Fundamentals of Electrical Engineering I
Author:
Don H. Johnson
Pub Year:
2013
Source:
Read: 20170325
Last Update: 20170325
Five Sentence Abstract:
The course focuses on the creation, manipulation, transmission, and reception of information by electronic means. Elementary signal theory; time and frequencydomain analysis; Sampling Theorem. Digital information theory; digital transmission of analog signals; errorcorrecting codes.
Thoughts:
Heavy focus on signals and systems theory over "practical" electronics. I would
not suggest this as a first course if you are interested in EE/EECS. If you are
looking for communications theory, this is perfect.
IMHO the 2007 MIT 6.002 Circuits and Electronics is a better place to start.
Further, the 2011 MIT 6.01SC was also more appealing to me as it mixes the
theory with a more hands on approach (python programming and robots). The next
course in this Rice U series, ELEC242 I think, looks good but is not available
online.
Notes:
// designates my notes.
designates important.
Chapter 1  Introduction
page 7:
 The conversion of informationbearing signals from one energy form into
another is known as energy conversion or transduction.
page 8:

A Mathematical Theory of Communication by Claude Shannon (1948)

a signal is merely a function. Analog signals are continuous valued; digital
signals are discretevalued. The independent variable of the signal could be
time (speech, for example), space (images), or the integers (denoting the
sequencing of letters and numbers in the football score)
page 8:
 The basic idea of communication engineering is to use a signal’s parameters
to represent either real numbers or other signals. The technical term is to
modulate the carrier signal’s parameters to transmit information
Chapter 2  Signals and Systems
page 17:
 The complex conjugate of z, written as z∗
page 18:
 z = a + jb = r∠θ
r = z = √(a2 + b2)
a = r cos (θ)
b = r sin (θ)
θ = arctan(b/a)

 the polar form of a complex number z can be expressed mathematically as:
page 21:
 The complex exponential cannot be further decomposed into more elemental
signals, and is the most important signal in electrical engineering
page 22:

T = 1/f

f = The number of times per second we go around the circle equals the
frequency f.

T = period, how long for one complex exponential cycle
These two decompositions are mathematically equivalent to each other.
 A*cos(2πft + φ) = Re[Ae^(jφ)e^(j2πft)]
A*sin(2πft + φ) = Im[Ae^(jφ)e^(j2πft)]

page 23:
 As opposed to complex exponentials which oscillate, real exponentials (Figure
2.3) decay.
s(t) = e^(−t/τ)
 The quantity τ is known as the exponential’s time constant, and corresponds
to the time required for the exponential to decrease by a factor of 1 , which
approximately equals 0.368. A decaying complex exponential is the product of a
real and a complex exponential.
page 24:
 ways of decomposing a given signal into a sum of simpler signals, which we
term the signal decomposition
page 25:

One of the fundamental results of signal theory (Section 5.3) will detail
conditions under which an analog signal can be converted into a discretetime
one and retrieved without error.

A discretetime signal is represented symbolically as s (n), where n =
{...,−1,0,1,...}.
page 26:

The most important signal is, of course, the complex exponential sequence.
s(n) = e^(j2πfn)

Discretetime sinusoids have the obvious form s(n) = A*cos(2πfn + φ).
 ∞
s(n) = sum s(m)δ(n − m)
m=−∞

page 27:

Another interesting aspect of discretetime signals is that their values do
not need to be real numbers. We do have realvalued discretetime signals
like the sinusoid, but we also have signals that denote the sequence of
characters typed on the keyboard. Such characters certainly aren’t real
numbers,

// like a math set, formally called alphabet (but not
limited to characters in any actual language alphabet)

discretetime systems are ultimately constructed from digital circuits, which
consist entirely of analog circuit elements.

Signals are manipulated by systems. Mathematically, we represent what a
system does by the notation y(t) = S[x(t)], with x representing the input
signal and y the output signal.

A system’s input is analogous to an independent variable and its output the
dependent variable. For the mathematically inclined, a system is a
functional: a function of a function (signals are functions).

// Systems can be linked like linux pipes
 w(t) = S1[x(t)], and y(t) = S2[w(t)]
page 28:
 y(t) = S1[x(t)] + S2[x(t)]
page 29:
 The gain can be positive or negative (if negative, we would say that the
amplifier inverts its input) and can be greater than one or less than one. If
less than one, the amplifier actually attenuates.
page 30:
 t
y(t) = integral x(α)dα
−∞


the value of all signals at t = −∞ equals zero.

