.10-summary.html

World 11 · Applications of the STFT (ch11-stft-apps/)

[~] 11.1 F0 Estimation from Spectral Peaks — ch11-stft-apps/11.1-f0-est.html
[~] 11.1.1 Useful Preprocessing — ch11-stft-apps/11.1.1-preprocessing.html
[~] 11.1.2 Getting Closer to Maximum Likelihood — ch11-stft-apps/11.1.2-closer-ml.html
[~] 11.1.3 References on F0 Estimation — ch11-stft-apps/11.1.3-f0-refs.html
[~] 11.2 Cross-Synthesis — ch11-stft-apps/11.2-cross-synth.html
[~] 11.3 Spectral Envelope Extraction — ch11-stft-apps/11.3-spec-envelope.html
[~] 11.3.1 Cepstral Windowing — ch11-stft-apps/11.3.1-cepstral.html
[~] 11.3.2 Linear Prediction Spectral Envelope — ch11-stft-apps/11.3.2-lp-envelope.html
[~] 11.3.2.1 LP Is Peak Sensitive — ch11-stft-apps/11.3.2.1-lp-peak.html
[~] 11.3.2.2 Linear Prediction Methods — ch11-stft-apps/11.3.2.2-lp-methods.html
[~] 11.3.2.3 Computation of LP Coefficients — ch11-stft-apps/11.3.2.3-lp-comp.html
[~] 11.3.2.4 LP Order Selection — ch11-stft-apps/11.3.2.4-lp-order.html
[~] 11.3.2.5 Summary of LP Spectral Envelopes — ch11-stft-apps/11.3.2.5-lp-summary.html
[~] 11.3.3 Spectral Envelope Examples — ch11-stft-apps/11.3.3-env-examples.html
[~] 11.3.3.1 Signal Synthesis — ch11-stft-apps/11.3.3.1-sig-synth.html
[~] 11.3.3.2 Envelope by Cepstral Windowing — ch11-stft-apps/11.3.3.2-env-cepstral.html
[~] 11.3.3.3 Envelope by Linear Prediction — ch11-stft-apps/11.3.3.3-env-lp.html
[~] 11.3.3.4 LP in Matlab and Octave — ch11-stft-apps/11.3.3.4-lp-matlab.html
[~] 11.4 Spectral Modeling Synthesis — ch11-stft-apps/11.4-sms.html
[~] 11.4.1 Additive Synthesis (Early) — ch11-stft-apps/11.4.1-additive.html
[~] 11.4.2 Additive Synthesis Analysis — ch11-stft-apps/11.4.2-additive-anal.html
[~] 11.4.2.1 Following Spectral Peaks — ch11-stft-apps/11.4.2.1-peaks-follow.html
[~] 11.4.2.2 Sinusoidal Peak Finding — ch11-stft-apps/11.4.2.2-peak-find.html
[~] 11.4.2.3 Tracking Peaks Across FFTs — ch11-stft-apps/11.4.2.3-peak-tracking.html
[~] 11.4.3 Sines + Noise Modeling — ch11-stft-apps/11.4.3-s-plus-n.html
[~] 11.4.3.1 Sines+Noise Analysis — ch11-stft-apps/11.4.3.1-sn-anal.html
[~] 11.4.3.2 S+N Synthesis — ch11-stft-apps/11.4.3.2-sn-synth.html
[~] 11.4.3.3 Sines+Noise Summary — ch11-stft-apps/11.4.3.3-sn-summary.html
[~] 11.4.4 Sines + Noise + Transients — ch11-stft-apps/11.4.4-snt.html
[~] 11.4.4.1 S+N+T Time-Frequency Maps — ch11-stft-apps/11.4.4.1-snt-tf.html
[~] 11.4.4.2 S+N+T Noise Model — ch11-stft-apps/11.4.4.2-snt-noise.html
