Index for this Document
- 20 dB boost
: 15.2.1
- 3 dB boost : 15.2.1
- coherenceml : 9.6.1
- A-weighted dB scale : 15.2.2.4
- absolutely integrable : 11.2.1
- ADSR envelope : 8.2.4.4
- alias operator : 8.2.15
- aliased sinc function : 7.7 | 8.4.13
- aliasing : 8.2.15 | 13.2
- aliasing operator : 8.2.15
- aliasing theorem : 8.4.11
- continuous time : 13.2.1
- AM index : 5.3.5
- amplitude of a sinusoid : 5.1
- amplitude response : 9.3.2
- analytic signal : 5.3.7
- anti-aliasing lowpass filter : 8.2.15
- anti-Hermitian : 8.4.2
- antilinear : 6.9.1
- antilogarithm, antilog : 15.1
- antisymmetric functions : 8.3
- Argand diagram : 3.6
- attack level : 8.2.4.4
- autocorrelation : 9.4.3
- average power : 6.8 | 16.3
- Banach space : 6.8.3
- bandlimited : 4.8
- bandlimited downsampling : 8.2.14
- bandlimited interpolation : 8.4.13
- of spectra : 8.2.11
- time or frequency domain : 8.2.11
- bandlimited signals cannot be time limited : 12.3
- base (of a logarithm) : 15.1
- beats : 5.3.5
- bel : 15.2
- Bessel function : 5.3.6.1
- Bessel generating function : 5.3.6.1
- bin number (DFT) : 7.8
- bin numbers : 7.8
- bits (binary digits) : 16.1.2
- Blackman window : 9.1.4
- Bluestein FFT : 10.4
- cardinal sine : 13.1.2
- carrier wave : 5.3.5 | 5.3.11.1
- Cartesian coordinates : 3.6
- Cauchy-Schwarz inequality : 6.9.3
- causal : 5.3.12 | 8.2.4.3
- causal signal : 8.2.8
- causal signals : 8.2.8
- causal signals, periodic : 8.2.8
- causal zero padding : 8.2.9
- causalperiodicsignals : 8.2.8
- characteristic of a logarithm : 15.1
- chirp signals : 10.4
- chirp z transform algorithm : 10.4
- circular convolution : 8.2.4
- circular cross-correlation : 9.4.1
- click removal : 9.4.2
- CODEC : 16.2.3
- coefficient of projection : 7.6
- coherence function : 9.6 | 9.6
- column vector : 17.1
- comb filter : ^ | 5.1.5
- common logarithm : 15.1
- commutativity of convolution : 8.2.4.1
- companding : 15.2.3
- completing the square : 3.2
- complex amplitude : 5.3.11.1
- complex conjugate : 3.7
- complex matrix : 17
- complex matrix transpose : 17
- complex multiplication : 3.5
- complex numbers : 3 | 3.3 | 3.5 | 3.7
- complex numbers in matlab : 18.1
- complex plane : 3.6
- complex roots of a polynomial : 3.3
- complex vector space : 6.10.4
- complexity of FFT : 10.1.2.1
- conjugation and reversal symmetries (DFT) : 8.4.2
- constant modulus : 5.3
- continuous-time aliasing : 13.2.1
- convolution : 8.2.4 | 8.2.4
- ADSR example : 8.2.4.4
- filter interpretation : 8.2.4.2
- filter representation : 9.3
- frequency domain : 8.4.6
- graphical : 8.2.4.6
- matched filter example : 8.2.4.5
- smoother example : 8.2.4.3
- filter interpretation : 8.2.4.2
- convolution as a filter : 8.2.4.2
- convolution commutativity : 8.2.4.1
- convolution theorem : 8.4.5
- convolution theorem dual : 8.4.6
- correlation : 8.2.5
- correlation analysis : 9.4
- correlation operator : 8.2.5