// linear systems, double the input double the output as a
simple test (not 100%)

// linear systems output 0 on input 0
page 31:

“They’re [linear systems] the only systems we thoroughly understand!”

Systems that don’t change their inputoutput relation with time are said to
be timeinvariant.

The collection of linear, timeinvariant systems are the most thoroughly
understood systems

electric circuits are, for the most part, linear and timeinvariant.
Nonlinear ones abound, but characterizing them so that you can predict their
behavior for any input remains an unsolved problem.
Chapter 3  Analog Signal Processing
page 39:

When we say that “electrons flow through a conductor,” what we mean is that
the conductor’s constituent atoms freely give up electrons from their outer
shells. “Flow” thus means that electrons hop from atom to atom driven along by
the applied electric potential.

A missing electron, however, is a virtual positive charge. Electrical
engineers call these holes, and in some materials, particularly certain
semiconductors, current flow is actually due to holes.

Current flow also occurs in nerve cells found in your brain. Here, neurons
“communicate” using propagating voltage pulses that rely on the flow of
positive ions (potassium and sodium primarily, and to some degree calcium)
across the neuron’s outer wall.
page 40:

For every circuit element we define a voltage and a current. The element has
a vi relation defined by the element’s physical properties. In defining the
vi relation, we have the convention that positive current flows from positive
to negative voltage drop.

p(t) = v(t)i(t) // (p)ower is measured in watts./span>

A positive value for power indicates that at time t the circuit element is
consuming power; a negative value means it is producing power.

as in all areas of physics and chemistry, power is the rate at which energy
is consumed or produced. Consequently, energy is the integral of power.
 t
E(t) =integral p(α)dα
−∞


positive energy corresponds to consumed energy and negative energy
corresponds to energy production.

—the resistor, capacitor, and inductor— impose linear relationships between
voltage and current.
page 41:
 Some times, the vi relation for the resistor is written i = Gv, with G, the
conductance, equal to 1/R. Conductance Rhas units of Siemens (S)
p(t) = Ri^2(t) = v^2(t)/R // Instantaneous power consumption
of a resistor.

As the resistance approaches infinity, we have what is known as an open
circuit: No current flows but a nonzero voltage can appear across the open
circuit. As the resistance becomes zero, the voltage goes to zero for a
nonzero current flow. This situation corresponds to a short circuit. A
superconductor physically realizes a short circuit.

The capacitor stores charge and the relationship between the charge stored
and the resultant voltage is q = Cv. The constant of proportionality, the
capacitance, has units of farads (F),

As current is the rate of change of charge, the vi relation can be expressed
in differential or integral form.
page 42:
 The inductor stores magnetic flux, with larger valued inductors capable of
storing more flux. Inductance has units of henries (H),
page 43:

voltage source’s vi relation is v = vs regardless of what the current might
be. As for the current source, i = −is regardless of the voltage. Another
name for a constantvalued voltage source is a battery,

If a sinusoidal voltage is placed across a physical resistor, the current
will not be exactly proportional to it as frequency becomes high, say above 1
MHz. At very high frequencies, the way the resistor is constructed introduces
inductance and capacitance effects. Thus, the smart engineer must be aware of
the frequency ranges over which his ideal models match reality well.
page 44:

Kirchhoff’s Current Law (KCL): At every node, the sum
of all currents entering a node must equal zero.

Kirchhoff’s Voltage Law (KVL): The voltage law says
that the sum of voltages around every closed loop in the circuit must equal
zero.</span
page 48:
 Resistors in series: The series combination of two resistors acts, as far as
the voltage source is concerned, as a single resistor having a value equal to
the sum of the two resistances.
page 49:
page 51:
 Note that in determining this structure [//of
series/parallel relationships//], we started away from the terminals,
and worked toward them. In most cases, this approach works well; try it first.
 RT = R1  (R2  R3 + R4)
RT = (R1*R2*R3 + R1*R2*R4 + R1*R3*R4) / (R1*R2 + R1*R3 + R2*R3 + R2*R4 + R3*R4)


A simple check for accuracy is the units: Each component of the numerator
should have the same units (here Ω^3 ) as well as in the denominator (Ω^2).
The entire expression is to have units of resistance; thus, the ratio of the
numerator’s and denominator’s units should be ohms.