[~] 11.4.5 S+N+T Sound Examples — ch11-stft-apps/11.4.5-snt-sounds.html
[~] 11.5 Time Scale Modification — ch11-stft-apps/11.5-tsm.html
[~] 11.5.1 TSM and S+N+T — ch11-stft-apps/11.5.1-tsm-snt.html
[~] 11.5.2 TSM by Resampling STFTs Across Time — ch11-stft-apps/11.5.2-tsm-resample.html
[~] 11.5.3 Phase Continuation — ch11-stft-apps/11.5.3-phase-cont.html
[~] 11.5.4 TSM Examples — ch11-stft-apps/11.5.4-tsm-examples.html
[~] 11.5.4.1 Phase-Continued STFT TSM — ch11-stft-apps/11.5.4.1-pc-stft.html
[~] 11.5.4.2 Relative-Phase-Preserving STFT TSM — ch11-stft-apps/11.5.4.2-rpp-stft.html
[~] 11.5.4.3 SOLA-FS TSM — ch11-stft-apps/11.5.4.3-sola-fs.html
[~] 11.5.5 Further Reading — ch11-stft-apps/11.5.5-reading.html
[~] 11.6 Gaussian Windowed Chirps (Chirplets) — ch11-stft-apps/11.6-chirplets.html
[~] 11.6.1 Chirplet Fourier Transform — ch11-stft-apps/11.6.1-chirplet-ft.html
[~] 11.6.2 Modulated Gaussian-Windowed Chirp — ch11-stft-apps/11.6.2-mod-gauss-chirp.html
[~] 11.6.3 Identifying Chirp Rate — ch11-stft-apps/11.6.3-chirp-rate.html
[~] 11.6.3.1 Chirplet Frequency-Rate Estimation — ch11-stft-apps/11.6.3.1-fr-est.html
[~] 11.6.3.2 Simulation Results — ch11-stft-apps/11.6.3.2-sim-results.html
[~] 11.7 FFT Filter Banks — ch11-stft-apps/11.7-fft-fb.html
[~] 11.7.1 Audio Filter Banks — ch11-stft-apps/11.7.1-audio-fb.html
[~] 11.7.2 Basic Idea — ch11-stft-apps/11.7.2-basic.html
[~] 11.7.3 Summing STFT Bins — ch11-stft-apps/11.7.3-summing.html
[~] 11.7.4 Inverse Transforming STFT Bin Groups — ch11-stft-apps/11.7.4-ift-groups.html
[~] 11.7.5 Improving the Channel Filters — ch11-stft-apps/11.7.5-improve.html
[~] 11.7.6 Fast Octave Filter Banks — ch11-stft-apps/11.7.6-fast-octave.html
[~] 11.7.7 Spectral Rotation of Real Signals — ch11-stft-apps/11.7.7-spec-rot.html
[~] 11.7.8 Improving the Octave Band Filters — ch11-stft-apps/11.7.8-improve-octave.html
[~] 11.7.9 Aliasing on Downsampling — ch11-stft-apps/11.7.9-alias-ds.html
[~] 11.7.10 Restricting Aliasing to Stop-Bands — ch11-stft-apps/11.7.10-alias-stop.html
[~] 11.7.10.1 Tightening the IFFTs — ch11-stft-apps/11.7.10.1-tighten-ifft.html
[~] 11.7.11 Real Filter Bank Example — ch11-stft-apps/11.7.11-real-fb-ex.html
[~] 11.7.12 Optimal Band Filters — ch11-stft-apps/11.7.12-opt-band.html
[~] 11.8 FFT Filter-Bank Summary & OLA Duality — ch11-stft-apps/11.8-fb-summary.html
[~] 11.9 Pointers to Sound Examples — ch11-stft-apps/11.9-sound-examples.html

