Conference PaperPDF Available

Abstract

The main characteristic of shelving fiters, as commonly used in audio equalization, is to amplify or attenuate a certain frequency band by a given gain. For parametric equalizers, a fiter structure is desirable that allows independent adjustment of the width and center frequency of the band, and the gain. In this paper, we present a design for arbitrary-order shelving fiters and a suitable parametric digital fiter structure. A low-shelving fiter design based on Butterworth fiters is decomposed such that the gain can be easily adjusted. Transformation to the digital domain is performed, keeping gain and denormalized cut-off frequency independently controllable. Finally, we obtain band- and high-shelving fiters using a simple manipulation, providing the desired parametric filter structure.
PARAMETRIC HIGHER-ORDER SHELVING FILTERS
Martin Holters and Udo Z
¨
olzer
Department of Signal Processing and Communications, Helmut-Schmidt-University
Holstenhofweg 85, 22043 Hamburg, Germany
phone: + (49) 40 6541-3468, fax: + (49) 40 6541-2822, email: {martin.holters,udo.zoelzer}@hsu-hh.de
web: www.hsu-hh.de/ant
ABSTRACT
The main characteristic of shelving filters, as commonly used
in audio equalization, is to amplify or attenuate a certain fre-
quency band by a given gain. For parametric equalizers, a
filter structure is desirable that allows independent adjust-
ment of the width and center frequency of the band, and the
gain. In this paper, we present a design for arbitrary-order
shelving filters and a suitable parametric digital filter struc-
ture. A low-shelving filter design based on Butterworth fil-
ters is decomposed such that the gain can be easily adjusted.
Transformation to the digital domain is performed, keeping
gain and denormalized cut-off frequency independently con-
trollable. Finally, we obtain band- and high-shelving filters
using a simple manipulation, providing the desired paramet-
ric filter structure.
1. INTRODUCTION
For audio equalization, recursive shelving filters are com-
monly employed. Their function is to amplify or attenuate
a specific frequency band, while leaving signal components
outside that band mainly unchanged. For equalizers which
can be tuned during operation, special parametric filter struc-
tures are desirable which allow for easy and independent con-
trol of the respective band’s width and center frequency and
the gain in that band.
For first-order low- and high-shelving filters and second-
order band-shelving filters, such designs based on an all-pass
decompositions were presented in [1, 2]. In [3] a decom-
position of second-order low- and high-shelving filters and
fourth-order band-shelving filters was presented that allows
the gain to be adjusted without recomputation of the other
filter coefficients, but where the band limits cannot be easily
adjusted.
In the following, we will first derive arbitrary order low-
shelving filters in the continuous-time domain based on a
Butterworth design. These designs will then be transformed
to the discrete-time domain and a parametric realization will
be presented. Finally, by low-pass/high-pass and low-pass/
band-pass transformations, high-shelving and band-shelving
filters will be obtained.
2. CONTINUOUS-TIME LOW-SHELVING FILTERS
In [4] the transfer function of frequency-normalized first- and
second-order low-shelving filters with gain g are given by
H
LS,1
(s) =
s + g
s + 1
(1)
and
H
LS,2
(s) =
s
2
+
2gs + g
s
2
+
2s + 1
, (2)
s-plane
σ
j
ω
1
g
(a) M = 1.
s-plane
σ
j
ω
1
g
(b) M = 2.
s-plane
σ
j
ω
1
6
g
(c) M = 6.
Figure 1: Pole/zero locations in the s-plane of low-shelving
filters with g = 2 for different filter orders M.
respectively. The pole and zero locations of these filters are
shown in Fig. 1 (a) and (b). These can be generalized to
filters of order M as
H
LS,M
(s) =
M
m=1
s +
M
ge
j
α
m
s + e
j
α
m
,
α
m
=
1
2
2m 1
2M
π
(3)
of which (1) and (2) are special cases. Fig. 1 (c) gives an
example of the resulting pole and zero locations for M = 6.
