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    But an engineering degree or expensive software is not required to design and analyze them. In fact, whoever you are and whatever your background, this book will help you understand, design, analyze and use digital filters. This book was written to make digital filters more accessible to everyone. Practicing engineers will appreciate its straightforward approach and the simple formulas that readily lend themselves to real-time applications. Others will find that digital filter design and analysis is really not as difficult as they may have thought. For each IIR filter type (Butterworth, Linkwitz-Reilly, Bessel, Chebychev I & II, Variable Q, Allpass, Equalization, Notch and Shelf), the reader will find one equation for each coefficient. Plug in what you know - cutoff frequency, sample rate - and the equations will give you the coefficient values; no expensive software, transforms or complicated manipulations are needed. This approach does have its limitations. Although the book does explain how to create higher orders by combining lower orders, there are no equations for IIR filters larger than fourth order. Several FIR methods (Fourier Series and Frequency Sampling Methods) are included and they do apply to any order. Since elliptical (Cauer) IIR filters and the Remez and Parks-McClellan algorithms for equiripple FIR design require specialized software and do not lend themselves to simple formulas, they are not included. The second edition includes a new chapter on filter applications which shows you how to choose filters to perform various functions. There is also a new section on fixed point filter implementation. In addition, there are many formatting changes aimed at making the book clearer and easier to use. IIR filter equations are mathematically the same as in the first edition, but are presented in a simpler way: the common denominator equation is written only once per filter type, and the simple relationships that often exist between numerator coefficients are shown. That is, if b3 = b1, this is written, rather than repeating the full equation. As with the first edition, the book gives the simplest possible equations for the design of IIR and FIR filters and examples for their use. Nothing from the first edition has been left out.