- correlation theorem : 8.4.7
- cosine, two vectors : 6.9.6
- cps : 5.1
- critical bandwidth of hearing : 5.3.5
- cross-correlation : 9.4.1
- cross-correlation, circular : 9.4.1
- cross-correlation, unbiased : 9.4.2
- cross-covariance : 9.4.3
- cross-spectral density : 9.4.1
- cross-talk : 7.7
- cubic spline : 14.5
- cycles per second : 5.1
- cyclic convolution : 8.2.4
- dB for display : 15.2.2.5
- dB per decade : 15.2.1
- dB per octave : 15.2.1
- dB properties : 15.2.1
- dB relative to full scale : 15.2.2
- dB scale : 15.2
- dB SPL : 15.2.2.3
- dBA : 15.2.2.4
- dBFS : 15.2.2
- dBm scale : 15.2.2.1
- dBV scale : 15.2.2.2
- DCT : 10.6.1
- de Moivre's theorem : 3.10
- de Moivre's theorem, proof : 4.15
- decibel : 15.2
- decimal numbers : 16.1.2
- decimation : 8.2.14
- decimation in frequency : 10.1.1
- decimation in time : 10.1.1 | 10.1.1
- decimation theorem : 8.4.11
- delta function : 11.2.2
- DFT : 7
- applications : 9
- as a digital filter : 7.7
- bin amplitude response : 18.4.2
- definition : 2.1
- math outline : 2.4
- normalized : 7.10
- as a digital filter : 7.7
- DFT mathematics overview : 2.3
- DFT matrix : 7.12 | 7.12
- DFT matrix in matlab : 18.4.3
- DFT sinusoids : 7.2.2 | 18.4.1
- differentiability of audio signals : 14.6
- differentiation theorem : 12.1
- digit : 16.1.2
- digital filter : 9.3
- Discrete Cosine Transform (DCT) : 10.6.1
- Discrete Fourier Transform (DFT) : 2.1 | 7 | 8.1
- Discrete Time Fourier Transform (DTFT) : 11.1
- downsampling operator : 8.2.14
- downsampling theorem : 8.4.11
- DTFT : 11.1
- duality (Fourier) : 8.4.6
- dynamic range : 15.2.3
- dynamic range of magnetic tape : 15.2.3
- energy : 15.2
- energy of a signal : 6.8
- energy theorem : 8.4.9 | 8.4.9
- entire function : 5.3.6.1
- essential singularity : 14.5
- Euclidean norm : 6.8
- Euler's Identity : 3.9 | 3.9 | 4 | 15.1.2
- even and odd functions : 8.3
- even functions : 8.3
- exp(j theta) : 4.12
- expected value : 16.3
- exponent : 15.1
- exponentials : 5.2
- exponents
- factored form of a polynomial : 3.1
- factoring a polynomial : 3.1
- fast convolution : 8.4.5
- Fast Fourier Transform (FFT) : 10
- feedback FM : 5.3.6
- FFT : 10
- audio signal processing : 10.5
- Bluestein FFT : 10.4
- complexity : 10.1.2.1
- decimation in time : 10.1.1
- mixed-radix Cooley-Tukey : 10.1
- number theory transform : 10.6.2
- Rader FFT : 10.3
- radix 2 : 10.1.2
- software : 10.7
- Bluestein FFT : 10.4
- FFT notation : 8.1.1
- FFT window : 7.7 | 9.1.4
- filter : 8.2.4.2
- fixed-point FFTs : 10.1.3
- flip operator : 8.2.2 | 8.2.2
- FM index : 5.3.6.2
- FM modulation frequency : 5.3.6.1
- FM synthesis spectrum : 5.3.6.2
- folding frequency : 8.4.13
- formants : 9.2.1
- Fourier duality : 8.4.6
- Fourier series : 7.9
- Fourier series and the DFT : 11.3
- Fourier series coefficient : 11.3
- Fourier symmetries : 8.4.3
- Fourier theorems : 8 | 8.4
- Fourier theorems (DFT) : 8 | 8.4