2.1 Filter properties
The magnitude response of the filters according to (3) can be
found to be
H
LS,M
( j
ω
)
2
=
ω
2M
+ g
2
ω
2M
+ 1
,
of which examples are depicted in Fig. 2. As can be easily
seen,
H
LS,M
(0)
= g and
H
LS,M
()
= 1, with a transitional
region around
ω
= 1. As desired, the slope in the transitional
region increases with the filter order M. At the normalized
cut-off frequency
ω
c
= 1, the magnitude response is
H
LS,M
( j
ω
c
)
2
=
g
2
+ 1
2
,
14th European Signal Processing Conference (EUSIPCO 2006), Florence, Italy, September 4-8, 2006, copyright by EURASIP
ω
0.1
1
10 100
H
LS,M
( j
ω
)
2
0 dB
10 dB
20 dB
M = 1
M = 2
M = 6
Figure 2: Magnitude responses for continuous-time low-
shelving filters of different orders M with gain g = 10
(20 dB).
ω
0.1
1
10 100
H
LS,6
( j
ω
)
2
20 dB
10 dB
0 dB
10 dB
20 dB
Figure 3: Magnitude responses for continuous-time low-
shelving filters of order M = 6 and varying gain g.
i.e. approximately 3 dB below the maximum. It should be
noted that this yields an asymmetry between amplification
(g > 1) and attenuation (g < 1), see Fig. 3.
By construction, the filters have minimum-phase behav-
ior. This can be exploited in several equalization applica-
tions, for example when input-to-output latency is a concern.
2.2 Parametric representation
To develop a filter structure later on where the parameters
gain, center-frequency and bandwidth are decoupled and can
be adjusted independently, we will first develop a represen-
tation of the low-shelving filters where the gain can be easily
manipulated. We start by rewriting the complex-valued first-
order sections of (3),
H
(m)
LS,M
(s) =
s +
M
ge
j
α
m
s + e
j
α
m
,
as
H
(m)
LS,M
(s) = 1 +V
e
j
α
m
s + e
j
α
m
, V =
M
g 1.
Combining H
(m)
LS,M
and H
(M+1m)
LS,M
, having complex con-
jugate poles and zeros as e
j
α
m
= e
j
α
M+1m
, yields the para-
metric real-valued second-order section
¯
H
(m)
LS,M
(s) = H
(m)
LS,M
(s)·H
(M+1m)
LS,M
(s)
= 1 + 2V
1 + c
m
s
s
2
+ 2c
m
s + 1
+V
2
1
s
2
+ 2c
m
s + 1
(4)
with c
m
= cos(
α
m
). If M is odd, (3) furthermore has one
real-valued first-order section
H
(
M+1
2
)
LS,M
(s) =
s +
M
g
s + 1
= 1 +V
1
s + 1
. (5)
ω
0.1
1
10 100
H
LS,6
( j
ω
)
2
20 dB
10 dB
0 dB
10 dB
20 dB
Figure 4: Magnitude responses for continuous-time low-
shelving filters of order M = 6 and varying gain g, alternative
design for gain symmetry.
Thus, the low-shelving filter of (3) can be rewritten in
terms of parametric real-valued first- and second-order sec-
tions according to (5) and (4) as
H
LS,M
= H
(
M+1
2
)
LS,M
(s)
| {z }
for odd M only
·
b
M
2
c
m=1
¯
H
(m)
LS,M
(s).
2.3 Design alternatives
The filter defined by (3) can in fact be understood as the
combination of a Butterworth low-pass with normalized cut-
off frequency 1 and the inverse of a Butterworth low-pass
with cut-off frequency
M
g. In a similar manner, shelving fil-
ters based on Chebyshev and elliptic filters can be designed.
As expected, their magnitude responses have steeper roll-off,
but oscillation inside and/or outside the amplified/attenuated
band [5].