In system theory, systems can be cascaded without changing the inputoutput
relation of intermediate systems. In cascading circuits, this ideal is rarely
true unless the circuits are so designed.

for series combinations, voltage and resistance are the key quantities, while
for parallel combinations current and conductance are more important. In
series combinations, the currents through each element are the same; in
parallel ones, the voltages are the same.
page 53:
 For any circuit containing resistors and sources, the vi relation will be of
the form: v = R_eq*i + v_eq and is the Thévenin equivalent circuit for any
such circuit is that of Figure 3.18.
page 55:
 MayerNorton equivalent: i = v/R_eq  i_eq, where i_eq = v_eq/R_eq is the
MayerNorton equivalent source.
page 56:
 Which one is used depends on whether what is attached to the terminals is a
series configuration (making the Thévenin equivalent the best) or a parallel
one (making MayerNorton the best).
page 58:

Because complex amplitudes for voltage and current also obey Kirchhoff’s
laws, we can solve circuits using voltage and current divider and the series
and parallel combination rules by considering the elements to be impedances.

The entire point of using impedances is to get rid of time and concentrate on
frequency.
page 59:

Even though it’s not, pretend the source is a complex exponential. We do
this because the impedance approach simplifies finding how input and output are
related. If it were a voltage source having voltage vin = p (t) (a pulse),
still let vin = Vinej2πf t. We’ll learn how to “get the pulse back” later.

With a source equaling a complex exponential, all variables in a linear
circuit will also be complex exponentials having the same frequency. The
circuit’s only remaining “mystery” is what each variable’s complex amplitude
might be. To find these, we consider the source to be a complex number (Vin
here) and the elements to be impedances.

We can now solve using series and parallel combination rules how the complex
amplitude of any variable relates to the sources complex amplitude.
page 60:
 Example 3.3 // Good explaination of using
impedence.
page 62:

V_out/V_in = H(f) // Transfer Function

Implicit in using the transfer function is that the input is a complex
exponential, and the output is also a complex exponential having the same
frequency.
page 63:
 the transfer function completely describes how the circuit processes the
input complex exponential to produce the output complex exponential. The
circuit’s function is thus summarized by the transfer function. In fact,
circuits are often designed to meet transfer function specifications.
page 64:
 magnitude has even symmetry: The negative frequency portion is a mirror image
of the positive frequency portion: H(−f) = H(f). The phase has odd
symmetry: ∠H(−f) = −∠H(f). These properties of this specific example apply
for all transfer functions associated with circuits.
page 67:

The node method begins by finding all nodes–places where circuit elements
attach to each other–in the circuit. We call one of the nodes the reference
node; the choice of reference node is arbitrary, but it is usually chosen to be
a point of symmetry or the “bottom” node. For the remaining nodes, we define
node voltages e_n that represent the voltage
between the node and the reference. These node voltages constitute the only
unknowns; all we need is a sufficient number of equations to solve for them. In
our example, we have two node voltages. The very act of
defining node voltages is equivalent to using all the KVL equations at your
disposal.

In some cases, a node voltage corresponds exactly to the voltage across a
voltage source. In such cases, the node voltage is specified by the source
and is NOT an unknown.
page 68:
 A little reflection reveals that when writing the KCL equations for the sum
of currents leaving a node, that node’s voltage will always appear with a
plus sign, and all other node voltages with a minus sign. Systematic
application of this procedure makes it easy to write node equations and to
check them before solving them. Also remember to check units at this point.
page 72:
 Resistors, inductors, and capacitors as individual elements certainly provide
no power gain, and circuits built of them will not magically do so either.
Such circuits are termed electrical in distinction to those that do provide
power gain: electronic circuits.
page 74:
 dependent sources cannot be described as impedances
page 80:

i(t) = I_0 · e^(q/kT)*v(t) − 1

q represents the charge of a single electron in coulombs, k is Boltzmann’s
constant, and T is the diode’s temperature in K. At room temperature, the
ratio kT/q = 25 mV. The constant I_0 is the qleakage current, and is usually
very small

diode’s schematic symbol looks like an arrowhead; the direction of current flow
corresponds to the direction the arrowhead points.

