DC Blocker Frequency Response
Figure B.11 shows the frequency response of the dc blocker
for several values of 
. The same plots are given over a
log-frequency scale in Fig.B.12. The corresponding
pole-zero diagrams are shown in Fig.B.13. As approaches
, the notch at dc gets narrower and narrower. While this may seem
ideal, there is a drawback, as shown in Fig.B.14 for the
case of 
: The impulse response duration increases as 
.
While the ``tail'' of the impulse response lengthens as approaches
1, its initial magnitude decreases. At the limit, 
, the pole and
zero cancel at all frequencies, the impulse response becomes an
impulse, and the notch disappears.
![\includegraphics[width=\twidth ]{eps/dcblockerfr}](http://www.dsprelated.com/josimages_new/filters/img1459.png) |
for various values of
![\includegraphics[width=\twidth ]{eps/dcblockerfrlf}](http://www.dsprelated.com/josimages_new/filters/img1460.png) |
![\includegraphics[width=\twidth]{eps/dcblockerpz}](http://www.dsprelated.com/josimages_new/filters/img1461.png) |
.![\includegraphics[width=\twidth ]{eps/dcblockerir}](http://www.dsprelated.com/josimages_new/filters/img1462.png)
Note that the amplitude response in Fig.B.11a and
Fig.B.12a exceeds 1 at half the sampling rate.
This maximum gain is given by
. In applications for
which the gain must be bounded by 1 at all frequencies, the dc blocker
may be scaled by the inverse of this maximum gain to yield
![\begin{eqnarray*}
H(z) &=& g\frac{1-z^{-1}}{1-Rz^{-1}}\\
y(n) &=& g[x(n) - x(n-1)] + R\, y(n-1), \quad\hbox{where}\\
g &\isdef & \frac{1+R}{2}.
\end{eqnarray*}](http://www.dsprelated.com/josimages_new/filters/img1464.png)
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DC Blocker Software Implementations
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Allpass Filter Design