The asymmetry of the magnitude responses between am-
plification and attenuation (see Fig. 3) can be avoided by us-
ing
H
ˆ
LS,M
(s) =
M
m=1
s +
2M
ge
j
α
m
s +
1
2M
g
e
j
α
m
instead of (3), yielding the magnitude responses of Fig. 4. In
fact, for this design, taking the reciprocal gain is equivalent
to inverting the filter. However, this approach does not lend
itself to the decoupling as performed above, so we stay with
the design of (3).
3. DISCRETE-TIME REALIZATION
To obtain discrete-time filters, we simply apply a bilinear
transformation [6]. In the same step, we also denormalize
the cut-off frequency, so that we arrive at the transformation
s =
1
K
1 z
1
1 + z
1
, K = tan
B
2
, (6)
where
B
denotes the filter bandwidth in radians per sample.
Substituting (6) in (4) and (5) gives
¯
H
(m)
LS,M
(z) =
1 + 2V K
K+c
m
+2Kz
1
+(Kc
m
)z
2
1+2Kc
m
+K
2
+(2K
2
2)z
1
+(12Kc
m
+K
2
)z
2
+V
2
K
2
1+2z
1
+z
2
1+2Kc
m
+K
2
+(2K
2
2)z
1
+(12Kc
m
+K
2
)z
2
(7)
14th European Signal Processing Conference (EUSIPCO 2006), Florence, Italy, September 4-8, 2006, copyright by EURASIP
K
a
1
0,m
z
1
z
1
2c
m
K
2
K
c
m
2
V
K V
Figure 5: Parametric realization of a second-order section
¯
H
(m)
LS,M
(z).
a
z
1
V
2
Figure 6: Parametric realization of a first-order section
H
(
M+1
2
)
LS,M
(z).
and
H
(
M+1
2
)
LS,M
(z) = 1 +V K
1+z
1
1+K+(K1)z
1
, (8)
respectively.
Realization of (7) with two parallel second-order sys-
tems, such that these sub-systems only depend on K and
hence the cut-off frequency and are added to a direct-path
using weights that only depend on V and hence the gain, is
straight-forward. But as the two non-trivial summands of (7)
have the same denominator, they can share the feed-back part
of the filter structure and only require distinct feed-forward
parts. By further modifying the filter structure to reduce the
number of operations required, the realization of Fig. 5 can
be derived, where
a
1
0,m
=
1
1 + 2Kc
m
+ K
2
.
The first-order section of (8) actually is a standard low-
shelving filter and can be realized with any of the known
approaches. For convenience, we reproduce the design pre-
sented in [2] which uses the all-pass decomposition
H
(
M+1
2
)
LS,M
(z) = 1 +
V
2
·
1 +
a + z
1
1 + az
1
, a =
K 1
K +1
yielding the realization shown in Fig. 6.
π
0 0.1 0.2 0.3 0.4
0.5 0.6
0.7 0.8
0.9
1
H
BS,M
(e
2
π
f / f
S
)
2
0 dB
10 dB
20 dB
Figure 7: Magnitude responses of band-shelving filters with
order M = 6, gain g = 10, bandwidth
B
= 0.1
π
and center
frequencies
0
= [0, 0.2
π
, 0.4
π
, 0.6
π
, 0.8
π
,
π
].
4. HIGH- AND BAND-SHELVING FILTERS
From the low-shelving filters, high- and band-shelving filters
can easily be obtained as
H
HS,M
(z) = H
LS,M
(z)
and
H
BS,M
(z) = H
LS,M
z
c
0
z
1 c
0
z
, c
0
= cos (
0
),
where
0
is the desired center-frequency of the band-shelv-
ing filter [7]. The resulting magnitude response is given by
H
BS,M
e
j
2
=
(c
0
cos)
2M
+ (K sin)
2M
g
2
(c
0
cos)
2M
+ (K sin)
2M
,
as depicted in Fig. 7 for various center frequencies.
The center frequency here specifies the frequency at
which the maximum gain is reached. This generally is not
the center of the filter’s active band in the sense of being the
arithmetic or geometric mean of the band edges. Instead,
tan
2
0
2
= tan
c,1
2
tan
c,2
2
where
c,i
are the band edges where
H
BS,M
e
j
c,i
2
=
g
2
+1
2
.
Especially, for
0
0, the band-shelving filter becomes
a low-shelving filter, and thus
0
is at the lower end of the
active band, and likewise for
0
π
, the filter becomes a
high-shelving filter with
0
at the upper end of the active
band.
To retain the decoupling of the filter parameters, no new
coefficients depending on
0
are computed, but instead, the
unit delays of Fig. 5 and 6 are replaced with an all-pass as
z
1
A(z) = z
1
c
0
z
1
1 c
0
z
1
. (9)
Note that (9) has the proper limits, i.e. A(z) = z
1
for
0
= 0 and A(z) = z
1
for
0
=
π
, so that the same im-
plementation may be used for low-, band- and high-shelving
filters, provided the realization of the frequency shifting all-
pass is numerically stable for
|
c
0
|
= 1.
14th European Signal Processing Conference (EUSIPCO 2006), Florence, Italy, September 4-8, 2006, copyright by EURASIP
f /Hz
100
1k
10k
200
2k
20k500 5k
|
H( f )
|
2
5 dB
0 dB
5 dB
10 dB
(a) M = 1.
f /Hz
100
1k
10k
200
2k
20k500 5k
|
H( f )
|
2
5 dB
0 dB
5 dB
10 dB
(b) M = 2.
f /Hz
100
1k
10k
200
2k
20k500 5k
|
H( f )
|
2
5 dB
0 dB
5 dB
10 dB
(c) M = 6.
Figure 8: Design example results for different filter orders.
5. DESIGN EXAMPLE
Let us consider a digital parametric three-band equalizer op-
erating at a sampling rate of 48 kHz. The equalizer is realized
as a cascade of shelving filters as presented in this paper. The
parameters of the three bands are set to
f
0,1
= 0 Hz, f
B,1
= 500 Hz, G
1
= 5 dB,
f
0,2
= 2 kHz, f
B,2
= 2 kHz, G
2
= 10 dB,
f
0,3
= 10 kHz, f
B,3
= 14 kHz, G
3
= 5 dB.
We shall compare realizations utilizing filter orders M =
1, 2 and 6. (Due the frequency shifting all-pass, the effective
filter order of course is 2M.) The frequency-dependent coef-
ficients execpt for the a
1
0,m
are the same across filter orders
and can be computed to be
K
1
= 0.032737, c
0,1
= 1.00000,
K
2
= 0.131652, c
0,2
= 0.96593,
K
3
= 1.303225, c
0,3
= 0.25882.
Depending on the filter order, we furthermore find the
gain-dependent V
band,M
as
V
1,1
= 0.77828, V
1,2
= 0.33352, V
1,6
= 0.10069,
V
2,1
= 2.16228, V
2,2
= 0.77828, V
2,6
= 0.21153,
V
3,1
= 0.43766, V
3,2
= 0.25011, V
3,6
= 0.09148.
For the sake of brevity, the resulting values for the a
1
0,m
are
omitted.
In Fig. 8, the resulting magnitude responses of the in-
dividual shelving filters (dashed) and of their cascade (solid
line) are depicted. As can clearly be seen, the 0 dB-valley be-
tween 500 Hz and 1 kHz can only be achieved for the higher-
order filters. For M = 1, i.e. the traditional biquad case, in
the third band around 10 kHz, the desired gain of 5 dB is
not reached at all. This shows that higher-order shelving fil-
ters with their steep band-edges are a necessity for equalizers
that are used to model a specific magnitude response.
6. COMPUTATIONAL PERFORMANCE
While the parametric realization of the first-order section in
Fig. 6 has the minimum number of two multipliers for two
coefficients, the realization of the second-order section in
Fig. 5 needs nine multipliers (not counting multiplication
by 2) considerable more than a direct-form implementa-
tion would need.
