Miscellaneous Errata

EE341 -- Discrete-Time Linear Systems -- Winter 2001

• Signals, Systems and Transforms by Phillips and Parr
  • Inside back cover: (see corrections to p. 536, Table 12.1)
  • Chapter 3
    • p. 128, problem 3.19: the equation given could not correspond to an LTI system unless it was specified that x1(t) started at time t=0, which would give an incomplete description of the system. The upper limit of the integral must be either a constant or infinity.
  • Chapter 4
    • In Table 4.3, line 5, final column, it should also have C_{-1}=jX_0/4
  • Chapter 5
    • In problem 5.18b, the graph on p. 237 indicates two different heights. Use 0.5 for this problem.
    • In Table 5.2, the second to last line is missing a delta between )(. This is the same as the line below it: the Ck's are just "samples" of the FT of g(t).
    • Equation 5.14 on p. 188 should have positive jt0(w/a) in the exponent, not negative.
    • Equation 5.35 on p. 206 should be e^(jw_0kt) instead of e^(jw_0t). Also, they left out the upper infinity term on the summation.
  • Chapter 6
    • Figure 6.22(b) on p. 263: the -w_1 should be -w_2
    • p. 269 after first eqn: Euler is spelled wrong
    • p. 287, Figure P6.16: the triangle wave is X(omega) (not X_1(omega))
  • Chapter 7
    • On p. 290, eqn 7.2 for the inverse Laplace transform, it should be the integral of F(s)e^(st)ds, not F(s)e^(st)dt.
  • Chapter 9
    • Page 389: in the line after equation 9.17 delta[t] should be delta(t), last equation on the page should have [] instead of () for the delta terms
    • problem 9.30: all of the plain x terms should be x[n]
  • Chapter 10
    • page 431, first paragraph, there's typo on the 3rd line: x[10]h[-5] and x[10]h[-6] instead of x[10]y[-5], x[10]y[-6].
    • Top of p. 442: "bonded-input" should be "bounded-input"
    • p. 448, 9th line from bottom: y[n]=cos(2n) should be x[n]=cos(2n)
    • p. 433: "excent" -> "except"
    • p. 446, eqn 10.50: missing y in last term, should be ... + a_N y[n-N] = 0
  • Chapter 11
    • p. 481: Empty line in Z-transform of the unit step function should be 1/(1-z^{-1}) = z/(z-1)
    • p. 511, figure 11.13 (a): should be labeled u[n] not u[-n]
  • Chapter 12
    • p. 505: 4th line from the bottom BIRO -> BIBO
    • p. 506, 4th line: "unity" should be "unit"
    • p. 527: right after eqn 12.4, omega should be omega_s; in eqn 12.7 omega_0 should be omega_s
    • p. 528, line 5: should be omega_M < omega_s/2 (not >)
    • p. 536, Table 12.1: (same changes in table on inside book cover)
      change f(t) to f[n] in heading; item 12, change x(n) to x[n] in ak formula, add k to exponent in ak formula
    • p. 537, linearity eqn: the X_i[n] on the right hand side of the equation should be X_i(Omega)
    • p. 538, example 12.5: x[n] equation should be: x[n] = delta[n-3]+0.5delta[n-4] + 0.25delta[n-5]+... etc
      (omit T and change t to n in both lines of the equation)
    • p. 538, 1st line of frequency shift eqn: there is a missing OMEGA at the end of the eqn. The formula should be:
      DTFT[e^(jOMEGA_0 n) x[n]]= Sum [e^(jnOMEGA_0) x[n] e^(-jnOMEGA)]
      where the sum goes from n=-Infinity to Infinity
      Also, eqn 12.23 should be e^{jnOMEGA} (no - sign)
    • p. 539: 2nd eqn in time reversal proof should have k not -k in the first term (final term is correct)
    • p. 541 eqn 12.29: needs a 1/2pi term on the right hand side of the equation
    • p. 541, Table 12.2
      item 3, change [Omega] to (Omega)
      item 5, change to $e^{jnOMEGA_0}x[n]$ (omit the negative sign on the exponential)
      item 9, change to circular convolution instead of linear convolution in the frequency domain
    • p. 542, eqn 12.31: both sums should be indexed with n not k
    • p. 545, line 1: "The period of X(OMEGA) is OMEGA=2pi." -> "The period of X(OMEGA) is 2pi"