Because of the diode’s nonlinear nature, we cannot use impedances nor
series/parallel combination rules to analyze circuits containing them.
page 82:
unsorted:
Chapter 4  Frequency Domain
page 107:

all signals can be expressed as a superposition of sinusoids

Let s(t) be a periodic signal with period T. We want to show that periodic
signals, even those that have constantvalued segments like a square wave,
can be expressed as sum of harmonically related sine waves: sinusoids having
frequencies that are integer multiples of the fundamental frequency. Because
the signal has period T, the fundamental frequency is 1/T.
page 108:
 Key point: Assuming we know the period, knowing the Fourier coefficients is
equivalent to knowing the signal. Thus, it makes no difference if we have a
timedomain or a frequencydomain characterization of the signal.
page 109:

A signal’s Fourier series spectrum ck has interesting properties.

Property 4.1: (conjugate symmetry) If s(t) is real, c_k = c∗_−k (realvalued
periodic signals have conjugatesymmetric spectra).

Property 4.2: If s(−t) = s(t), which says the signal has even symmetry about
the origin, c_−k = c_k.

Property 4.3: If s(−t) = −s(t), which says the signal has odd symmetry, c_−k
= −c_k.

Property 4.4: The spectral coefficients for a periodic signal delayed by τ,
s(t − τ), are c_k*e^−(j2πkτ)/T , where ck denotes the spectrum of s(t).
Delaying a signal by τ seconds results in a spectrum having a linear phase
shift of −(2πkτ)/T in comparison to the spectrum of the undelayed signal.
page 110:
 Theorem 4.1: Parseval’s Theorem Average power calculated in the time domain
equals the power calculated in the frequency domain.
page 112:

The complex Fourier series and the sinecosine series are identical, each
representing a signal’s spectrum. The Fourier coefficients, a_k and b_k,
express the real and imaginary parts respectively of the spectrum while the
coefficients c_k of the complex Fourier series express the spectrum as a
magnitude and phase.

Equating the classic Fourier series (4.11) to the complex Fourier series
(4.1), an extra factor of two and complex conjugate become necessary to
relate the Fourier coefficients in each.
IMAGE EQ after 4.11
page 114:
 You can unambiguously find the spectrum from the signal (decomposition
(4.15)) and the signal from the spectrum (composition). Thus, any aspect of
the signal can be found from the spectrum and vice versa. A signal’s frequency
domain expression is its spectrum. A periodic signal can be defined either in
the time domain (as a function) or in the frequency domain (as a spectrum).
page 115:
 For a periodic signal, the average power is the square of its
rootmeansquared (rms) value. We define the rms value of a periodic signal
to be
page 120:

A new definition of equality is meansquare equality: Two signals are said to
be equal in the mean square if rms(s1 − s2) = 0

The Fourier series value “at” the discontinuity is the average of the values
on either side of the jump.

// To encode information we can use the Fourier
coefficients.

Assume we have N letters to encode: {a_1 , ..., a_N}. One simple encoding
rule could be to make a single Fourier coefficient be nonzero and all others
zero for each letter. For example, if an occurs, we make c_n = 1 and c_k = 0, k
!= n. In this way, the nth harmonic of the frequency 1/T is used to represent a
letter. Note N/T that the bandwidth—the range of frequencies required for the
encoding—equals . Another possibility is Tto consider the binary representation
of the letter’s index. For example, if the letter a_13 occurs, converting 13 to
its base2 representation, we have 13 = 1101. We can use the pattern of zeros
and ones to represent directly which Fourier coefficients we “turn on” (set
equal to one) and which we “turn off.”
page 122:

Because the Fourier series represents a periodic signal as a linear
combination of complex exponentials, we can exploit the superposition
property. Furthermore, we found for linear circuits that their output to a
complex exponential input is just the frequency response evaluated at the
signal’s frequency times the complex exponential. Said mathematically, if x(t)
= e^(j2πkt)/T, then the output y(t) = H(k/T)*e^(j2πkt)/T because f = k . Thus,
if x(t) is periodic thereby having a Fourier series, a linear circuit’s output
to this signal will be the superposition of the output to each component.

