DIGITAL FILTERS Analysis, Design, and Applications by A. Antoniou ERRATA. Page 10, Table 1.1: The upper limit of the summation should be K.

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1 DIGITAL FILTERS Analysis, Design, and Applications by A. Antoniou ERRATA Printing #1 Page vii, line 4 : Replace Geophysicists by Geoscientists. Page 1, Table 1.1: The upper limit of the summation should be K. Page 1, Table 1.1: Adder input x k (nt ) should read x K (nt ). Page 18, line 2: Change l Hospital s to l Hôpital s. Page 21, line +12: Replace n by n. Page 61: Theorem 2.11 should read as follows: Theorem 2.11 Parseval s discrete-time formula A discrete-time signal and its z transform evaluated on the unit circle z = 1 satisfy Parseval s discrete-time formula given by f(nt ) 2 = 1 ωs ω s F (e jωt ) 2 dω and if T =1s,then f(n) 2 = 1 2π 2π F (e jω ) 2 dω Page 61: The part of the proof after line +12 should read as follows: [ G(z) = f (nt )z n = f(nt )(z 1 ) n = F (z 1 ) Hence G(1/v) =F (v). From Theorem 2.1 Z[f(nT )g(nt ) = [f(nt )g(nt )z n = 1 2πj Γ ( ) z F (v)g v 1 dv v If we let z = 1 and replace g(nt )byf (nt )andg(1/v) byf (v), we get f(nt )f (nt )= 1 F (v)f (v)v 1 dv 2πj Γ Now if we let v = e jωt, we obtain Parseval s formula. Count from the bottom of the page for negative lines. 1

2 Page 64, Prob. 2.17, part (b): Replace lim z by lim z 1 Page 15, Fig. 4.7: Replace label a by d. Page 121, Fig. 4.15a: The symbols a, a 1, b 1, b 2, should read a, a 1, b 1, b 2, respectively. Page 135: The top two illustrations have been printed upside down but are otherwise correct. Page 137, Fig. P4.24: Add caption labels (a) and (b) to the middle and bottom graphs, respectively. Page 15, Fig. 5.9: Add caption label (a) to the top graph. Page 153, line 2: Replace two by three. Page 168, line +4 after Fig. 5.15: Replace three by four. Page 182, lines +5 to +9 after Fig. 6.3 should read: function 1 for t ɛ p ɛ (t) = 2ɛ (6.3) otherwise depicted in Fig. 6.4a, whose limit as ɛ has often been used to define the continuous-time impulse function. From Eq. (6.1), we can readily obtain the Fourier transform of p ɛ (t) as and so Fp ɛ (t) = p ɛ (t)e jωt dt = ɛ ɛ lim ɛ [Fp ɛ (t) = 1 1 2ɛ e jωt dt = sin ωɛ ωɛ Page 183, Fig. 6.4a: Replace p (t) byp ɛ (t). Page 183, Fig. 6.4a: Replace 1 by 1. 2L 2ɛ Page 183, Fig. 6.4b: Replace y-axis label S b (n, t) bys δ (n, t). Page 184, line 3: Replace F (t) by F (jω). Page 191, line 11: Replace Page 191, line 12: Replace by. by. Page 193, line 6: Replace e jωt by e jω t. 2

