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- 20 dB boost
: 15.2.1
- 3 dB boost
: 15.2.1
- coherenceml
: 9.6.1
- A-weighted dB scale
: 15.2.2.5
- 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 frequency
: 5.3.5
- 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
| 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
- 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 Full Scale (dBFS)
: 15.2.2.6
- 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
: 15.2.2.4
- dBA
: 15.2.2.5
- dBFS
: 15.2.2
- dBm scale
: 15.2.2.1
- dBu scale
: 15.2.2.2
- dBV scale
: 15.2.2.3
- 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
- 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
- properties of : 4.3
- rational : 4.6
- 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
- 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
- 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
- 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
: 15.2.2.4
- 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
: 15.2.2.5
- 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
| 6.8.3
- 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
- linearly independent
: 6.10.2
- logarithm
: