Signals, Systems, Signal with MATLAB© · Signals, Systems, Transforms and Digital Signal...

transcript

Errata

Signals, Systems, Transforms and Digital Signal

Processing with MATLAB©

Michael J. Corinthios

First Edition June 2009

Back cover

First sentence should read:

Signals, Systems, Transforms, and Digital Signal Processing with MATLAB®

has as its principal objective simplification without compromise of rigor. Graphics, called by the author ‘the language of scientists and engineers’, physical interpretation of subtle mathematical concepts, and a gradual transition from basic to more advanced topics are meant to be among the important contributions of this book

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

Preface

First sentence should read:

Simplification without compromise of rigor is the principal objective in this presentation of the subject of signal analysis, systems, transforms and digital signal processing. Graphics, the language of scientists and engineers, physical interpretation of subtle mathematical concepts and a gradual transition from basic to more advanced topics, are meant to be among the important contributions of this book.

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

Chapter 1

Fig. 1.17 ( c ):

Erase foreign diagonal line inadvertently added on electric circuit.

Second paragraph

Should read:

In evaluating the convolution integral, as in Equation (1.30),

Probs 1.11 and 1.12 Replace

inverted !

Prob 1.23

a) A system has an impulse response ….

b) Evaluate the convolutions ….

Problem 1.34

y( t) = R_{2}(t) = …

Problem 1.42 page 37 Part c)

Replace

( )2 10v t n−

( )10bv t n−

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

Chapter 3

Example 3.20

Should read

Chapter 4

Problem 4.6

Let f(t) be a periodic signal of period …

Evaluate the Fourier series coefficients and the Fourier transform over the interval (‐1, 1) of

a) f(t),

b) the causal function g(t) = …

Problem 4.23

Let x(t) …

Let the signal y(t) be a periodic signal …

Problem 4.24

b) … Evaluate the Fourier transform …

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

Chapter 5

Problem 5.15

The following, part c), would be a good addition to the book problem.

c) For cases a) and b) above find the continuous‐time functions f_1(t) and f_2(t) which when ideally sampled would produce the signals x(t) and v(t), respectively, and write the outputs y_1(t) and y_2(t) as functions of f_1(t) and f_2(t) and the shifted versions of the step function u(t).

Prblem 5.22

For the d‐c current motor shown in Fig. 5.82 assuming a

constant voltage E_{e} in the inductor circuit, a negligible

inductance of the armature circuit and negligible load …

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

Chapter 6

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

Last paragraph

Replace

( )sin tγ

( )sin nγ

Eq. (6.91)

Should read

( ) ( )( )

M Mk k

k kk kN N

k kk k

b z b zY zH z

X z a z a z

− −

= = =+

∑ ∑

Eq. (6.97)

Replace

− Ω

Section 6.24 Two‐Dimensional Signals

Equation (6.153) should read

Unit Step 2DSequence

Equation (3.162)

Should read:

1 21 2

1, , 0[ , ]

0, , 0.n n

u n nn n

>⎧= ⎨ <⎩

Causal Exponential

Equation (3.163)

Should read:

01 21 2 1 2

1 21 2

, ,[ , ]

0, , 0.

n na a n nx n n

n n⎧ >

= ⎨<⎩

Before Fig. 645

Eraze redundant

the unit

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

Chapter 7

before We note that

‐1/2 is missing. Should read

1( ) ...2

nV z e zα

∞− −

= − =∑

Line before last:

Replace

=1/2 +/4=

=1/2 +1/4=

Correct to read

Fig. 7.18 and Fig. 7.19

Replace

Equation (7.100):

Replace

Example 7.6

Replace

( )5000cos t

( )5000cos tπ

Example 7.7

Replace

Before Equation (7.101)

Replace

. Evaluate the system output

, evaluate the system output

After Equation (7.101)

Replace

/LKL πΠ

/LK πΠ

Sec. 7.8.3

Replace

Example 7.8 should read:

Equation (7.107)

In RHS replace

Should read

last paragraph

Should read:

Note: The properties listed in Table 7.3 are those of the DFS….

Fig. 7.56 should be:

In Section Answers to selected problems

Last two problems should be numbered 7.32 and 7.33 instead of 7.31 and 7.32.

In other words

Replace Heading: Problem 7.31 by 7.32

Replace Heading: Problem 7.32 by 7.33

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

Chapter 8

Example 8.10 first four lines

Should read:

Evaluate and verify the transformation between the canonical

and Jordan state space models of a system of transfer function%

H(s)= ….