3 Page 197: Eq. (6.19) should read: a n = 1 T T/2 T/2 f(t)e jnω st dt (6.19) Page 26, Fig. 6.13: (i) Reverse each of the two arrows between the circles with labels X(s) and X(jω); (ii) Replace ˆx(jω) in the middle circle at the right-hand column by ˆX(jω); (iii) The formula jω 1 In z next to the arrow between the circles with labels T ˆx(jω) andx D (z) should read jω 1 ln z; T (iv) The symbols T next to the arrows between the bottom two circles should be replaced by Z. Page 21, line 11: Replace ˆx 6 (nt )byˆx 6 (t) Page 21, line 16: Replace x 7 (nt )byx 7 (t) Page 214, Fig. 6.17a: Replace x(kt) byy(kt). Page 227, Example 7.2: Change denominator coefficient b 1j in H A (s) tob j. Page 232, Fig. 7.6: The label of the y axis should read x(τ); the label of the x axis should read τ. Page 279, eqn. (9.12): Add braces as follows: H(z) = { 1 (N 3)/2 h(nt )(z (N 1)/2 n ± z [(N 1)/2 n ) z (N 1)/2 n= + 1 [ } (N 1)T 2 h (z ± z ) 2 (9.12) Page 283, line +9: Change Fig. 5a to Fig. 9.5a. Page 283, line +12: Insert the phrase with ω s =2π/T =1. just before the word According. Page 292, line +8: The formula for the kth-order Chebyshev polynomial should read as follows: T k (x) = { cos (k cos 1 x) for x 1 cosh (k cosh 1 x) for x > 1 Page 39: Add caption FIGURE P9.13 to the top illustration. 3

4 Page 319: The equation above Eq. (1.12) should read: = 1 2 cos (ω ct 1 ω c t 2 )+ 1 2 E{cos (ω ct 1 + ω c t 2 +2y)} Page 32, line 8: The equation should read: P T = X T (jω) 2 Page 321, Fig. 1.4: The symbol dτ is the width of the elemental area shown along the t 2 axis. 2T dω 2π Page 323, line 3: Section heading should read: DISCRETE-TIME RANDOM PROCESSES Page 342, line +6: Replace σ 2 c i by σ 2 Δc i. Page 346: Eq. (11.24) should read: Page 346: The equations after line +1 should read: = β 1 β 1 2 S M b 1 (11.24) S M β S M b and S M β 1 S M b 1 Page 347, Fig. 11.6: Replace labels E and m 2 by E and m 2, respectively. Page 357, line 4: Equation should read: X 1 = 1 2π = M ωs /2 ω s /2 πm[δ(ω ω )+δ(ω + ω ) dω Page 36, Fig. 11.1: Add label 1 next to outgoing branch from node x(n). Page 36, Fig. 11.1: Reverse the arrow in the lower branch with transmittance E 1. Page 362, line +5: The equation should read i.e., add tildes on the G s. Page 363: G i 2 2 = G j 2 2 4

5 (i) Eq. (11.63) should read (ii) Eq. (11.64) should read (iii) Eq. (11.66c) should read T = T = [ ˆF1 1 2 [ ˆF1 1 ˆF ˆF 2 1 (11.63) (11.64) â 21 =(K 1 K 2 )/(1 + γ ) (11.66c) (iv) The equation should read T = T = Page 364: Eq. (11.67) should read: [ F1i p [ F1i 1 p ˆF 2i p F 2i 1 p λ = 1 H 2 (11.67) Page 371, caption of Fig a: Replace the comma after Eq. (11.77) by a period. Page 371, bottom of the page: Correct the right-hand inequality signs in the three equations as follows:.5 b < b < k 1 2k +1 b < 2k 2(k +1)... Page 377, Fig : The constants of the left-hand multipliers should be α 1 and α 2 and those of the next two multipliers to the right should be β 1 and β 2, i.e., the α s and the β s should be interchanged. Page 38, lines +2 to +4 after Fig : Replace Q k by Q k [x threetimes. Page 387: Prob , should read as follows: (a) Apply error-spectrum shaping to the scaled cascade canonic realization obtained in Prob