Thus, the output has a Fourier series, which means that it too is periodic.
Its Fourier coefficients equal c_k*H(k/T). To obtain the spectrum of the
output, we simply multiply the input spectrum by Tthe frequency response. The
circuit modifies the magnitude and phase of each Fourier coefficient. Note
especially that while the Fourier coefficients do not depend on the signal’s
period, the circuit’s transfer function does depend on frequency, which means
that the circuit’s output will differ as the period varies.
page 123:

we have calculated the output of a circuit to a periodic input without
writing, much less solving, the differential equation governing the circuit’s
behavior. Furthermore, we made these calculations entirely in the frequency
domain. Using Fourier series, we can calculate how any linear circuit will
respond to a periodic input.

S(f) is the Fourier transform of s(t) (the Fourier transform is symbolically
denoted by the uppercase version of the signal’s symbol) and is defined for
any signal for which the integral converges.
page 124:

The quantity sin(t)/t has a special name, the sinc (pronounced “sink”)
function, and is denoted by sinc(t)

The Fourier transform relates a signal’s time and frequency domain
representations to each other. The direct Fourier transform (or simply the
Fourier transform) calculates a signal’s frequency domain repre sentation from
its timedomain variant (4.34). The inverse Fourier transform (4.35) finds the
timedomain representation from the frequency domain. Rather than explicitly
writing the required integral, we often symbolically express these transform
calculations as F(s) and F^−1(S), respectively.
page 125:
page 129:
 all linear, timeinvariant systems have a frequencydomain inputoutput
relation given by the product of the input’s Fourier transform and the
system’s transfer function. Thus, linear circuits are a special case of linear,
timeinvariant systems.
page 130:
 X(f)H1(f) and it serves as the second system’s input, the cascade’s output
spectrum is X(f)H1(f)H2(f). Because this product also equals X(f)H2(f)H1(f),
the cascade having the linear systems in the opposite order yields the same
result. Furthermore, the cascade acts like a single linear system, having
transfer function H1(f)H2(f). This result applies to other configurations of
linear, timeinvariant systems as well;
page 132:
Chapter 5  Digital Signal Processing
page 155:
 Note that if we represent truth by a “1” and falsehood by a “0,” binary
multiplication corresponds to AND and addition (ignoring carries) to XOR.
page 158:
 Amplitude Quantization = analog signals converted to
digital (ADC)
page 159:

the original amplitude value cannot be recovered without error.

signaltonoise ratio, which equals the ratio
of the signal power and the quantization error power.
page 161:
page 162:

each element of the symbolicvalued signal s (n) takes on one of the values
{a1, . . . , aK } which comprise the alphabet A.

5.6 DiscreteTime Fourier Transform (DTFT)
page 166:
 5.7 Discrete Fourier Transforms (DFT)
page 168:
page 169:

5.9 Fast Fourier Transform (FFT)

The computational advantage of the FFT comes from recognizing the periodic
nature of the discrete Fourier transform. The FFT simply reuses the
computations made in the halflength transforms and combines them through
additions and the multiplication by e^(−j2πk/N), which is not periodic over
N/2, to rewrite the lengthN DFT. Figure 5.12 (Length8 DFT decomposition)
illustrates this decomposition.
page 170:
 basic computational element known as a butterfly(Figure 5.13 (Butterfly))
page 171:
 Exervise 5.18 Answer from pg 199: The transform can have any greater than or
equal to the actual duration of the signal. We simply “pad” the signal with
zerovalued samples until a computationally advantageous signal length results.
page 173:
page 174:

Exercise 5.22 Answer from page 200: In discretetime signal processing, an
amplifier amounts to a multiplication, a very easy operation to perform.

linear, shiftinvariant systems // Slightly different
terminology from analog to digital. This is to emphasis integer vals
only.
page 175:
 A discretetime signal s(n) is delayed by n0 samples when we write s(n − n0),
with n0 > 0. Choosing n0 to be negative advances the signal along the
integers. As opposed to analog delays (Section 2.6.3: Delay), discretetime
delays can only be integer valued. In the frequency domain, delaying a signal
corresponds to a linear phase shift of the signal’s discretetime Fourier
transform: s(n − n0) ↔ e^−(j2πfn0)S(e^j2πf)).
 In analog systems, the differen
tial equation specifies the inputoutput relationship in the timedomain. The corresponding discretetime
specification is the difference equation.