World 12 · Multirate Filter Banks (ch12-multirate/)

[~] 12.1 Upsampling and Downsampling — ch12-multirate/12.1-up-down.html
[~] 12.1.1 Upsampling (Stretch) Operator — ch12-multirate/12.1.1-upsample.html
[~] 12.1.2 Downsampling (Decimation) Operator — ch12-multirate/12.1.2-downsample.html
[~] 12.1.2.1 Example: Downsampling by 2 — ch12-multirate/12.1.2.1-ds-by-2.html
[~] 12.1.2.2 Example: Upsampling by 2 — ch12-multirate/12.1.2.2-us-by-2.html
[~] 12.1.3 Filtering and Downsampling — ch12-multirate/12.1.3-filter-ds.html
[~] 12.2 Polyphase Decomposition — ch12-multirate/12.2-polyphase.html
[~] 12.2.1 Two-Channel Case — ch12-multirate/12.2.1-two-channel.html
[~] 12.2.2 N-Channel Polyphase Decomposition — ch12-multirate/12.2.2-n-channel.html
[~] 12.2.3 Type II Polyphase Decomposition — ch12-multirate/12.2.3-type2.html
[~] 12.2.4 Filtering and Downsampling, Revisited — ch12-multirate/12.2.4-filter-ds2.html
[~] 12.2.5 Multirate Noble Identities — ch12-multirate/12.2.5-noble.html
[~] 12.3 Critically Sampled PR Filter Banks — ch12-multirate/12.3-cs-pr.html
[~] 12.3.1 Two-Channel Critically Sampled FB — ch12-multirate/12.3.1-2ch-cs.html
[~] 12.3.2 Amplitude-Complementary 2-Channel FB — ch12-multirate/12.3.2-amp-comp.html
[~] 12.3.3 Haar Example — ch12-multirate/12.3.3-haar.html
[~] 12.3.4 Polyphase Decomp of Haar Example — ch12-multirate/12.3.4-haar-polyphase.html
[~] 12.3.5 Quadrature Mirror Filters (QMF) — ch12-multirate/12.3.5-qmf.html
[~] 12.3.6 Linear Phase QMF Banks — ch12-multirate/12.3.6-linphase-qmf.html
[~] 12.3.7 Conjugate Quadrature Filters (CQF) — ch12-multirate/12.3.7-cqf.html
[~] 12.3.8 Orthogonal Two-Channel Filter Banks — ch12-multirate/12.3.8-ortho-2ch.html
[~] 12.4 Perfect Reconstruction Filter Banks — ch12-multirate/12.4-pr-fb.html
[~] 12.4.1 Simple Examples of PR — ch12-multirate/12.4.1-simple-pr.html
[~] 12.4.2 Sliding Polyphase Filter Bank — ch12-multirate/12.4.2-sliding-pp.html
[~] 12.4.3 Hopping Polyphase Filter Bank — ch12-multirate/12.4.3-hopping-pp.html
[~] 12.4.4 Sufficient Condition for PR — ch12-multirate/12.4.4-suff-pr.html
[~] 12.4.5 Necessary & Sufficient Conditions for PR — ch12-multirate/12.4.5-ns-pr.html
[~] 12.4.6 Polyphase View of the STFT — ch12-multirate/12.4.6-pp-stft.html
[~] 12.4.7 Polyphase View of OLA-STFT — ch12-multirate/12.4.7-pp-ola.html
[~] 12.4.8 Polyphase View of WOLA-STFT — ch12-multirate/12.4.8-pp-wola.html
[~] 12.5 Paraunitary Filter Banks — ch12-multirate/12.5-paraunitary.html
