GRAMMATICAL ERRATA

CHAPTER 1
Page 1; 2nd paragraph, 4th sentence; "Greeks and Romans have used light..."
Page 1; 2nd paragraph, 8th sentence; "... a variety of signals have been in study studied."
Page 2; When listing definitions of analysis, each sentence needs a period at the end. (Currently only the 3rd definition has a period).
Page 2; bottom paragraph, 6th sentence; "....and its expansion using the Euler's formula."
Page 4; 2nd paragraph; The 1st sentence should read "Spectral analysis and design are some of the basic building blocks in our study."
Page 4; 2nd paragraph; The last sentence should read "..... in terms or sine and cosines as the start of communication theory."
Page 4; Last paragraph; The 2nd sentence should read "In the first example, part of the time signal...".
Page 5; Last paragraph; Sentence 8 should read "We can simulate this by putting the watermelon on a stand, using a smaller hammer like device, giving a slight tap on the watermelon and recording the response."
Page 6; 2nd paragraph; The 2nd sentence should read "A simple method is to send a signal with ..." .
Page 7; First complete paragraph; 5th sentence: "We will be studying in much more detail of the frequency ..."
Page 7; Last sentence of the 1st paragraph should read "... formant frequencies are not be enough to... "
Page 9; 1st sentence of section 1.1-4 should read "... writing a signal in terms of functions that can..." .
*Page 10; sentence immediately above Interesting Functions, " Most of our the signals we deal with ..."
*Page 12; 2nd line above equation 1.1-15, "... is the half life, T_h, which is widely ..."
Page 17; 8th sentence of section 1.2-5 should read "... be expressed in terms of its even and odd parts by..."
Page 19; 2nd figure, the y axis should read "x_le(t)"
Page 22; Figure 1.2-7 is missing.
Page 23; Figure 1.3-1.  To match the text description, "B" should be marked on the y axis = to the height of the rectangle.  Both triagngles should be enlarged so that the high side stops at the closest upper corner of the rectangle, & the entire diagram should be shifted to the left so that the left edge of the left triangle resides at t = 0.
Page 32; The sentence immediately under Equation 1.4-19c should read "These impulses differ in the way how the value... "
Page 40; 2nd line of calculation for energy E_x, the integral innards should read "e^-2*alpha*t".
Page 42; 3rd sentence from the bottom should read "... We have made use of the fact that that..."
Page 52;  2nd line below 1.6-13, "... period T = (2pi/w_o).  We can see ..."
Page 68; 1.2-1a should read "x_i(t+1)"
Page 70; Problem 1.4-3b should also have t bounded by "|t| < 1/T"
Page 71; Problem 1.5-2a; the argument of x1(t) should be [(t-1)/2] to match the solution.

CHAPTER 2
Page 1; 1^st Paragraph, Sentence 3;  “The convolution operation is basic … analysis and in dealing with determining …”
Page 1; 1^st Paragraph, Sentence 4.  “… impulse functions and they are which were defined in terms …”
Page 1; 2nd Paragraph, Sentence 1.  “The impulse function …”
Page 1; 2^nd Paragraph, Sentence 4 and 5.  “Convolution operation is basic to all linear system analysis…”
Page 1; 2nd Paragraph, Sentence 7.  “… lends itself for a to spectral analysis..."
Page 1; 3^rd Paragraph, Sentence 3.  “One of these signals could be a delayed, or advanced, version of the other.”
Page 2; 1st sentence, "... of the function x(t), is a function of tau, and compares the function and with its shifted version."
Page 2; 2nd sentence, "... we use the cross correlation function and which is defined by..."
Page 2; equation 2.1-3,  The symbol for convolution is defined as "**".  Later in the chapter "*" is used.
Page 2; 2nd sentence below 2.1-3, "... note that the result of both auto and cross correlations result in functions that are function of tau..."
Page 2; 1st sentence above 2.1-6, "If the The two functions x(t)..."
Page 3; 1st sentence after 2.1-12, "... are nonnegative which results in Schwarz's..."
Page 4; 2nd line from the bottom, "... impulse function to the convolution."
Page 4; Section 2.2-1, Property 2, "The convolution operation satisfies..."
Page 4; Section 2.2-1, Property 3, "The convolution operation satisfies..."