So the proposed structure is beneficial only if the fil-
ter parameters are changed frequently, as recomputation of
the coefficients is relatively cheap thanks to the decoupled
design. In particular, changing the bandwidth
B
requires
one trigonometric function evaluation for the complete fil-
ter, which is unavoidable when the filter is constructed using
the bilinear transform, and M divisions to determine the a
1
0,m
.
Changing the gain requires one exponentiation to determine
the gain per section, which also seems unavoidable.
The frequency shift to obtain band-shelving filters can
be efficiently realized with all-passes in one-multiplier form.
This also needs only one trigonometric function evalua-
tion for the complete filter whenever the center-frequency is
changed.
7. CONCLUSIONS
We have presented an approach to design minimum-phase
shelving filters of arbitrary order. For this design, we
have derived a parametric filter structure in which center-
frequency, bandwidth and gain of the shelving filter can be
adjusted independently and cheaply. This realization is suit-
able for several equalization applications where the filter pa-
rameters have to be updated frequently.
REFERENCES
[1] P. A. Regalia and S. K. Mitra. Tunable digital fre-
quency response equalization filters. IEEE Trans.
Acoust., Speech, Signal Processing, 35(1):118–120, Jan-
uary 1987.
[2] U. Z
¨
olzer and T. Boltze. Parametric digital filter struc-
tures. In Proc. 99th AES Convention, Preprint No. 4099,
New York, October 1995.
[3] F. Keiler and U. Z
¨
olzer. Parametric second- and fourth-
order shelving filters for audio applications. In Proc.
IEEE 6th Workshop on Multimedia Signal Processing,
pages 231–234, Siena, Italy, September 2004.
[4] U. Z
¨
olzer. Digital Audio Signal Processing. John Wiley
& Sons, Chichester, UK, 1997.
[5] S. J. Orfanidis. High-order digital parametric equalizer
design. J. Audio Eng. Soc., 53(11):1026–1046, Novem-
ber 2005.
[6] R. M. Golden. Digital filter synthesis by sampled-
data transformation. IEEE Trans. Audio Electroacoust.,
16(3):321–329, September 1968.
[7] M. N. S. Swamy and K. S. Thyagarajan. Digital band-
pass and bandstop filters with variable center frequency
and bandwidth. Proc. IEEE, 64(11):1632–1634, 1976.
14th European Signal Processing Conference (EUSIPCO 2006), Florence, Italy, September 4-8, 2006, copyright by EURASIP
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Thesis
Full-text available
In this dissertation, the discussion is centered around the sound energy decay in enclosed spaces. The work starts with the methods to predict the reverberation parameters, followed by the room impulse response measurement procedures, and ends with an analysis of techniques to digitally reproduce the sound decay. The research on the reverberation in physical spaces was initiated when the first formula to calculate room's reverberation time emerged. Since then, finding an accurate and reliable method to predict reverberation has been an important area of acoustic research. This thesis presents a comprehensive comparison of the most commonly used reverberation time formulas, describes their applicability in various scenarios, and discusses their accuracy when compared to results of measurements. The common sources of uncertainty in reverberation time calculations, such as bias introduced by air absorption and error in sound absorption coefficient, are analyzed as well. The thesis shows that decreasing such uncertainties leads to a good prediction accuracy of Sabine and Eyring equations in diverse conditions regarding sound absorption distribution. The measurement of the sound energy decay plays a crucial part in understanding the propagation of sound in physical spaces. Nowadays, numerous techniques to capture room impulse responses are available, each having its advantages and drawbacks. In this dissertation, the majority of commonly used measurement techniques are listed, whereas the exponential swept-sine is described in more detail. This work elaborates on the external factors that may impair the measurements and introduce error to their results, such as stationary and non-stationary noise, as well as time variance. The dissertation introduces Rule of Two, a method of detecting nonstationary disturbances in sweep measurements. It also shows the importance of using median as a robust estimator in non-stationary noise detection. Artificial reverberation is a popular sound effect, used to synthesize sound energy decay for the purpose of audio production. This dissertation offers an insight into artificial reverberation algorithms based on recursive structures. The filter design proposed in this work offers precise control over the decay rate while being efficient enough for real-time implementation. The thesis discusses the role of the delay lines and feedback matrix in achieving high echo density in feedback delay networks. It also shows that four velvet-noise sequences are sufficient to obtain smooth output in interleaved velvet noise reverberator. The thesis shows that the accuracy of reproduction increases the perceptual similarity between measured and synthesised impulse responses. The insights collected in this dissertation offer insights into the intricacies of reverberation prediction, measurement and synthesis. The results allow for reliable estimation of parameters related to sound energy decay, and offer an improvement in the field of artificial reverberation.
