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Glossary
Definition: FFT
(Fast Fourier Transform) An efficient computational algorithm for computing the
m10249m102493DFT.
Solutions
Index
A
absolutely integrable, Stable vs. Unstable
alias , Aliasing
aliasing , The sampling theorem, Aliasing
all the bands contain the same information but at different frequencies , The sampling theorem
alphabet, Symbolic Signals, Symbolic-valued Signals
amplitude response, THE AMPLITUDE RESPONSE
analog, Discrete-Time Signals
analog-to-digital converters , Sampling of continuous-time signals
antialiasing prefilter , Aliasing
argument, Complex Numbers
autocorrelation, Autocorrelation Function, Glossary
B
bandlimited, Sampling Period/Rate
bi-quad, Introduction
bilateral z-transform, Basic Definition of the Z-Transform
binary encoding , Sampling of continuous-time signals
bounded input-bounded output (bibo), Stable vs. Unstable
boxcar filter, Discrete-Time Systems in the Time-Domain, Examples for Systems in the Time
buffering, Efficiency of Frequency-Domain Filtering
butterfly, Deriving the FFT
C
causal, Causal vs. Noncausal, Pole/Zero Plots and the Region of Convergence
characteristic polynomial, Homogeneous Solution, Homogeneous Solution
circulant matrix, Understanding Conditions on Matrix for Shift Invariance
circular convolution, Compute IDFT of Y[k]
complex exponential sequence, Complex Exponentials, Complex Exponentials
complex exponentials, Introduction
complexity, FFT and the DFT
composite, Conclusion
computational advantage, Deriving the FFT
computational algorithm, The FFT Algorithm, Glossary
conjugate, Complex Numbers
continuous system, Continuous vs. Discrete
continuous time fourier transform, Introduction
continuous-time fourier transform, Introduction
control theory, Examples of Pole/Zero Plots
correlation of two signals measure the degree of their similarity., DIGITAL CORRELATION
countably infinite, Filtering in the Frequency Domain
D
decimation, Decimation in time FFT
delayed, Systems in the Time-Domain
difference equation, Discrete-Time Systems in the Time-Domain, Systems in the Time-Domain,
Introduction, Summary, Glossary
direct method, Solving a LCCDE, Solving a LCCDE
discrete fourier transform (dft), Sampling DTFT
discrete system, Continuous vs. Discrete
discrete time fourier transform, Introduction
discrete-time fourier transform, Introduction
discrete-time sinc function, DTFT Examples, Discrete-Time Fourier Transform (DTFT)
E
ecg, DTFT and Convolution
electrocardiogram, Glossary
envelop delay, WHY LINEAR-PHASE: MORE
F
fast fourier transform, Fast fourier transform (FFT)
fft, The FFT Algorithm, Glossary
fir, Discrete-Time Systems in the Time-Domain, Examples for Systems in the Time Domain
form, Deriving the FFT
fourier series, Equations, Equations
fourier transform, Basic Definition of the Z-Transform
frames, Spectrograms
frequency characteristic , FREQUENCY RESPONSE OF LTI (LSI) SYSTEMS
frequency domain, Properties of CTFT
frequency response , FREQUENCY RESPONSE OF LTI (LSI) SYSTEMS
functional, Introduction to Systems
G
geometric series, DTFT Examples, Discrete-Time Fourier Transform (DTFT)
group delay, WHY LINEAR-PHASE: MORE
H
hanning window, Spectrograms
homogeneous solution, Direct Method, Direct Method
I
iir, Discrete-Time Systems in the Time-Domain, Examples for Systems in the Time Domain,
impulse response, Understanding Conditions on Matrix for Shift Invariance, Summary: LSI
in order the samples represent correctly the analog signal, the sampling frequency must be greater
than twice the maximum frequency of the analog signal:, The sampling theorem
indirect method, Solving a LCCDE, Solving a LCCDE
infinite impulse-response, Introduction
initial conditions, Discrete-Time Systems in the Time-Domain, Difference Equation
L
linear, Linear vs. Nonlinear
linear discrete-time systems, Systems in the Time-Domain
linear shift invariant system, LSI/LTI Systems, Glossary
linear time-invariant, Introduction
live, Illustrations
lti, Introduction
M
method of sequence (vector),, Cross-correlation and auto-correlation
modulus, Complex Numbers
N
narrow-band spectrogram, Short Time Fourier Transform
noise removal, Efficiency of Frequency-Domain Filtering, FIR Filter Example
nonanticipative, Causal vs. Noncausal
noncausal, Causal vs. Noncausal
nonlinear, Linear vs. Nonlinear
not, Speed Comparison
nyquist interval , The sampling theorem
nyquist rate , The sampling theorem
O
optimal, L-∞ Optimal Lowpass Filter Design Lemma
order, Difference Equation
P
particular solution, Direct Method, Direct Method
phase delay, WHY LINEAR-PHASE?
pitch (fundamental frequency) , Correlation of periodic signals
pole-zero cancellation, Examples of Pole/Zero Plots
poles, Introduction to Poles and Zeros of the Z-Transform, Glossary
postfilter , Aliasing
power series, Region of Convergence
properties, Properties of CTFT
proportional , FFT and the DFT
Q
quantization , Sampling of continuous-time signals
R
S
sampling , SIGNAL SAMPLING
sampling frequency , Sampling of continuous-time signals
sampling interval, Sampling of continuous-time signals
sampling is just a multiplication of the analog signal x(t) with a sampling signal (or function)
s(t):, Sampling of continuous-time signals
sampling period , Sampling of continuous-time signals
shift-invariant, Discrete-Time Systems in the Time-Domain, Systems in the Time-Domain
signal, Signals Represent Information
slide (shift) – multiply – add. , Cross-correlation and auto-correlation
solution , Cross-correlation and auto-correlation, Auto-correlation, Correlation and data
communication, Aliasing, Associativity, Impulse response for causal system and signal, System
identification , From the DTFT to the DFT, Frequency response, FREQUENCY RESPONSE OF
LTI (LSI) SYSTEMS, Eigen-function and eigen-value in DSP systems , Frequency response in
spectrogram, Short Time Fourier Transform
stable, Stable vs. Unstable, Pole/Zero Plots and the Region of Convergence
symmetries, How does the FFT work?
system identification , System identification
T
the stagecoach effect, Sampling too slowly
time domain, Properties of CTFT
time index , Sampling of continuous-time signals
time invariant, Time Invariant vs. Time Variant
time variant, Time Invariant vs. Time Variant
time-reversed impulse response, Understanding Conditions on Matrix for Shift Invariance
time-varying behavior, Note
toeplitz matrices, Understanding Conditions on Matrix for Shift Invariance
transfer function, Conversion to Z-Transform, Conversion to Laplace-Transform
twiddle factor, Summary of FFT algorithms
twiddle factors, How does the FFT work?
U
uncountably infinite, Filtering in the Frequency Domain
uniform sampling , Sampling of continuous-time signals
unilateral z-transform, Basic Definition of the Z-Transform
unit sample, Unit Sample, Unit Step, Unit Sample
unit-sample response, Filtering in the Frequency Domain
unstable, Stable vs. Unstable
W
wide-band spectrogram, Short Time Fourier Transform
window, Spectrograms
Z
z-plane, The Complex Plane
z-transform, Basic Definition of the Z-Transform
z-transforms, Table of Common z-Transforms
zero-pad, Filtering in the Frequency Domain
zeros, Introduction to Poles and Zeros of the Z-Transform, Glossary
Attributions
Collection: ECE 454 and ECE 554 Supplemental reading
Edited by: Thad Welch