CHAPTER 4
Page 1, 3rd line above 4.2-2, "... frequency interval between the adjascent adjacent line spectra ...
Page 2; 1st complete sentence "... which does not provide with any spectral information..."
Page 2; 2nd line below equation 4.2-7, "... Fourier transform, indication indicating the transform is a ..."
Page 3; 3rd sentence below equation 4.2-8d, "Most practical signals we deal with are real signals."
Page 3; 5th sentence below equation 4.2-8d, "... like the form in the (4.2-8d), as the..."
Page 3; 7th sentence below equation 4.2-8d, "Engineers in the communications area like the form..."
Page 3; 2nd sentence above equation 4.2-9, "In the synthesis equation, i.e., the inverse trnasorm transform given by ..."
Page 4; 2nd sentence in example 4.2-1, "... series coefficients of x_T(t) is are given in ...".
Page 4; sentence below 4.2-12, "... can be computer from the Fourier Series from (4.2-4) and is..."
Page 5; 4th sentence from the top "First let x(t) is be defined over..."
Page 5; sentence below 4.2-15b, "... is not time limited to a T second interval..."
Page 8;  Section 4.2-2, point 4, last line "This width is referred to as as the half-power..."
Page 9; line immediately above 4.3-1, "...Raleigh's energy theorem, and is discussed next."
Page 11; 4th line from top; "...total energy in the functionb using the  ..."
Page 13; 1st line above section 4.3-4, "... both time time-limited and ..."
Page 14, Example 4.3-4.  References to Figure 4.2-2 should be changed to read Figure 4.2-1.
Page 21; 1st sentence below 4.4-9b, "Figures 4.4-1a and b gives a signal and its spectrum."
Page 22, 2nd sentence above section 4.4-3.  Not sure what point this sentence is supposed to make.
Page 23, 1st line below 4.4-12b, " as the envelope-and-pahse phase description."
Page 46, 1st sentence below 4.6-3, " Most of the functions we deal with are real."
Page 47, 1st sentence below 4.6-10, "... the autocorrelation function Rx(tau) looses the phase information..."
Page 50, 1st sentence above section 4.7, "is very effective in computing the the period of the vowel."
Page 50, 5th line of section 4.7, "... some practical mesures measures of bandwidth.]
Page 66, 2nd line above 4.11-10a, "... the spectra of these puilses pulses have the so called ..."

CHAPTER 6
Page 2, equation 6.2-4, "T[a₁x(t) a₁x₁(t) + ..."
Page 3, b., For the inputs x₁(t) and x₂(t) m₁(t) and m₂(t), ..."
Page 4, equation 6.2-7d, "(Dealy Delay device)"
Page 6, line above 6.3-7, "The current voltage in the capacitor..."
Page 6, 5th line below 6.3-7, "... assumed to be zero with when t_o is equal to ...
Page 6, 6.3-10, right after the 2nd = sign, the Laplace transform of the integral of the current should be taken, not the derivative of the voltage.
Page 10, line below 6.3-22b, "We can say that that the circuit...".
Page 12, line below 6.4-2, "...x(t) is causal if it is equal to zero for zero for t < 0".
Page 13, line below 6.4-4, "The system is an invertible if...".
Page 16, line above 6.5-11, "The Laplace transform of this function of this function is given..."
Page 18, 2nd line below 6.5-20, "...to a phaser phasor input e^jwt..."
Page 85, problem 6.5-1, "In section 6.5 6.3, an RL RC circuit...".  This probably should ask you to use an RL circuit to approximate an integrator.