Here, the output signal y (n) is related to its past values y (n − l), l =
{1, . . . , p}, and to the current and past values of the input signal x (n).
The system’s characteristics are determined by the choices for the number of
coefficients p and q and the coefficients’ values {a1 , . . . , ap} and {b0, b1
, . . . , bq }.

Aside: There is an asymmetry in the coefficients: where is a0 ? This
coefficient would multiply the y (n) term in (5.42). We have essentially
divided the equation by it, which does not change the inputoutput
relationship. We have thus created the convention that a0 is always one.
page 176:
 // Set the initial conditions of the difference equation
to 0.
page 178:
page 179:

a unitsample input, which has X ej2πf = 1, results in the output’s Fourier
transform equaling the system’s transfer function.

In the timedomain, the output for a unitsample input is known as the
system’s unitsample response, and is denoted by h (n). Combining the
frequencydomain and timedomain interpretations of a linear, shift invariant
system’s unitsample response, we have that h (n) and the transfer function are
Fourier transform pairs in terms of the discretetime Fourier transform.
page 180:

(sampling in one domain, be it time or frequency, can result in aliasing in
the other) unless we sample fast enough. Here, the duration of the
unitsample response determines the minimal sampling rate that prevents
aliasing.

For IIR systems, we cannot use the DFT to find the system’s unitsample
response: aliasing of the unit sample response will always occur.
Consequently, we can only implement an IIR filter accurately in the time domain
with the system’s difference equation. Frequencydomain implementations are
restricted to FIR filters.
page 181:
 The spectrum resulting from the discretetime Fourier transform depends on
the continuous frequency variable f . That’s fine for analytic calculation,
but computationally we would have to make an uncountably infinite number of
computations.
page 185:
 we can process, in particular filter, analog signals “with a computer” by
constructing the system shown in Figure 5.24. To use this system, we are
assuming that the input signal has a lowpass spectrum and can be bandlimited
without affecting important signal aspects. Bandpass signals can also be
filtered digitally, but require a more complicated system. Highpass signals
cannot be filtered digitally.
page 186:
 It could well be that in some problems the timedomain version is more
efficient (more easily satisfies the real time requirement), while in others
the frequency domain approach is faster. In the latter situations, it is the
FFT algorithm for computing the Fourier transforms that enables the superiority
of frequencydomain implementations.
Chapter 6  Information Communication
page 202:
 In the case of singlewire communications, the earth is used as the current’s
return path. In fact, the term ground for the reference node in circuits
originated in singlewire telegraphs.
page 203:
page 207:

Transmitted signal amplitude does decay exponentially along the transmission
line. Note that in the highfrequency regime the space constant is small,
which means the signal attenuates little.

Wireless channels exploit the prediction made by Maxwell’s equation that
electromagnetic fields propagate in free space like light. When a voltage is
applied to an antenna, it creates an electromagnetic field that propagates in
all directions (although antenna geometry affects how much power flows in any
given direction) that induces electric currents in the receiver’s antenna.

The fundamental equation relating frequency and wavelength for a propagating
wave is

Thus, wavelength and frequency are inversely related: High frequency
corresponds to small wavelengths. For example, a 1 MHz electromagnetic field
has a wavelength of 300 m. Antennas having a size or distance from the ground
comparable to the wavelength radiate fields most efficiently. Consequently, the
lower the frequency the bigger the antenna must be. Because most information
signals are baseband signals, having spectral energy at low frequencies, they
must be modulated to higher frequencies to be transmitted over wireless
channels.
page 208:
 At the speed of light, a signal travels across the United States in 16 ms, a
reasonably small time delay. If a lossless (zero space constant) coaxial
cable connected the East and West coasts, this delay would be two to three
times longer because of the slower propagation speed.
page 209:

The maximum distance along the earth’s surface that can be reached by a
single ionospheric reflection is 2Rarccos(R/R+h_i), which ranges between
2,010 and 3,000 km when we substitute minimum and maximum ionospheric altitudes
(80180km).

