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Errata for First through Fourth Printings of
Discrete-Time Signal Processing
byOppenheimandSchaferwithBuck
Page Where Correction
13 Line after Example 2.1 Thewordsequencesshouldbeitalicized.
18 Eq. (2.26a) ThemiddletermshouldbeT{x [n]}+T{x [n]}
1 2
26 First line after Example 2.12 Example2.3should be Example 2.12
26 Equation before Eq. (2.55) add “for 0 ≤ k ≤ N −1”
28 Second Equation n−N+1 0.
sl sl
758 Problem 10.15 It should refer to Fig. P10.15-1 and Eq. (10.30)
759 Problem 10.18 Thethirdsentenceshouldread“Thesignalx[n]isalsowindowedwithan
L-point rectangular...” Also, the problem should read “Will the peaks
jω jω
in |V2(e )| and |V1(e )| have the same height?”
761 Problem 10.26 Add “Assume that x[n] and w[n] are real.” to the end of the first para-
graph.
jω jω
763 Problem 10.29(a) ThesecondWR(e )shouldbeWH(e ).
765 Problem 10.33 Insert “real” so that the problem reads “Suppose that x (t) is a real,
continuous-time stationary....” c
769 Problem 10.40(c) Insert N so that the fourth sentence reads “...overall output is y[n] =
Nw[0]x[n] ...
−jω n
773 Fig. P10.44-1 Theinput to the multiplier should be e c
774 Problem 10.44 Theequation above Fig. P10.44-3 should read
˜
X [n] = X [Mk −Mk +n], 0≤n≤N−1
z NM c ∆
774 Fig. P10.44-3 Theoutput should be X [n], not x [n].
z z
3
787 Example11.3 Thethird equation should read jXI[k] = 1 X XR[m]V4[k −m]
4
m=0
3 3
787 Example11.3 Thefourth equation should be X not X
k=0 h=0
jω ∗ −jω
790 Six lines after Eq. (11.59c) Theequation should read jXi(e ) = jXi (e )
802 Problem 11.5(c) ωc should be ω0.
805 Fig. P11.20-1 The two zero samples at the end of x [n] should be removed for consis-
tency with the other plots. 2
2
Page Where Correction
2
819 Eq. (A.45a) Remove the |m | term since the process is defined as zero-mean just
above. x
2
819 Eq. (A.47b) Removethe−|mx| term.
820 Eq. (A.54) Replace both n’s on the right hand side with m’s.
830 Answer2.1(d) Should read “If n0 ≥ 0, (2).”
831 Answer2.7(a) Should read “Periodic. N=12.”
831 Answer2.9(c) Add“Otheranswersarepossible.”
√
831 Answer2.11 Theanswershouldbe2 2sin(π(n+1)/4)
jω jω j(ω−2π/M) j(ω+2π/M)
832 Answer2.17(b) W(e )shouldbe(1/2)R(e )−(1/4)R(e ) −(1/4)R(e )
n−1
832 Answer2.20(a) h[n] should be (−1/a) u[n−1]
833 Answer3.9(c) AddtheRegionofConvergence“|z| < 2.”
835 Answer3.18(b) Thenumerator of the fraction should be −2j.
jω −jωτd/T
835 Answer4.7(a) Thecorrect answer for X(e ) is (1/T)Sc(jω/T) 1+αe for
|ω| ≤ π jω
835 Answer4.8(c) AddT sotheanswerreadsTX(e )|
ω=0
836 Answer4.11(b) TheanswershouldreadT = 1/20,unique.
836 Answer4.16(b) TheanswershouldreadM/L = 2/3,unique.
836 Answer4.17(b) Thecorrect answer is x˜ [n] = sin(7πn/8)
d
n n−1
836 Answer5.4(b) Theanswershouldreadh[n] = (3/4) u[n]−2(3/4) u[n−1]
837 Answer5.11(c) TheanswershouldreadFalse.
837 Answer5.11(d) TheanswershouldreadTrue.
jω
838 Answer5.15(a) A(e )shouldbe1+4cos(ω).
jω
838 Answer5.15(c) A(e )shouldbe3+2cos(ω).
jω
838 Answer5.15(d) A(e )shouldbe2cos(ω/2).
jω
838 Answer5.15(e) A(e )shouldbe2sin(ω).
−aT
842 Answer7.1(a) H(z)shouldinclude the Region of Convergence |z| > e .
−aT
842 Answer7.1(b) H(z)shouldinclude the Region of Convergence |z| > e .
ˆ ˆ
843 Answer7.3(a) Addδ1 =2δ1/(1+δ1)aftertheanswergivenforδ2.
843 Answer7.3(b) Addδ1 =0.05750beforetheanswerforδ2.
843 Answer7.3(c) Change the answer to read “Use the same δ1 and δ2.” Keep the same
equation.
843 Answer7.5(a) Addβ =3.3953.
843 Answer7.6(b) MshouldbeM =63. ∆ωiscorrect.
844 Answer7.15 Shouldread“HammingandHanning: M+1 = 81,Blackman: M+1 =
121.”
844 Answer7.18 Thevalues of |Ω| given are wrong. The correct answer is
|Hc(jΩ)| < 0.04, |Ω| ≤ 324.91 rad/sec,
0.995 < |Hc(jΩ)| < 1.005, |Ω| > 509.52 rad/sec.
˜
844 Answer8.2(a) The left hand side should be X3[k]. The 3X[k/3] on the right hand side
˜
should be 3X[k/3].
844 Answer8.4(a) Theashouldbeα.
845 Answer8.4(b) Theashouldbeα.
N
845 Answer8.5(e) Theainthenumeratorshouldbea .
845 Answer8.9(a) Add“forn = 0,1,...,4” at the end of the sentence.
845 Answer8.9(b) Thecorrect answer is
Definex [n] = P W−(n+9m)x[n+9m]forn=0,...,8.
2 m 27
ComputeX [k],the9-point DFT of x [n].
2 2
jω
X2[2] = X(e )| .
ω=10π/27
846 Answer8.12(a) Changek = 2,4tok = 0,2
847 Answer9.3(b) Replace N with 8.
−j(2π/19)n n2/2
847 Answer9.10 Addntotheexponentofr[n]soitreadsr[n] = e W .
3
Page Where Correction
847 Answer9.14 All values of m should be increased by one, so the answers are given for
m=1,2,3and4.
−j2π(7/32) j2π(25/32)
847 Answer9.20 Thecorrect answer is y[32] = X(e ) = X(e ).
848 Answer10.3(c) Should be N = 256.
848 Answer10.3(d) Should be 62.5 Hz.
848 Answer10.13 Add“Xr[k] = 0forr 6= 0,1.” at the end.
2
848 Answer10.15 Changeλtobeλ=π/76000rad/sample .
848 Answer10.19 Should be L = M +1 = 262.
848 Answer10.20(a) Should be A = 21 dB.
848 Answer10.20(b) Change0.0058tobe0.0891.
849 Answer11.3 Theanswersgiven are incorrect. One correct answer is
x [n] = δ[n−1]−(1/2)δ[n−2],
1
x [n] = (1/2)δ[n−1]−δ[n−2].
2
Add“Otheranswersarepossible.” after the equations.
849 Answer11.4(a) Add“for0 ≤ ω ≤ π”after cos(2ω)
849 Answer11.7(b) Add“Otherchoices are possible.” at the end of the sentence
849 Answer11.18 Add“Otherchoices are possible.” after the equations given.
4
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