CHAPTER 7
**Throughout, inconsistent spacing between numbers and "Hz".
page 1 "Chapter 7N"
page 1, 1st paragraph, line 10, "These days, the telephone along with a computer  forms an integral part off of most ..."
**page 1, 1st paragraph, line 13, "... such as filtering, made it very popular.
**page 1, 3rd paragraph, the 3rd sentence is identical to the 4th sentence in the 1st paragraph.
**page 2, then 1st paragraph is essentially identical to sentences 5 & 6 on page 1, 1st paragraph.
*page 3, second sentence below the figure, "The sampled values, x(nt_s) is are assumed..."
**page 4, equation 7.2-4, both equations should be summed over the variable k.
**page 4, equation 7.2-5a, inconsistent notation.  The fraction "1/2" does not match the form of other fractions in the text.
**page 7, 1st sentence in section 7.2-2.  Towards the end of the sentence, some spaces after the commas need to be inserted.
**page 7, last sentence above example 7.2-1, "... if we select the sampling rate is equal to the... "
**page 8, 1st sentence of the last paragraph, "The spectrum of the given signal along with the spectrum of the sampled... "
**page 11, 2nd line under top most equation, "... we can evaluate the (7.2-17) at this value."
**page 12, 2nd line under "Notes:", "... k is an ineger integer and k... "
**page 14, example 7.2-4, "In this example, we would like to answer the question of sampling the given signal at exactly at the... "
**page 15, 6th line from the bottom, for clarity should read "(100)(100)(16)(6)(7) = 6.72 Mbits."
**page 16, last sentence of the 1st paragraph, "An interested reader should consult... ".
**page 20, "is less than a. 5% and b. 10% of the peak... "
**page 25, 7-2-45 should read 7.2-45.
*page 25, 2 lines below, "... where m is the largest integer..."
**page 99, problem 7.2-2, "c. What can you say about..."
page 100, problem 7.2-10, "... the possible sampling rates (see 7.2-45) possible rates so that the ..."
page 100, problem 7.2-10.  The end of the 2nd sentence has two periods.

CHAPTER 10
*Page 1, 2nd paragraph, 8th line, "One way to avoid this problem is to first shift the band ..."
*Page 1, 2nd paragraph, 11th line, "A second example is, that if telephone communications ..."
*Page 1, 2nd paragraph, 12th line, "... how much copper we would need ..."
*Page 1, 2nd paragraph, last sentence, "It is would be like a student ..."
*Page 3, 11th line below equation 10.1-1, "... are referred to as angle modulation ..."
*Page 3, last line of section below 10.1-1, "Digital modulation is a vast area and the presentation on this topic is minimal."
*Page 3, 2nd line, 1st full paragraph from the bottom, 2nd sentence, "... referred to as the demodulation."
*Page 4, 5th line below equation 10.2-1, "... a detailed discussion on the limiters later."
*Page 4, 3rd line above section 10.2-1, "...will be smooth and do does not have ..."
*Page 5, 2nd line, "... summing the two signals and then use using a nonlinear device... "
*Page 5, 7th line below equation 10.2-4, " dual-gate FET, and by making use ..."
*Page 6, 1st sentence above section 10.3-1, "... is also called an amplitude modulation ..."
*Page 6, 2nd line below equation 10.3-2, should read "... m(t) is the message or the information signal."
*Page 7,  1st sentence of section 10.3-2, "... i.e., undoing the modulation, is called the demodulation ..."


MATH ERRATA
CHAPTER 1
*page 51, equation 1.6-12a, the denominator of the 1st equation should read "(a₂ + jb₂w)(a₂ - jb₂w)

CHAPTER 2 HOMEWORK SOLUTIONS
2.2-2) All delta function arguments associated with y(t) should be "t" and not the greek letter "alpha".
2.2-2b) The figure labeled x(t-alpha) should have the horizontal axis marked as "alpha", not "t"
2.2-2b) Bounds are incorrect and should read ".5 < t -.5 < 1.5 or 1 < t < 1.5 2.0"
2.2-2b) when 2 < t < 3, bounds on the integral should be "t-0.5" and "t 0.5".  Alternatively, you can integrate from "t-1.5" to "1.5".
2.2-2b) There's a math error in the integral evaluated immediately below these bounds.  The equation should read (t*alpha²/2 - alpha³/3 -t*alpha²/2 + alpha).  When evaluated, this will eventually yield y(t) = (t³ - 6t² + 10.5t -5.5)/6.

CHAPTER 3 HOMEWORK SOLUTIONS
3.1-5) second line from the bottom, "1/T - 1/2T sin2k..."

CHAPTER 7 HOMEWORK SOLUTIONS
**7.2-7, part b, "The frequencies frequency located at 50 Hz and 100 Hz would pass through."   The 1st term of the output equation y(t) should also be dropped.