- aliasing theorem : 8.4.11
- convolution theorem : 8.4.5
- convolution theorem dual : 8.4.6
- correlation theorem : 8.4.7
- downsampling theorem : 8.4.11
- energy theorem (Rayleigh) : 8.4.9
- Parseval's theorem : 8.4.8
- periodic interpolation (in time) : 8.4.13
- power theorem : 8.4.8
- shift theorem : 8.4.4
- stretch (repeat) theorem : 8.4.10
- zero-padding (spectral interpolation) theorem : 8.4.12
- convolution theorem : 8.4.5
- Fourier transform : 11.2
- Fourier transform cases : 11
- Fourier transform existence : 11.2.1
- Fourier Transform theorems : 12
- continuous-time aliasing : 13.2.1
- differentiation : 12.1
- scaling or similarity : 12.2
- uncertainty principle : 12.3
- differentiation : 12.1
- frame : 8.2.10
- frequency bin : 7.8
- frequency domain : 5.1.6
- frequency modulation : 5.3.6 | 5.3.6
- frequency resolution : 5.3.5
- frequency response : 9.3.1
- frequency-domain aliasing : 8.2.15 | 8.2.15
- FS (Fourier Series) : 11.3
- FT (Fourier Transform) : 11.2
- fundamental theorem of algebra : 3.4
- Gaussian function : 12.3.1
- generalized function : 11.2.2
- generating function : 5.3.6.1
- geometric sequence : 7.1
- geometric sequence frequencies : 13.4
- geometric series : 7.1 | 7.1
- geometric signal theory : 6
- Gibb's phenomenon : 7.7
- Good-Thomas FFT algorithm : 10.2
- Gram-Schmidt orthogonalization : 6.10.6
- graphical convolution : 8.2.4.6
- half-open interval : 8.1
- Hann window : 9.1.5
- Hanning window : 9.1.5
- Heisenberg uncertainty principle : 12.3.1
- Hermitian spectra : 8.4.3
- Hermitian symmetry : 8.4.2
- Hermitian transpose : 6.9 | 7.12 | 17
- Hertz : 5.1
- hexadecimal : 16.1.2
- Hilbert transform : 5.3.7
- Hz : 5.1
- ideal lowpass filter : 8.4.13.1
- idempotent : 18.3.5
- identity matrix : 17.1
- IDFT : 2.2 | 8.1
- imaginary exponents : 4.9
- imaginary part : 3.5
- impulse response : 8.2.4.2 | 9.3
- impulse signal : 8.2.4.2 | 9.3
- impulse train : 11.3.1
- impulse, continuous time : 11.2.2
- impulse-train signal : 8.2.4.2
- indicator function : 8.4.4.2
- inner product : 6.9
- inner product in matlab : 18.3.3
- integrable function : 11.2.1
- intensity : 15.2
- intensity level : 15.2.2.3
- interpolation kernel : 13.1.2
- interpolation operator : 8.2.12 | 8.2.12
- inverse DFT : 2.2 | 8.1
- inverse DFT matrix : 7.12
- irrational number : 4.7
- ITU-R 468 noise weighting : 15.2.2.4
- just-noticeable difference (JND) : 15.2
- lag : 8.2.5
- lagged product : 8.2.5
- linear algebra : 6.10.6
- linear combination : 5.3.11.2 | 6.6
- linear number systems for digital audio : 16.1
- linear phase : 8.4.4.2
- linear phase FFT windows : 8.4.4.4
- linear phase signals : 8.4.4.2
- linear phase term : 8.4.4 | 8.4.4.1 | 8.4.4.1
- linear transformation : 17.1
- linear vector space : 6.7
- linear, time-invariant filters and convolution : 9.3
- linearity of the DFT : 8.4.1
- linearly dependent : 6.10.4
- 3 dB boost : 15.2.1