INDEX: Finding Hidden Patterns in Datasets
A
- addition formulas
- aliasing
- alignment (for adding lists)
- amplitude
- analyst
- ‘and’ statement
- angle between vectors
- apparent period
- approximate
- approximation
- augmented matrix
B
C
- Cauchy-Schwarz Inequality
- Cauchy sequence
- cfspline (MATLAB function)
- Chebyshev approximation
- Chebyshev’s Inequality
- closed interval
- column vector
- codomain
- commensurable numbers
- complete space
- complex exponential function
- complex Fourier series
- complex numbers
- component functions
- cond (MATLAB command)
- conclusion of an implication
- conditional sentence
-
condition number
condition number for a function
condition number of a matrix - conjecture
- connectives
- continuity
- contrapositive
- convergent sequence
- convex
-
cosine function
origin of word - countably infinite
- counterexample
- crossover
-
cubic splines
cubic spline as interpolates - curvature
- cycle, $p$-cycle
- cyclic frequency
D
- data point
- data sets
- data value
- degree measure of an angle
- degrees of freedom
- DeMorgan’s laws
- dense
- designing filters
- determinant
- deterministic
- dfs (MATLAB function)
- digital filters
- digital signal
- direct proof
- discrete-domain data
- discrete-domain function
-
discrete Fourier series
definition -
discrete Fourier transform
definition -
discrete orthogonal functions
discrete orthogonal functions - discrete signal
- divides
- domain of a function
- double-angle formulas
- dscorth (MATLAB function)
E
- echelon (reduced row-echelon form)
- echoing (MATLAB)
- Economics Algorithm
- eigenvalue
- eigenvector
- element
- ellipsis
-
entry
$i^{\text{th}}\,$ entry in a list - equality of lists
- equivalence
- Euclidean norm
- event
- expression
- extending a function
F
-
fast Fourier transform
efficient implementation of DFT -
filter coefficients
from a given transfer function - filters
- findfil (MATLAB function)
- fit
- fitness
- Fourier series (continuous)
- frequency of sinusoids
- Frobenius norm
- functions
- function notation
- fundamental period
G
- generation
- genetic (MATLAB function)
- genetic algorithm
- Gibbs’ phenomenon
- gradient
- grad measure of an angle
-
Gram-Schmidt orthogonalization procedure
algorithm
H
- half-angle formulas
- half-open interval
- Hamming, R.W.
- harmonics
- Hilbert space
- horizontal orientation for lists
- hypothesis (plural ‘hypotheses’)
- hypothesis of an implication
I
- imaginary part of the complex exponential function
- implications
- improving filters
- increasing order
- induction argument
- infimum
- initialization
- inner product
- inner product space
- input
- insight
- integers, $\,\Bbb Z$
- interpolation
- interval notation
- invertibility
- irrational numbers
- iterative techniques
J
K
L
- Lanczos smoothing
- least common multiple
- least positive period
- least-squares approximation
- length of a list
- linear combination
- linear dependence on a parameter
- linearizing technique
- linearly dependent set
- linearly independent set
- linear system
- linear transformation
- lists
- listed
- local random behavior
-
logic (implication equivalent to contrapositive)
logic (appendix)
M
- maps to
- Martingale Algorithm
- MATLAB
- matrix laboratory
- mean (average)
- mean-square error
- member
- metric space
- minimax approximation
- Minimizing Vector Theorem
- mutation
- mutually orthogonal functions
N
- natural cubic spline
- negations
- neighbor
- nonlin (MATLAB function)
- noise
- nonlinear least squares approximation
- nonrec (MATLAB function)
- nonrecursive filter
- norm
- normed space
- norm (MATLAB command)
- $2$-norm
- notation
O
- objective function
- open interval
- operations on lists
- ‘or’ statement
- orientation (vertical or horizontal)
- orthogonal functions
- orthogonality properties of sine and cosine
- orthogonal matrix
- orthogonal projections
- orthogonal vectors
-
oscillation
in polynomial interpolation - output
- output list
P
- peak
- period (of transfer function)
- periodic function, definition
- periodicity
-
periodogram
definition - pervfft (MATLAB function)
- phase shift
- piecewise continuous periodic function
- point spread
- Pointwise Convergence Theorem
- polyfit (MATLAB command)
- polyval (MATLAB command)
- prstop (MATLAB function)
- proving a sentence
Q
R
- $\Bbb R^\infty$
- radian frequency
- radian measure of an angle
- rand (MATLAB command)
- ramps
- random behavior
- random sample
- random walk
- range of a function
- range of a linear transformation
- rank
- rational numbers are countable
- rational numbers, $\,\Bbb Q$
- rcond (MATLAB command)
- real numbers, $\,\Bbb R$
- real part of the complex exponential function
- real-valued function of a real variable
- recursive filters
- redundancy
- relative error
-
relatively prime
uniqueness of decomposition - reproduction
-
reshaping techniques
to identify periodic components
S
- Sampling Theorem
- scaling periodic functions
- scaling of a list
- Schwarz Inequality
- sensitivity of solutions
- sentence
- series number
- shares
- sigma factors
- signal
- signal analysis
-
sine function
origin of word -
singular values
definitions and results - sinusoid
- size
-
smoothing filters
smoothing by $K$’s - span
- splines
- spline (MATLAB command)
- statement
- stochastic process
- stock market data
- strings
- symtofc (MATLAB function)
- subspace
T
- time
- time list
-
time series
historical
- tptest (MATLAB function)
- transfct (MATLAB function)
-
transfer function
definition - transpose
- trapezoid rule
- triangle approach to trigonometry
- trigonometric identities
- trough
- truncated Fourier series
- truth set
- turning point test