how to calculate quality factor from slope for IIR biQuad filters.

[Deleted_U_Intel]

I am on workin on a live project which is an DSP application. we are using the BIQUAD IIR filter for performing the filtering. for calculating the filter coefficients we are using the formulas given in http://www.harmony-central.com/Computer/Programming/Audio-EQ-Cookbook.txt
for calculating the Alpha value from this formula sheet for the HPF and LPF Quality factor or Bandwidth is required and we have slope specified in the
specification. so i want to know that how the Quality Factor is calculated from slope. please help us out. waiting eagerly for ur reply.

[Vladimir_Dudnik]

Hi, there is answer from our expert:

From my point of view quality and slope are directly connected with filter order, and he should take into account that numerical problems can arise for filter orders as low as 15 (for doubles) and less for floats.

Let him try MatLab:

Signal Processing Toolbox

IIR Filter Design

The primary advantage of IIR filters over FIR filters is that they typically meet a given set of specifications with a much lower filter order than a corresponding FIR filter. Although IIR filters have nonlinear phase, data processing within MATLAB is commonly performed "off-line," that is, the entire data sequence is available prior to filtering. This allows for a noncausal, zero-phase filtering approach (via the filtfilt function), which eliminates the nonlinear phase distortion of an IIR filter.

The classical IIR filters, Butterworth, Chebyshev Types I and II, elliptic, and Bessel, all approximate the ideal "brick wall" filter in different ways. This toolbox provides functions to create all these types of classical IIR filters in both the analog and digital domains (except Bessel, for which only the analog case is supported), and in lowpass, highpass, bandpass, and bandstop configurations. For most filter types, you can also find the lowest filter order that fits a given filter specification in terms of passband and stopband attenuation, and transition width(s).

The direct filter design function yulewalk finds a filter with magnitude response approximating a desired function. This is one way to create a multiband bandpass filter.

You can also use the parametric modeling or system identification functions to design IIR filters. These functions are discussed in Parametric Modeling.

The generalized Butterworth design function maxflat is discussed in the section Generalized Butterworth Filter Design.

The following table summarizes the various filter methods in the toolbox and lists the functions available to implement these methods.

Filter MethodDescriptionFilter FunctionsAnalog PrototypingUsing the poles and zeros of a classical lowpass prototype filter in the continuous (Laplace) domain, obtain a digital filter through frequency transformation and filter discretization.Complete design functions:

besself, butter, cheby1, cheby2, ellip

Order estimation functions:

buttord, cheb1ord, cheb2ord, ellipord

Lowpass analog prototype functions:

besselap, buttap, cheb1ap, cheb2ap, ellipap

Frequency transformation functions:

lp2bp, lp2bs, lp2hp, lp2lp

Filter discretization functions:

bilinear, impinvarDirect DesignDesign digital filter directly in the discrete time-domain by approximating a piecewise linear magnitude response.yulewalkGeneralized Butterworth DesignDesign lowpass Butterworth filters with more zeros than poles.maxflatParametric Modeling Find a digital filter that approximates a prescribed time or frequency domain response. (See the System Identification Toolbox documentation for an extensive collection of parametric modeling tools.)Time-domain modeling functions:

lpc, prony, stmcb

Frequency-domain modeling functions:

invfreqs, invfreqz

Filter Requirements and Specification Classical IIR Filter Design Using Analog Prototyping

Regards,
Vladimir