    • p. 545, example 12.7: X_0(OMEGA)= e^{-j OMEGA} + e^{-j 2*OMEGA}, and sum is over n not k
    • p. 545, eqn 12.42: the sum is over n not k
    • p. 546, figure 12.15: text formating error in caption, should be X_0(OMEGA)
    • p. 547, figure 12.16: the plot (or the areas of the impulses) should be scaled with respect to fig. 12.15 by 2 * pi/3. as it is plotted now, they both are the same height
    • p. 550 eqn 12.45: e^{-jxxx} terms should all have +j since this is an inverse DFT
    • p. 554, equation 12.52: x[n] in the sum on the RHS of the equation should be replaced with X[k]
    • p. 554 example 12.9: X[2] = 1 - 2 + 3 - 4 = -2 and X[3] = 1 + j2 - 3 - j4 = -2 -j2 (note conjugate symmetry)
    • p. 559, eqn 12.54: the last two eqns should have + rather than -, and all 4 should have the k set to be a specific value (0,1,2,3), which simplify to (dropping the subscript 4) W^0=1, W^2=-1, W^3=-W^1
    • p. 560, 7th line from bottom: x_e[n] should be x_o[n]
    • p. 562, eqn for X[3] should be: X[3] = X1[1] - W X2[1] = -2 - (-j)(-2) = -2 -j2
    • p. 562, 1st eqn in DIF FFT section: k range should be 0, 1, ...,N-1
    • p. 564: X[0] = X_1[0] + X_1[0] = 4 + 6 = 10 should be X[0] = X_1[0] + X_1[1] = 4 + 6 = 10
    • p. 575, 1st y[n] eqn: change 1=0 to l=0
    • p. 576, last 2 eqns: x[1] -> y[1], x[2] -> y[2]
    • p. 579, figure 12.35: b) there's a 1 that should be 0 at the 3rd inside position (the 8 o'clock position) and a 4 that should be 0 on the outside circle. f) there's a 0 missing in the inside circle (the 2 o'clock position)
    • p. 580: the comment of the Matlab example should say 12.18 not 11.18
    • p. 597: figure 12.6c should be labeled v[n] (not v(t)); figure 12.6d should be labeled w[n] (not w(t))
  • Appendix C
    • p. 636, eqn 1: add constraints that the sum=0 for a=0 and sum=(n+1) for a=1
• Signals, Systems and Transforms by Phillips and Parr (older printing)
  Some printings of the text (same edition, but not my printing) have the following errors:
  • inside cover, eqn #7 of F.T. table: e^(at) should be e^(-at)
  • on p. 329 Figure 7.14 (a): -e^(-at)u(t) should be -e^(-at)u(-t)
  • on p. 115, table 3.1, line 2: XH(s_1)e^(e_1 t) should be XH(s_1)e^(s_1 t)
  • p. 242: h(t) = (omega_c/pi) sinc (omega_c t)
  • p. 287, Figure P6.17: the triangle wave is M(omega)
  • p. 577, fig. 12.14, the first graph should be labeled X_0(OMEGA) vs. X_0(omega) (the discrete time frequency variable, not the continuous time one)
• Handouts
  • HW1 assignment: typo in answers to extra problems, corrected in version posted 1/10 11:30AM
  • sample exam problems: typo in problem 1b - "odd" should be "even", current version is correct
  • sample exam solutions: error in 6a (also not stable) and 6b (also not causal), current version is correct
  • HW 4 solutions: 5c - the final answer should have a difference between the two terms; 5d - the final answer should have the 1/3 factors, current version is correct
  • HW 5 assignment: answers to extra problems for 11.25 had some errors. A new version is now posted.
  • HW 6 assignment: answers to extra problem for 12.6(c) was missing the factor of 2 amplitude scaling coefficient. Current posting is correct.
  • Sample final solutions and formula sheet had typos corrected, see current version (as of 3/11 8:20AM)
• Lecture Notes
  • p. 50 of lecture notes, example 3: sum_n |h[n]| = 3/4 (not 3/2)
  • p. 73 of notes had some problems (corrected in class). A new version is posted on the handouts page.
  • in lecture I mentioned that the power of 2 FFT was the best; in fact Cooley and Tukey said in 1965 that the power of 3 is slightly more efficient. However, power of 2 is more convenient for digital computers that represent things in bits.

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