[~] 12.5.1 Lossless Filters — ch12-multirate/12.5.1-lossless.html
[~] 12.5.2 Lossless Filter Examples — ch12-multirate/12.5.2-lossless-ex.html
[~] 12.5.3 Properties of Paraunitary FBs — ch12-multirate/12.5.3-para-props.html
[~] 12.5.4 Examples (Paraunitary) — ch12-multirate/12.5.4-para-ex.html
[~] 12.6 Filter Banks Equivalent to STFTs — ch12-multirate/12.6-fb-eq-stft.html
[~] 12.6.1 Polyphase Analysis of Portnoff STFT — ch12-multirate/12.6.1-portnoff-pp.html
[~] 12.7 MPEG Filter Banks — ch12-multirate/12.7-mpeg.html
[~] 12.7.1 Pseudo-QMF Cosine Mod Filter Bank — ch12-multirate/12.7.1-pseudo-qmf.html
[~] 12.7.2 PR Cosine Modulated Filter Banks — ch12-multirate/12.7.2-pr-cos.html
[~] 12.7.3 MPEG Layer III Filter Bank — ch12-multirate/12.7.3-mp3-fb.html
[~] 12.8 Review of STFT Filterbanks — ch12-multirate/12.8-review-stft-fb.html
[~] 12.8.1 STFT, Rect, No Overlap — ch12-multirate/12.8.1-rect-no-ol.html
[~] 12.8.2 STFT, Rect, 50% Overlap — ch12-multirate/12.8.2-rect-50.html
[~] 12.8.3 STFT, Triangular, 50% Overlap — ch12-multirate/12.8.3-tri-50.html
[~] 12.8.4 STFT, Hamming, 75% Overlap — ch12-multirate/12.8.4-hamming-75.html
[~] 12.8.5 STFT, Kaiser β=10, 90% Overlap — ch12-multirate/12.8.5-kaiser-90.html
[~] 12.8.6 Sliding FFT, Zero-Padded — ch12-multirate/12.8.6-sliding-zp.html
[~] 12.9 Wavelet Filter Banks — ch12-multirate/12.9-wavelet-fb.html
[~] 12.9.1 Geometric Signal Theory — ch12-multirate/12.9.1-geom-sig.html
[~] 12.9.1.1 Natural Basis — ch12-multirate/12.9.1.1-nat-basis.html
[~] 12.9.1.2 Normalized DFT Basis for C^N — ch12-multirate/12.9.1.2-dft-basis.html
[~] 12.9.1.3 Normalized Fourier Basis — ch12-multirate/12.9.1.3-ft-basis.html
[~] 12.9.1.4 Normalized DTFT Basis — ch12-multirate/12.9.1.4-dtft-basis.html
[~] 12.9.1.5 Normalized STFT Basis — ch12-multirate/12.9.1.5-stft-basis.html
[~] 12.9.1.6 Continuous Wavelet Transform — ch12-multirate/12.9.1.6-cwt.html
[~] 12.9.1.7 Discrete Wavelet Transform — ch12-multirate/12.9.1.7-dwt.html
[~] 12.9.1.8 Discrete Wavelet Filterbank — ch12-multirate/12.9.1.8-dwt-fb.html
[~] 12.9.1.9 Dyadic Filter Banks — ch12-multirate/12.9.1.9-dyadic.html
[~] 12.9.1.10 Dyadic Filter Bank Design — ch12-multirate/12.9.1.10-dyadic-design.html
[~] 12.9.1.11 Generalized STFT — ch12-multirate/12.9.1.11-gen-stft.html
[~] 12.10 Further Reading — ch12-multirate/12.10-further.html
[~] 12.11 Conclusions — ch12-multirate/12.11-conclusions.html