... In Fig. 3 an increasing gain for increasing frequency can be identified for frequencies above 100Hz. This gain is modeled by a highshelving filter H s,HS of second-order after [13] 2 . The gain in high frequencies is caused due to the higher interaction of high-frequency sound with the sphere. ...
Conference Paper
In this paper, we present a method to auralize acoustic scattering and occlusion of a single rigid sphere with parametric filters and neural networks to provide fast processing and estimation of parameters. The filter parameters are estimated using neural networks based on the geometric parameters of the simulated scene, e.g., relative receiver position and size of the rigid spherical scatterer. The modeling differentiates an unoccluded and an occluded source-receiver path, for which different filter structures were used. In contrast to simulating occlusion and scattering numerically or analytically methods, the proposed approach provides rendering with low computational load making it suitable for real-time auralization in virtual reality. The presented method provides a good fit for modeling the acoustic effects of a rigid sphere. Further, a listening test was conducted, which resulted in plausible reproduction of the scattering and occlusion of a rigid sphere.
... Designs of first-order low-frequency and high-frequency shelving filters and second-order peak filters were presented in [1], [2] based on an all-pass decomposition. Second-and fourth-order parametric shelving filters were also designed in [3] and the design of higher order shelving filters was proposed in [4]. A comprehensive account about the parametric filters of different orders and their role in audio equalization has been described in [5]. ...
Conference Paper
Full-text available
Peak and shelving filters are parametric infinite impulse response filters which are used for amplifying or attenuating a certain frequency band. Shelving filters are parametrized by their cutoff frequency and gain, and peak filters by center frequency, bandwidth and gain. Such filters can be cascaded in order to perform audio processing tasks like equalization, spectral shaping and modelling of complex transfer functions. Such a filter cascade allows independent optimization of the mentioned parameters of each filter. For this purpose, a novel approach is proposed for deriving the necessary local gradients with respect to the control parameters and for applying the instantaneous backpropagation algorithm to deduce the gradient flow through a cascaded structure. Additionally , the performance of such a filter cascade adapted with the proposed method, is exhibited for head-related transfer function modelling, as an example application.
Chapter
The possibility of modifying the signal spectrum is a very common requirement for all digital audio signal processing (DASP) applications [1–9]. Considering a general scheme as shown in Fig. 3.1, the device for its implementation, generally known as a filter, is almost always present in both professional and consumer equipment. For example, the variation of the spectrum may be necessary for the acoustic correction of the listening environment or instead, more simply, it may be guided by the musical tastes of the listener.
Article
Full-text available
Low-pass and high-pass non-integer shelving filter designs, which are suitable for acoustic applications, are presented in this work. A first design is based on a standard fractional-order bilinear transfer function, while a second one is based on the transposition of the integer-order transfer function into its power-law counterpart. Both transfer functions are approximated using the Oustaloup approximation tool, while the implementation in the case of the power-law filters is performed through the employment of the concept of driving-point impedance synthesis. An attractive benefit is the extra degree of freedom, resulting from the variable order of both fractional-order and power-law filters, which allows improved design flexibility compared to the case of integer-order filters. From the implementation point of view, only one building block is required to realize both filter types, thanks to the employment of the Voltage Conveyor.
Article
Full-text available
Tunable digital frequency response equalization fiters, which feature adjustable gain at specified frequencies while leaving the remainder of the spectrum unaffected, are advanced. The filter structure is such that the frequency response parameters are independently related to the multiplier coefficients, which permits simple frequency response adjustment by varying the coefficient values. The resulting structure exhibits low coefficient sensitivity characteristics. Copyright © 1987 by The Institute of Electrical and Electronics Engineers, Inc.