Replace We have found

Referring to Example 8.4 we may write

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

Chapter 9

Figure9.32

Caption of Figure9.32 should read

\caption{Magnitude spectrum ( )H jω of ninth order elliptic filter.

Problem 9.23 At the end of this problem add the line:

Verify the solution using Matlab and evaluate and plot the poles and zeros of the resulting filter.

In the section

9.57 Answers to Selected problems

On Page 674

Problem 9.23

After the equation

H_{HPdenorm}(s)= 2.5/…

add the new line

H_{HPdenorm}(s)= (0.891509 s^4)/(4.58063 10^13 + 2.3154 10^10 s + 1.87451 10^7 s^2 + 5078.98 s^3 + s^4).

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

Chapter 10

After Equation (10.51)

Replace

ensures

ensure

Bottom of page: Example 10.3

Replace

Consider the ladder network of Fig. 10.2.

Consider the ladder network of Fig. 10.3.

Replace

Paragraph following Eq. (10.250)

Replace

Fig. 10.34 known as

Fig. 10.36 known as

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

Chapter 11

Equation (11.23)

Replace, respectively,

kc and kz

kC and kZ

Add Prony’s Method (page 790) to index terms.

Sec. 11.30

Replace to read

Example 11.21

Replace

cos(gamma_i^n + theta_i)

cos(gamma_i n + theta_i)

Section 11.34 Pade Approximation

In the Pad\'{e} approximation approach …

such that the filter impulse response h[n]=… best matches a desired impulse response …

Problems 11.42 to Prob 11.45

Replace h[n‐N] by h[N‐n]

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

Chapter 12

Problem 12.1

A system has the impulse response%

( ) ( )sin ...Th t tR tπ= =

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

Chap 14

Sec. 14.9.3

Delete first redundant paragraph.

Second paragraph first line

Replace

Gray code‐to‐binary

binary‐to‐Gray code

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

Chap 15

Fig. 15.19 should be as follows:

After Equation (15.105) should read

Fig. 15.20 Replace as follows

Should read:

Fig. 15‐21 Correct as shown:

Section 15.29.2 Realization using JK Flip‐Flops

The realization using JK$ flip‐flops is similarly obtained …. The resulting Karnaugh maps of J_2, J_1, K_2 and K_1 are shown in Fig. 15.47.

From the tables we may define the micro‐operations as functions of states and conditions.

We have

\mu_{1} & = (START \leftarrow ON)

\mu_{12} & = S_{10},

\mu_{13} & = & S_{11}UEQ0.\overline{AEQ0}. \\

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

Chap 17

Sec. 17.7 Other Approximating Sequences

Last equation 17.61

Redundant; same as 17.59. Delete it.

After Equation (17.78) should read

Section 17.16 now reads

Sec. 17.19

Should read

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

Chap 18

Table 18.5

The transform of is nna u n⎡ ⎤⎣ ⎦( )

az z aaz

π ψ−

−−

−z .

The transform of ( ) is 1 nn a u n⎡ ⎤+ ⎣ ⎦( )

1 ( ) ( )1

a z a zaz

π ψ ψ− −

⎧ ⎫⎨ ⎬⎩ ⎭

− −−

The transform of is [ ]ru nn ( ) ( ) ( )( )

( ) ( ) ( )1

1 !1 , 1 ,

ir rr r ii i

iS r i z S r i z

zzπ ψ

−− −

−+∑ ∑ .

The transform of is [ru nn − ] ( ) ( )

( )( ) ( ) 1

1 !, ,

ir rii i

iS r i z S r i z

zzπ ψ− −

+−= =

−+∑ ∑ − .

Last line

The transform of is . rn ( ) ( ) ( )

1 2 , ( )r

S r i z zπ ψ=

− ∑

Correct table entry at n a^n u[n].

Table 18.12 last entry should read

Stirling Numbers First Kind definition:

( ) ( ) ( )0

21, 1n m km

n mn ks n m s S n m k kn m kn m k

⎛ ⎞⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟

⎝ ⎠⎝ ⎠

−− +≡ = − − +− −− +∑

(Note that the last S is upper case).

Abu Ja’far … AlKhwarizmi:

Line 26: Replace wass by was

Signals, Systems, Signal with MATLAB© · Signals, Systems, Transforms and Digital Signal...

Documents