World 13 · Summary and Conclusions

[~] 13.1 Summary and Conclusions — ch13-summary/13.1-summary.html

Appendix World A · Notation (appendix/notation/)

[~] A.1 Frequency and Time — appendix/notation/A.1-freq-time.html
[~] A.2 Signal Notation — appendix/notation/A.2-sig-notation.html
[~] A.3 Fourier Transform Notation — appendix/notation/A.3-ft-notation.html

Appendix World B · Continuous Fourier Theorems (appendix/ct-fourier/)

[~] B.1 Radians versus Cycles — appendix/ct-fourier/B.1-radians-cycles.html
[~] B.2 Differentiation Theorem — appendix/ct-fourier/B.2-diff.html
[~] B.3 Differentiation Theorem Dual — appendix/ct-fourier/B.3-diff-dual.html
[~] B.4 Scaling Theorem — appendix/ct-fourier/B.4-scaling.html
[~] B.5 Shift Theorem — appendix/ct-fourier/B.5-shift.html
[~] B.6 Modulation Theorem (Shift Dual) — appendix/ct-fourier/B.6-modulation.html
[~] B.7 Convolution Theorem — appendix/ct-fourier/B.7-conv.html
[~] B.8 Flip Theorems — appendix/ct-fourier/B.8-flip.html
[~] B.9 Power Theorem — appendix/ct-fourier/B.9-power.html
[~] B.10 The Continuous-Time Impulse — appendix/ct-fourier/B.10-ct-impulse.html
[~] B.11 Gaussian Pulse — appendix/ct-fourier/B.11-gauss.html
[~] B.12 Rectangular Pulse — appendix/ct-fourier/B.12-rect.html
[~] B.13 Sinc Impulse — appendix/ct-fourier/B.13-sinc.html
[~] B.14 Impulse Trains — appendix/ct-fourier/B.14-impulse-train.html
[~] B.15 Poisson Summation Formula — appendix/ct-fourier/B.15-psf.html
[~] B.16 Sampling Theory — appendix/ct-fourier/B.16-sampling.html
[~] B.17 The Uncertainty Principle — appendix/ct-fourier/B.17-uncertainty.html
[~] B.17.1 Second Moments — appendix/ct-fourier/B.17.1-2nd-moments.html
[~] B.17.2 Time-Limited Signals — appendix/ct-fourier/B.17.2-time-limited.html
[~] B.17.3 Time-Bandwidth Products Unbounded Above — appendix/ct-fourier/B.17.3-tb-unbounded.html
[~] B.18 Relation of Smoothness to Roll-Off Rate — appendix/ct-fourier/B.18-smooth-rolloff.html

Appendix World C · Statistical Signal Processing (appendix/stats/)

[~] C.1 Stochastic Processes — appendix/stats/C.1-stoch.html
[~] C.1.1 Probability Distribution — appendix/stats/C.1.1-prob-dist.html
[~] C.1.2 Independent Events — appendix/stats/C.1.2-independent.html
[~] C.1.3 Random Variable — appendix/stats/C.1.3-rv.html
[~] C.1.4 Stochastic Process — appendix/stats/C.1.4-stoch-proc.html
[~] C.1.5 Stationary Stochastic Process — appendix/stats/C.1.5-stationary.html
[~] C.1.6 Expected Value — appendix/stats/C.1.6-expected.html
[~] C.1.7 Mean — appendix/stats/C.1.7-mean.html
[~] C.1.8 Sample Mean — appendix/stats/C.1.8-sample-mean.html
[~] C.1.9 Variance — appendix/stats/C.1.9-variance.html
[~] C.1.10 Sample Variance — appendix/stats/C.1.10-sample-var.html
[~] C.2 Correlation Analysis — appendix/stats/C.2-corr-analysis.html
[~] C.2.1 Cross-Correlation — appendix/stats/C.2.1-cross-corr.html
[~] C.2.2 Cross-Power Spectral Density — appendix/stats/C.2.2-cpsd.html
[~] C.2.3 Autocorrelation — appendix/stats/C.2.3-autocorr.html
[~] C.2.4 Sample Autocorrelation — appendix/stats/C.2.4-sample-autocorr.html
[~] C.2.5 Power Spectral Density — appendix/stats/C.2.5-psd.html
[~] C.2.6 Sample Power Spectral Density — appendix/stats/C.2.6-sample-psd.html
[~] C.3 White Noise — appendix/stats/C.3-white.html
[~] C.3.1 Making White Noise with Dice — appendix/stats/C.3.1-dice.html
[~] C.3.2 Independent Implies Uncorrelated — appendix/stats/C.3.2-ind-uncorr.html
[~] C.3.3 Estimator Variance — appendix/stats/C.3.3-est-var.html
[~] C.3.3.1 Sample-Mean Variance — appendix/stats/C.3.3.1-sample-mean-var.html
[~] C.3.3.2 Sample-Variance Variance — appendix/stats/C.3.3.2-sample-var-var.html

Appendix World D · Gaussian Function Properties (appendix/gaussian/)

