% errata.tex - list of errata for the book:
%
% Introduction to Signal Processing
% Sophocles J. Orfanidis
% Prentice Hall, Englewood Cliffs, NJ, 1996
% SBN 0-13-209172-0
%
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\begin{document}

\begin{center} \bf
Introduction to Signal Processing -- S. J. Orfanidis \\
Errata List -- \filedate \\[2ex]
(Errata with an asterisk $^*$ have been corrected in the second printing.)
\end{center}


\small
\begin{enumerate}

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\item[p.13$^*$]
In line 15 from top, instead of $\sin((2\pi n/4 + 2\pi mn)$, read
$\sin(2\pi n/4 + 2\pi mn)$.

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\item[p.52$^*$]
In fourth line from bottom,
$\arg{H(f)} = \phi(f) + \pi\, \mbox{sign}\,G(f)$ should be
$\arg{H(f)} = \phi(f) + \pi\, (1-\mbox{sign}\,G(f))/2$.

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\item[p.58$^*$]
In the last line of Problem 1.8(c), instead of {\em $f_s=4$ kHz},
read {\em $f_s=4$ Hz}.

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\item[p.358$^*$]
In line 8 from top, instead of {\em except at the 4th roots\/}, read
{\em except at the 8th roots}.

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\item[p.568$^*$]
In Eq.~(10.4.1), instead of $D=(A_g - 13)/14.36$, read $D=(A_g - 13)/14.6$.

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\item[p.628$^*$]
In line 7 from top, the correct expression for $C_4(x)$ should be
$C_4(x)=8x^4-8x^2+1$.

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\item[p.786$^*$]
The title of Ref.~[268] should read
``The Equivalence of Various Methods of Computing Biquad 
Coefficients for Audio Parametric Equalizers''.

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\item[p.15]
In second line from the top, instead of $f_3=\pm 1.5$ kHz, read $f_4=\pm 1.5$ kHz.

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\item[p.37]

The Poisson sum identity in the middle of the page should be
corrected to read:

\[
\ov{1}{T} \sum_{m=-\infty}^{\infty} \ov{1}{a + 2\pi j (f-mf_s)} = \ov{1}{1-e^{-aT}e^{-2\pi j fT}} - \ov{1}{2} 
\]

This requires that the sampled signal $x(nT)$ of Example 1.5.2 be redefined
such that $x(0) = 1/2$ instead of $x(0) = 1$, which gives at the top of page
37:

\[
\hat{X}(f) = \sum_{n=0}^{\infty} x(nT)e^{-2\pi j f T n} = 
\sum_{n=0}^{\infty} \bigl(e^{-aTn} - \ov 1 2 \delta(n)\bigr) e^{-2\pi jfTn} = 
\ov{1}{1-e^{-aT}e^{-2\pi j fT}} - \ov{1}{2}
\]

The Poisson summation formula requires that the signal $x(t)$ be continuous for
all $t$. The present example has a discontinuity at $t=0$ arising from the unit
step $u(t)$. Choosing $x(0)$ to be equal to $\bigl(x(0+)+x(0-)\bigr)/2 =
(1+0)/2 = 1/2$, enables the use of the Poisson summation formula. The issue has
been discussed in connection with the impulse-invariance filter design
method.\footnote{R. A. Gabel and R. A. Roberts, {\em Signals and Linear
Systems}, 3/e, Wiley, New York, 1987; L. B. Jackson, ``A Correction to Impulse
Invariance,'' {\em IEEE Signal Process. Lett.}, \fb{7}, 273 (2000); W. F. G.
Mecklenbr\"auker, ``Remarks on and Correction to the Impulse Invariant Method
for the Design of IIR Digital Filters,'' {\em Signal Process.}, \fb{80}, 1687
(2000).} Except for a level shift, the basic conclusions of this example remain
the same. Similar redefinitions must be introduced also in Problem 1.13.

The above Poisson sum identity can be found in standard mathematical
tables.\footnote{M. Abramowitz and I. A. Stegun, Eds., {\em Handbook of
Mathematical Functions}, Dover, New York, 1968, p.75.} Indeed, setting $z=(2\pi
f T - ja T)/2$, it is not hard to verify that the identity takes on the
standard form:

\[
\cot z = \sum_{m=-\infty}^{\infty}\ov{1}{z-\pi m} = \ov 1 z + 2z\sum_{m=1}^{\infty} 
\ov{1}{z^2-\pi^2 m^2}
\]


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\item[p.45]
In second equation from top, the last expression should read
$\int_{-f_s/2}^{f_s/2} T e^{2\pi j f t}\, df$.