6 (b) The modified realization is to be implemented in terms of fixed-point arithmetic and product quantization is to be by rounding. Compute and plot the relative, output-noise PSD versus frequency assuming the L 2 scaling obtained in Prob (c) Compare the results with those obtained without error-spectrum shaping in Prob Page 412, line +3: Eq. (16.22) should read Eq. (12.22). Page 442: Prob should read as follows: Obtain a digital realization for a general 2-port represented by Eqs. (12.14a) and (12.14b). Page 452, Fig. 13.5: Replace nt in the top, right-hand graph by ω s. Page 455, Fig. 13.7: Replace Eq. (6.22), Eq. (6.14), and Eq. (6.2) by Eq. (6.44), Eq. (6.36), and Eq. (6.42), respectively. Page 472, line 3: decimation-in-time should read decimation-in-frequency. Page 481, line 7: The line should read then for kl (k 1)(N 1) n (k +1)L k(n 1) 1 Page 49, line 13: Add with N even after recursive filter. Page 496, line +8: Replace x by x T. Page 57, line +17: Replace > α k (σ 1)g T k d k by α k (σ 1)g T k d k. Page 519: Delete 14.6ab and 14.7ab just before Example Page 535, Fig : Replace ω-axis labels 3., 3.5, 4., 4.5, and 5. by.3,.35,.4,.45, and.5, respectively. Page 538: Prob should read as follows: The step response y(t) of a digital filter is required to approximate the ideal step response t for t<2 2 for 2 t<3 y (t) = t +5 for 3 t<4 1 for 4 t 5 where t = nt. Formulate a least-squares objective function for the solution of the problem. Page 541, line 7: Add sixth-order before lowpass. Page 551, line +7: Replace ω Nj+1 by ω (Nj +1)j. 6

7 Page 563, line 13: Replace ρ r by ρ (r +1). Page 575, Eqs. (15.55c) to (15.55e) should read: a k = 1( c 2 k 1 c k+1 )fork =2, 3,..., c 2 a c 1 = 1 2 c c 2 a c = 1 2 c c 1 (15.55c) (15.55d) (15.55e) Page 577: Eqs. (15.58c) and (15.58d) should read: b k = 1( b 2 k 1 + b k )fork =2, 3,..., d 1 b d = 1 2 b d 1 (15.58c) (15.58d) Page 577: Eqs. (15.59c) and (15.59d) should read: b k = 1( d 2 k 1 d k )fork =2, 3,..., d 1 b d = 1 d 2 d 1 (15.59c) (15.59d) Page 589, Prob : Delete Lower in Lower passband edge and Lower stopband edge. Page 599, caption of Fig. 16.6: Add and interpolator after upsampler. Page 61: The last two lines before Example 16.2 should read by Gazsi (see Sec and [1 of Chap. 12) or by a method proposed by Vaidyanathan, Mitra, and Neuvo (see Additional References of Chap. 12, p. 438). Page 613: Correct Eq. (16.27) as follows: Page 613: Modify Eq. (16.28) as follows: H(e jωt ) 1 = H(e j(ω s/2 ω)t ) δ (16.27) H (e jωt ) 2 + H (e j(ωt π) ) 2 = G =1+2δ (16.28) Page 613, Eq. (16.29): Add a minus sign just after the equal sign. Page 619, line 4 above Table 16.2a: Replace the sentence Using this... impulse response as by By letting nt = t in Eq. (16.4) and then sampling the function h(t) att =(n.5)t for (N/2 1) n N/2, we have Page 623, line +7: Correct e [jω cnt +φ(nt ) to read e j[ω cnt +φ(nt ). Page 629, Fig : Connect node a to the adjacent multiplier. Page 629, line +5 after Fig : Replace a n by a n. 7

8 Page 646, line 1: Replace for 1 ω 3 by for1 ω 1. Page 647, line +2: Replace for 1 ω 3 by for1 ω 1. Page 648, line 17: Replace of the two filters in cascade by of the QMF bank. Page 648, line 11: Correct the equation to read 1 [d 2 A(s)d B ( s) d A ( s)d B (s) = N(s) 1 [d 2 A(s)d B ( s)+d A ( s)d B (s) = N(s) Page 648, line 9: Replace Butterworth by fifth-order Butterworth. Page 648, line 5: Replace Chebyshev by fifth-order Chebyshev. Page 65, Fig. P16.1: Replace the three L s next to the down arrows by M s. Page 65, line 11: Replace R n by R n. Page 651, line 6: Replace Equalize by Identify. Page 677, line 1: Replace Maison s by Mason s. 8