[~] D.1 Gaussian Window and Transform — appendix/gaussian/D.1-gauss-xform.html
[~] D.2 Gaussians Closed under Multiplication — appendix/gaussian/D.2-mult-closed.html
[~] D.2.1 Product of Two Gaussian PDFs — appendix/gaussian/D.2.1-product-pdfs.html
[~] D.3 Gaussians Closed under Convolution — appendix/gaussian/D.3-conv-closed.html
[~] D.4 Fitting a Gaussian to Data — appendix/gaussian/D.4-fit.html
[~] D.5 Infinite Flatness at Infinity — appendix/gaussian/D.5-inf-flat.html
[~] D.6 Integral of a Complex Gaussian — appendix/gaussian/D.6-int-complex.html
[~] D.6.1 Area Under a Real Gaussian — appendix/gaussian/D.6.1-area-real.html
[~] D.7 Gaussian Integral with Complex Offset — appendix/gaussian/D.7-complex-offset.html
[~] D.8 Fourier Transform of Complex Gaussian — appendix/gaussian/D.8-ft-complex.html
[~] D.8.1 Alternate Proof — appendix/gaussian/D.8.1-alt-proof.html
[~] D.9 Why Gaussian? — appendix/gaussian/D.9-why.html
[~] D.9.1 Central Limit Theorem — appendix/gaussian/D.9.1-clt.html
[~] D.9.2 Iterated Convolutions — appendix/gaussian/D.9.2-iterated-conv.html
[~] D.9.3 Binomial Distribution — appendix/gaussian/D.9.3-binomial.html
[~] D.10 Gaussian Probability Density Function — appendix/gaussian/D.10-gauss-pdf.html
[~] D.11 Maximum Entropy Property — appendix/gaussian/D.11-max-entropy.html
[~] D.11.1 Entropy of a Probability Distribution — appendix/gaussian/D.11.1-entropy-def.html
[~] D.11.2 Example: Random Bit String — appendix/gaussian/D.11.2-bit-example.html
[~] D.11.3 Maximum Entropy Distributions — appendix/gaussian/D.11.3-max-ent-dist.html
[~] D.11.3.1 Uniform Distribution — appendix/gaussian/D.11.3.1-uniform.html
[~] D.11.3.2 Exponential Distribution — appendix/gaussian/D.11.3.2-exp.html
[~] D.11.3.3 Gaussian Distribution — appendix/gaussian/D.11.3.3-gauss-me.html
[~] D.12 Gaussian Moments — appendix/gaussian/D.12-moments.html
[~] D.12.1 Gaussian Mean — appendix/gaussian/D.12.1-gauss-mean.html
[~] D.12.2 Gaussian Variance — appendix/gaussian/D.12.2-gauss-var.html
[~] D.12.3 Higher-Order Moments Revisited — appendix/gaussian/D.12.3-higher-moments.html
[~] D.12.4 Moment Theorem — appendix/gaussian/D.12.4-moment-thm.html
[~] D.12.5 Gaussian Characteristic Function — appendix/gaussian/D.12.5-char-fn.html
[~] D.12.6 Gaussian Central Moments — appendix/gaussian/D.12.6-central-moments.html
[~] D.13 Sums of Gaussian Random Variables — appendix/gaussian/D.13-sums.html

Appendix World E · Bilinear Audio Frequency Warping (appendix/warping/)

[~] E.1 The Bark Frequency Scale — appendix/warping/E.1-bark.html
[~] E.2 The Bilinear Transform — appendix/warping/E.2-bilinear.html
[~] E.3 Optimal Bilinear Bark Warping — appendix/warping/E.3-optimal-bark.html
[~] E.3.1 Computing ρ — appendix/warping/E.3.1-rho.html
[~] E.3.2 Optimal Frequency Warpings — appendix/warping/E.3.2-optimal-warp.html
[~] E.3.3 Bark Relative Bandwidth Mapping Error — appendix/warping/E.3.3-bark-err.html
[~] E.3.4 Error Significance — appendix/warping/E.3.4-err-sig.html
[~] E.3.5 Arctangent Approximations for ρ*(fs) — appendix/warping/E.3.5-arctan.html
[~] E.4 Application to Audio Filter Design — appendix/warping/E.4-filter-design.html
[~] E.4.1 Filter Design Example — appendix/warping/E.4.1-design-ex.html
[~] E.5 Equivalent Rectangular Bandwidth — appendix/warping/E.5-erb.html
[~] E.5.1 ERB Relative Bandwidth Mapping Error — appendix/warping/E.5.1-erb-err.html
[~] E.5.2 Arctangent Approximations for ρ*(fs), ERB — appendix/warping/E.5.2-erb-arctan.html
[~] E.6 Directions for Improvements — appendix/warping/E.6-improvements.html
[~] E.7 Summary — appendix/warping/E.7-summary.html