// delays of 6.810ms for a single reflection.
page 210:
 geosynchronous satallites need to be at at altitude of 35700km. They also need to work on frequencies not blocked by the ionosphere. Their delay si about 0.24 seconds.
page 211:
page 216:
 A commonly used example of a signal set consists of pulses that are negatives of each other (Figure 6.7).
s0(t) = ApT(t)
s1(t) = −ApT(t)

This way of representing a bit stream—changing the bit changes the sign of
the transmitted signal—is known as binary phase shift keying and abbreviated
BPSK.

The datarate R of a digital communication system is how frequently an
information bit is transmitted. In this example it equals the reciprocal of
the bit interval: R = 1/T. Thus, for a 1 Mbps (megabit per second)
transmission, we must have T = 1μs.
page 217:
page 218:

The first and third harmonics contain that fraction of the total power,
meaning that the effective bandwidth of our baseband signal is 3/2T or,
expressing this quantity in terms of the datarate, 3R/2. Thus, a digital
communications signal requires more bandwidth than the datarate: a 1 Mbps
baseband system requires a bandwidth of at least 1.5MHz. Listen carefully when
someone describes the transmission bandwidth of digital communication systems:
Did they say “megabits” or “megahertz?”

In frequencyshift keying(FSK), the bit affects the frequency of a carrier
sinusoid.
page 219:

Synchronization can occur because the transmitter begins sending with a
reference bit sequence, known as the preamble. This reference bit sequence is
usually the alternating sequence as shown in the square wave example19 and in
the FSK example (Figure 6.13).

This procedure amounts to what in digital hardware as selfclocking
signaling:
page 220:
 The second preamble phase informs the receiver that data bits are about to
come and that the preamble is almost over.
page 222:
page 230:
page 223:

As the received signal becomes increasingly noisy, whether due to increased
distance from the transmit ter (smaller α) or to increased noise in the
channel (larger N_0), the probability the receiver makes an error approaches
1/2.

As the signaltonoise ratio increases, performance gains–smaller probability
of error pe – can be easily obtained. At a signaltonoise ratio of 12 dB,
the probability the receiver makes an error equals 10−8. In words, one out of
one hundred million bits will, on the average, be in error.

Once the signaltonoise ratio exceeds about 5 dB, the error probability
decreases dramatically. Adding 1 dB improvement in signaltonoise ratio can
result in a factor of ten smaller pe .
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page 226:
page 227:

Create a vertical table for the symbols, the best ordering being in
decreasing order of probability.

Form a binary tree to the right of the table. A binary tree always has two
branches at each node. Build the tree by merging the two lowest probability
symbols at each level, making the probability of the node equal to the sum of
the merged nodes’ probabilities. If more than two nodes/symbols share the
lowest probability at a given level, pick any two; your choice won’t affect B
(A).

At each node, label each of the emanating branches with a binary number. The
bit sequence obtained from passing from the tree’s root to the symbol is its
Huffman code.
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Huffman showed that his (maximally efficient) code had the prefix property:
No code for a symbol began another symbol’s code. Once you have the prefix
property, the bitstream is partially selfsynchronizing: Once the receiver
knows where the bitstream starts, we can assign a unique and correct symbol
sequence to the bitstream.

// Otherwise you need a "comma" or some seperator but
between each symbol.
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 // Telegraph deployed in 1844!
page 230:
 // Adding a channel coder and decoder to each end of the
digital channel allows for error correcting bits to reduce errors further.
This is the Fundamental Model of Digital Communication.
FIG 6.20
 // Repetition code sends an odd number of bits (repeated)
and then votes to see what the value is. The repeated code has a higher
datarate which makes the scheme inefficient. Transmitting 3 bits for every 1
does not make up in accuracy what you lose in speed.
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 We define the Hamming distance between binary data words c1 and c2 , denoted
by d(c1,c2) to be the minimum number of bits that must be “flipped” to go
from one word to the other.
page 242:
 Communications networks are now categorized according to whether they use
packets or not. A system like the telephone network is said to be circuit
switched: The network establishes a fixed route that lasts the entire duration
of the message. Circuit switching has the advantage that once the route is
determined, the users can use the capacity provided them however they like. Its
main disadvantage is that the users may not use their capacity efficiently,
clogging network links and nodes along the way. Packetswitched networks
continuously monitor network utilization, and route messages accordingly. Thus,
messages can, on the average, be delivered efficiently, but the network cannot
guarantee a specific amount of capacity to the users.
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Appendix
page 270:
 FCC Frequency Allocation chart