Conference Paper
A parametric filter structure for first-order shelving and second-order peak filter transfer functions is derived. The approach is based on a decomposition of the transfer function into the minimum amount of direct branches and an all-pass section. It allows direct control of gain, bandwidth, and center/cutoff frequency for the boost case, and a coupled relation between gain and bandwidth for the cut case. Compared to other all-pass approaches, the new filter structure has fewer direct branches. Analytical formulas for the boost and cut case are derived.
Book
A fully updated second edition of the excellent Digital Audio Signal Processing. Well established in the consumer electronics industry, Digital Audio Signal Processing (DASP) techniques are used in audio CD, computer music and multi-media components. In addition, the applications afforded by this versatile technology now range from real-time signal processing to room simulation. Digital Audio Signal Processing, Second Edition covers the latest signal processing algorithms for audio processing. Every chapter has been completely revised with an easy to understand introduction into the basics and exercises have been included for self testing. Additional Matlab files and Java Applets have been provided on an accompanying website, which support the book by easy to access application examples. Key features include: A thoroughly updated and revised second edition of the popular Digital Audio Signal Processing, a comprehensive coverage of the topic as whole. Provides basic principles and fundamentals for Quantization, Filters, Dynamic Range Control, Room Simulation, Sampling Rate Conversion, and Audio Coding. Includes detailed accounts of studio technology, digital transmission systems, storage media and audio components for home entertainment. Contains precise algorithm description and applications. Provides a full account of the techniques of DASP showing their theoretical foundations and practical solutions. Includes updated computer-based exercises, an accompanying website, and features Web-based Interactive JAVA-Applets for audio processing. This essential guide to digital audio signal processing will serve as an invaluable reference to audio engineering professionals, R and D engineers, researchers in consumer electronics industries and academia, and Hardware and Software developers in IT companies. Advanced students studying multi-media courses will also find this guide of interest.
Article
A family of digital parametric audio equalizers based on high-order Butterworth, Chebyshev, and elliptic analog prototype filters is derived that generalizes the con-ventional biquadratic designs and provides flatter passbands and sharper bandedges. The equalizer filter coefficients are computable in terms of the center frequency, peak gain, bandwidth, and bandwidth gain. We consider the issues of filter order and bandwidth selection, and discuss frequency-shifted transposed, normalized-lattice, and minimum roundoff-noise state-space realization structures. The design equa-tions apply equally well to lowpass and highpass shelving filters, and to ordinary bandpass and bandstop filters.
Conference Paper
In this paper, we develop a parametric recursive second-order lowpass/highpass shelving filters and fourth-order bandpass shelving filters. These filters allow a better frequency selectivity for audio equalization as compared to the well-known first-order lowpass/highpass shelving filters and second-order peak filters. In the parametric structures, the cut-off frequencies and the gain factors can be set independently. We derive the filter designs for the discrete-time implementation. Furthermore, we apply a technique for the implementation of delay-free loops which is necessary to yield the exact inverse filter to realize symmetric boost and cut of a frequency band.
The design of digital filter transfer functions is facilitated by taking advantage of well-established design techniques developed for continuous (analog) filters. Digital approximations to continuous filter functions may be found by applying an appropriate sampled-data (z) transformation to the continuous filter transfer function. Three mathematical transformations are described that find the most application: 1) the standard z-transform, 2) the bilinear z-transform, and 3) the matched z-transform. The applicability of the three transformations is discussed and examples are presented of digital filters designed using these transformations.
Article
This paper presents a method of designing wave digital bandpass (BP) and bandstop (BS) filters whereby the center frequency and bandwidth can be independently controlled by simply changing the multiplier values. Also given are the canonic realizations for the BP and BS wave digital filters. This method of designing BP and BS wave digital filter results in a saving of coefficient registers.