Appendix World F · Examples in Matlab and Octave (appendix/matlab/)

[~] F.1 Matlab for Spectrum Analysis Windows — appendix/matlab/F.1-windows.html
[~] F.1.1 Blackman Window Example — appendix/matlab/F.1.1-blackman-ex.html
[~] F.1.2 Matlab listing: dpssw.m — appendix/matlab/F.1.2-dpssw.html
[~] F.2 Interpolating Spectral Peaks — appendix/matlab/F.2-interp.html
[~] F.2.1 Matlab listing: findpeaks.m — appendix/matlab/F.2.1-findpeaks.html
[~] F.2.2 Matlab listing: maxr.m — appendix/matlab/F.2.2-maxr.html
[~] F.2.3 Matlab listing: qint.m — appendix/matlab/F.2.3-qint.html
[~] F.2.4 Matlab listing: zpfmin.m — appendix/matlab/F.2.4-zpfmin.html
[~] F.2.5 Matlab listing: oboeanal.m — appendix/matlab/F.2.5-oboeanal.html
[~] F.3 Matlab for Computing Spectrograms — appendix/matlab/F.3-spectrograms.html
[~] F.3.1 Matlab listing: myspectrogram.m — appendix/matlab/F.3.1-myspectrogram.html
[~] F.3.2 Matlab listing: invmyspectrogram.m — appendix/matlab/F.3.2-invmyspectrogram.html
[~] F.3.3 Matlab listing: testmyspectrogram.m — appendix/matlab/F.3.3-testmyspectrogram.html
[~] F.4 Matlab for Unwrapping Spectral Phase — appendix/matlab/F.4-unwrap.html
[~] F.4.1 Matlab listing: unwrap.m — appendix/matlab/F.4.1-unwrap-m.html
[~] F.5 Non-Parametric Frequency Warping — appendix/matlab/F.5-nonpar-warp.html
[~] F.6 Fundamental Frequency Estimation — appendix/matlab/F.6-f0-est.html
[~] F.6.1 Test Program for F0 Estimation — appendix/matlab/F.6.1-f0-test.html

Appendix World G · Spectral Audio Modeling History (appendix/history/)

