Sign in

username:

password:



Not a member?

Search Online Books



Search tips

Free Online Books

Ads

Chapters

Physical Audio Signal Processing
    Acoustic Modeling with Digital Delay
       Comb Filters
          Feedback Comb Filter Amplitude Response

Chapter Contents:

Search Physical Audio Signal Processing

  

Book Index | Global Index

Would you like to be notified by email when Julius Orion Smith III publishes a new entry into his blog?

  

Feedback Comb Filter Amplitude Response

Figure 1.20 shows a family of feedback-comb-filter amplitude responses, obtained using a selection of feedback coefficients.

Figure: Amplitude response of the feedback comb-filter $ H(z) = 1/(1-g z^{-M})$ (Fig.1.18 with $ b_0=1$ and $ -a_M=g$) with $ M=5$ and $ g=0.1$, $ 0.5$, and $ 0.9$. a) Linear amplitude scale. b) Decibel scale.
\includegraphics[width=\twidth ]{eps/fbcfar}

Figure 1.21 shows a similar family obtained using negated feedback coefficients; the opposite sign of the feedback exchanges the peaks and valleys in the amplitude response.

Figure: Amplitude response of the phase-inverted feedback comb-filter, i.e., as in Fig.1.20 with negated $ g=-0.1$, $ -0.5$, and $ -0.9$. a) Linear amplitude scale. b) Decibel scale.
\includegraphics[width=\twidth ]{eps/fbcfiar}

As introduced in §1.6.2 above, a class of feedback comb filters can be defined as any difference equation of the form

$\displaystyle y(n) = x(n) + g\,y(n-M). $

Taking the z transform of both sides and solving for $ H(z)\isdef Y(z)/X(z)$, the transfer function of the feedback comb filter is found to be

$\displaystyle H(z) = \frac{1}{1-g\,z^{-M}}, \protect$ (2.5)

so that the amplitude response is