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\item[p.55]
In line 16 from top, instead of $[f_s/2, f_s/2]$, read $[-f_s/2, f_s/2]$.

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\item[p.58]
In bottom two equations, instead of $\cos\bigl(2\pi(f-f_0)\bigr)$, read
$\cos\bigl(2\pi(f-f_0)T\bigr)$, \\
and instead of $\cos\bigl(2\pi(f-f_0)L\bigr)$, read
$\cos\bigl(2\pi(f-f_0)LT\bigr)$.

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\item[p.73]
In second line from top, instead of ``staircase A/D converter'', read ``staircase D/A converter''.

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\item[p.121]
In Problem 3.5, the term $3(0.5)^{n-1}u(n)$ should be $3(0.5)^{n-1}u(n-1)$.

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\item[p.142]
Line 13 from bottom. Instead of ``the include file'', read
``the include-file''.

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\item[p.167]
Line 8 from bottom. Instead of ``We have from Eq. (4.2.20)'', read
``We have from Eq. (4.2.19)''.

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\item[p.214]
Problem 5.2(d) should read $x(n) = u(-n+5)$.
Also, replace 0.9 by 0.8 throughout Problem 5.4.

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\item[p.241]
In line 6 from bottom, instead of Example 6.3.4, read Example 6.3.2.

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\item[p.311]
In Problem 7.1, instead of ``A system has impulse response'', read
``A system has transfer function''.

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\item[p.485]
In line 7 from bottom, instead of $z^{-2}x_3 + z^{-3}z_3$, read
$z^{-2}x_2 + z^{-3}x_3$.

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\item[p.530]
The third line of Eq.~(9.9.14) should read: 
$\fb{y}_2 = \tilde{\fb{y}}_2 = \mbox{IFFT}\bigl(\mbox{FFT}(\fb{h}) \cdot \mbox{FFT}(\fb{x}_2)\bigr)$

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\item[p.531]
On bottom of Figure 9.9.1, the indicated absolute times $n=N, 2N, 3N$
should be $n=(N-M), 2(N-M), 3(N-M)$.

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\item[p.545]
In the third equation from bottom, the entries $\sqrt{2}/10\pi$ in the vector
$\fb{h}$ should be replaced by $-\sqrt{2}/10\pi$.

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\item[p.583]
On line 12 from bottom, instead of $b=(1-a)/2=0.9023$, read $b=(1+a)/2 = 0.9023$.

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\item[p.611]
On the text line after Eq.(11.6.23), instead of $a_{2i}$, read $a_{i2}$.

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\item[p.613]
In line 2 from top, instead of $1/0.7625$, read $1/0.7265$.

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\item[p.617]
In line 10 from top, instead of Eqs.~(11.6.26) and (11.6.24), read 
Eqs.~(11.6.33) and (11.6.35).

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\item[p.618]
On the lower left of Fig.~11.6.6, the stopband marking $1/(1+\varepsilon^2_{\mbox{pass}})$ should read
$1/(1+\varepsilon^2_{\mbox{stop}})$.

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\item[p.625]
On the $i=0$ row of the coefficient table, instead of $-0.3904$, read $+0.3904$.

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\item[p.626]
On the $i=0$ row of the coefficient table, instead of $-0.3902$, read $+0.3902$.

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\item[p.638]
In line 7 from top, the expression for the coefficient $a_{i3}$ should have an overall minus sign.

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\item[p.638]
In lines 5 and 14 from top, the factor $c$ should be removed from the numerator of the expression for the
coefficient $b_{i2}$.

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\item[p.676]
On line 9 from bottom, instead of $k'=4n-4,\, 4n,\, 4n+8,\, 4n+8$, 
read $k'=4n-4,\, 4n,\, 4n+4,\, 4n+8$.

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\item[p.700]
On line 10 from bottom, instead of $[-f_s'/2, f_s'\, 2]$, read $[-f_s'/2, f_s'/2]$.

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\item[p.760]
On the 6th comment line of {\tt sgfilt.m}, instead of $B(:,i)=\fb{b}_{M+1-i}$, 
read $B(:,i)=\fb{b}_{i-M-1}$.

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\item[p.776]
In Reference [75], instead of Z\"olser, read Z\"olzer.

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\item[p.783]
Reference [213] should read: \fb{5}, 187 (1986).

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\item[p.786]
The page no. of Ref.~[265] should be 876, instead of 479.

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\end{enumerate}






\end{document}