[~] G.1 Daniel Bernoulli's Modal Decomposition — appendix/history/G.1-bernoulli.html
[~] G.2 The Telharmonium — appendix/history/G.2-telharmonium.html
[~] G.3 Early Additive Synthesis in Film Making — appendix/history/G.3-early-additive.html
[~] G.4 The Hammond Organ — appendix/history/G.4-hammond.html
[~] G.5 Dudley's Channel Vocoder — appendix/history/G.5-dudley.html
[~] G.5.1 Speech Synthesis Examples — appendix/history/G.5.1-speech-ex.html
[~] G.6 Voder — appendix/history/G.6-voder.html
[~] G.7 Phase Vocoder — appendix/history/G.7-phase-voc.html
[~] G.7.1 FFT Implementation of the Phase Vocoder — appendix/history/G.7.1-pv-fft.html
[~] G.8 Additive Synthesis — appendix/history/G.8-additive.html
[~] G.8.1 Inverse FFT Synthesis — appendix/history/G.8.1-ifft-synth.html
[~] G.8.2 Chirplet Synthesis — appendix/history/G.8.2-chirplet-synth.html
[~] G.8.3 Nonparametric Spectral Peak Modeling — appendix/history/G.8.3-nonpar-peak.html
[~] G.8.4 Efficient Specialized Methods — appendix/history/G.8.4-efficient.html
[~] G.8.4.1 Wavetable Synthesis — appendix/history/G.8.4.1-wavetable.html
[~] G.8.4.2 Group-Additive Synthesis — appendix/history/G.8.4.2-group-add.html
[~] G.8.5 Further Reading, Additive Synthesis — appendix/history/G.8.5-add-reading.html
[~] G.9 Frequency Modulation (FM) Synthesis — appendix/history/G.9-fm.html
[~] G.9.1 FM Harmonic Amplitudes — appendix/history/G.9.1-fm-harmonics.html
[~] G.9.2 FM Brass — appendix/history/G.9.2-fm-brass.html
[~] G.9.3 FM Voice — appendix/history/G.9.3-fm-voice.html
[~] G.9.3.1 Further Reading about FM Synthesis — appendix/history/G.9.3.1-fm-reading.html
[~] G.10 Phase Vocoder Sinusoidal Modeling — appendix/history/G.10-pv-sin.html
[~] G.10.1 Computing Vocoder Parameters — appendix/history/G.10.1-vp.html
[~] G.10.1.1 Frequency Envelopes — appendix/history/G.10.1.1-freq-env.html
[~] G.10.1.2 Envelope Compression — appendix/history/G.10.1.2-env-comp.html
[~] G.10.1.3 Vocoder-Based AS Limitations — appendix/history/G.10.1.3-limits.html
[~] G.10.2 Further Reading on Vocoders — appendix/history/G.10.2-voc-reading.html
[~] G.11 Spectral Modeling Synthesis (History) — appendix/history/G.11-sms.html
[~] G.11.1 STFT Analysis/Mod/Resynth — appendix/history/G.11.1-stft-amrs.html
[~] G.11.2 Sinusoidal Modeling Systems — appendix/history/G.11.2-sms-systems.html
[~] G.11.3 Inverse FFT Synthesis (History) — appendix/history/G.11.3-ifft-hist.html
[~] G.11.4 Sines+Noise Synthesis (History) — appendix/history/G.11.4-sn-hist.html
[~] G.11.5 Multiresolution Sinusoidal Modeling — appendix/history/G.11.5-mrsm.html
[~] G.11.6 Transient Models — appendix/history/G.11.6-transient.html
[~] G.11.7 Time-Frequency Reassignment — appendix/history/G.11.7-reassign.html
[~] G.11.8 Perceptual Audio Compression — appendix/history/G.11.8-perceptual.html
[~] G.11.9 Further Reading — appendix/history/G.11.9-sms-reading.html
[~] G.12 Perceptual Audio Coding — appendix/history/G.12-perc-coding.html
[~] G.13 Future Prospects — appendix/history/G.13-future.html
[~] G.14 Summary — appendix/history/G.14-summary.html

Appendix World H · The PARSHL Program (appendix/parshl/)

[~] H.1 Choice of Hop Size — appendix/parshl/H.1-hop.html
[~] H.2 Filling the FFT Input Buffer (Step 2) — appendix/parshl/H.2-fill.html
[~] H.3 Peak Detection (Steps 3 and 4) — appendix/parshl/H.3-peak-det.html
[~] H.4 Peak Matching (Step 5) — appendix/parshl/H.4-peak-match.html
[~] H.5 Parameter Modifications (Step 6) — appendix/parshl/H.5-param-mod.html
[~] H.6 Synthesis (Step 7) — appendix/parshl/H.6-synth.html
[~] H.7 Magnitude-only Analysis/Synthesis — appendix/parshl/H.7-mag-only.html
[~] H.8 Preprocessing — appendix/parshl/H.8-pre.html
[~] H.9 Applications — appendix/parshl/H.9-apps.html
[~] H.10 Conclusions — appendix/parshl/H.10-conclusions.html
[~] H.11 Acknowledgments — appendix/parshl/H.11-acks.html
[~] H.12 Software Listing — appendix/parshl/H.12-software.html

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