List of Figures
List of Tables
Preface
1
Analog and Digital Signals
2
Transforms and Signal Representation
3
Analog and Digital Systems
4
Spectral Estimation Techniques
A
Useful Mathematics
B
Useful Concepts About Signal and Systems
Glossary
Bibliography
Index
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List of Tables
1.1
Notation used for continuous and discrete-time signals.
1.2
New signals
y
1
[
n
]
=
x
[
n
−
2
]
,
y
2
[
n
]
=
x
[
−
n
+
3
]
,
y
3
[
n
]
=
x
[
2
n
]
and
y
4
[
n
]
=
x
[
n
2
]
, obtained by manipulating
x
[
n
]
=
n
2
(
u
[
n
−
3
]
−
u
[
n
−
7
]
)
.
1.3
Total energy
E
and average power
P
for two kinds of signal assuming an infinite time interval.
1.4
Typical sampling frequencies.
1.5
The notation and values of the Nyquist frequency in distinct domains.
1.6
Input/output mapping for the quantizer specified by
ℳ
=
{
−
4
,
−
1
,
0
,
3
}
of Figure 1.52.
1.7
Input/output mapping for a generic quantizer designed for a Gaussian input with variance
σ
2
=
10
.
1.8
Examples of binary numbering schemes used as output codes in A/D conversion for
b
=
3
bits.
1.9
Comparison of quantization modes for fixed-point representations via examples.
1.10
Autocorrelation functions, their respective equation numbers and symbols.
1.11
Example of autocorrelation using Eq. (1.58) for the real-valued signal
x
[
n
]
=
δ
[
n
]
+
2
δ
[
n
−
1
]
+
3
δ
[
n
−
2
]
with
N
=
3
.
1.12
Example of autocorrelation using Eq. (1.58) for the complex-valued signal
x
[
n
]
=
(
1
+
j
)
δ
[
n
]
+
2
δ
[
n
−
1
]
+
3
δ
[
n
−
2
]
+
4
δ
[
n
−
3
]
with
N
=
4
.
2.1
Examples of transforms and applications.
2.2
Examples of inner product definitions.
2.3
The four pair of equations for Fourier analysis with eternal sinusoids and the description of their spectra:
c
k
,
X
(
f
)
(or
X
(
ω
)
),
X
[
k
]
and
X
(
e
jΩ
)
. For periodic continuous and discrete-time signals the periods are
T
0
and
N
0
, respectively, with fundamental (angular) frequencies
ω
0
=
2
π
∕
T
0
rad/s and
Ω
0
=
2
π
∕
N
0
rad. For continuous-time signals, one can alternatively use the linear frequency
f
instead of
ω
=
2
πf
, such that
f
0
=
1
∕
T
0
is the fundamental frequency in Hz.
2.4
Duality of periodicity and discreteness in Fourier analysis.
2.5
Units for each pair of Fourier equations in Table 2.3.
2.6
Summary of equations useful for signal processing with FFT.
3.1
Relations of the impulse response to the system function and frequency response of LTI systems.
3.2
Nomenclature of special frequencies used in filtering.
3.3
Some distinct options for the numerator of a SOS.
3.4
Parameters of a second-order system as described by Eq. (3.18).
3.5
Specifications of a commercial SAW filter.
3.6
Specifications of a commercial ceramic filter where
f
n
=
455
kHz is the nominal frequency and
f
c
is the center of the 6-dB BW.
3.7
Methods to convert
H
(
s
)
into
H
(
z
)
.
3.8
Main approximations adopted in the design of continuous-time filters
H
(
s
)
with their pros and cons with respect to phase and magnitude (mag.).
3.9
Pre-warped bilinear as a method to convert
H
(
s
)
into
H
(
z
)
.
3.10
Types of linear-phase FIR filters
3.11
Matlab/Octave functions to convert among the formats: transfer function (tf), zero-pole (zp) and second order sections (sos)
4.1
Difference in dB between the window main lobe and highest sidelobe amplitudes.
4.2
ESD functions.
E
is the total energy and the column “Ind. var” (independent variable) indicates the units and symbols used for the independent variable of each function. The units of
G
(
f
)
,
G
(
ω
)
∕
(
2
π
)
and
G
(
e
jΩ
)
∕
(
2
π
)
are J/Hz, J/(rad/s) and J/rad, respectively.
4.3
PSD functions.
P
is the average power and the column “Ind. var.” indicates the units and symbols used for the independent variable of each function.
F
f
and
F
ω
denote the Fourier transform in Hertz and rad/s, respectively. The units of
S
(
f
)
,
S
(
ω
)
∕
(
2
π
)
and
S
(
e
jΩ
)
∕
(
2
π
)
are W/Hz, W/(rad/s) and W/rad, respectively.
4.4
LPC result for different orders
P
for a ramp signal with added noise.
4.5
LPC result for different orders
P
for an AR(2) realization.
A.1
Analogy between using the histogram and DFT for estimation, where
ĝ
(
x
[
n
]
)
is the estimated function and
f
^
(
x
[
n
]
)
=
κĝ
(
x
[
n
]
)
its normalized version. The unit of
f
^
(
x
[
n
]
)
is indicated within parentheses.
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