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Principles of FIR design -- Overview -- In previous volumes -- In this volume -- In this chapter -- Software for use with this book -- Characteristics of FIR filters -- Effect of filter length -- Effect of windowing -- Linear phase -- Impulse response requirement -- Four basic categories of FIR impulse response for linear phase -- Zero location in linear phase filters -- Linear phase FIR frequency content and response -- Design methods -- Basic scheme -- Three design methods -- The comb and moving average filters -- FIR realization -- Direct form -- Cascade form -- Linear phase form -- Cascaded linear phase form -- Frequency sampling -- References -- Exercises -- FIR design techniques -- Overview -- Software for use with this book -- Summary of design methods -- Filter specification -- FIR design via windowed ideal lowpass filter -- Windows -- Net frequency response -- Windowed lowpass filters-passband ripple and stopband -- Attenuation -- Highpass, bandpass, and bandstop filters from lowpass filters -- Improving stopband attenuation -- Meeting design specifications -- FIR design via frequency sampling -- Using the inverse DFT -- Using cosine/sine summation formulas -- Improving stopband attenuation -- Filters other than lowpass -- Hilbert transformers -- Differentiators -- Optimized filter design -- Equiripple design -- Design goal -- Alternation theorem -- A common design problem for all linear phase filters -- Weighted error function -- Remez exchange algorithm -- References -- Exercises -- Classical IIR design -- Overview -- Laplace transform -- Definition -- Convergence -- Relation to Fourier transform -- Relation to z-transform -- Time domain response generated by poles -- General observations -- Prototype analog filters -- Notation -- System function and properties -- Computed frequency response -- General procedure for analog/digital filter design -- Analog lowpass Butterworth filters -- Design by order and cutoff frequency -- Design by standard parameters -- Lowpass analog Chebyshev type-I filters -- Design by order, cutoff frequency, and Epsilon -- Design by standard parameters -- Lowpass analog Chebyshev type-II filters -- Design by order, cutoff frequency, and Epsilon -- Design by standard parameters -- Analog lowpass elliptic filters -- Design by standard parameters -- Frequency transformations in the analog domain -- Lowpass to lowpass -- Lowpass to highpass -- Transformation via convolution -- Lowpass to bandpass -- Lowpass to bandstop (notch) -- Analog to digital filter transformation -- Impulse invariance -- The bilinear transform -- MathScript filter design functions -- Prony's method -- IIR optimization programs -- References -- Exercises -- Software for use with this book -- File types and naming conventions -- Downloading the software -- Using the software -- Single-line function calls -- Multi-line m-code examples -- How to successfully copy-and-paste M-code -- Learning To use M-code -- What you need with MATLAB and LabVIEW -- Vector/matrix operations in M-code -- Row and column vectors -- Vector products -- Inner product -- Outer product -- Product of corresponding values -- Matrix multiplied by a vector or matrix -- Matrix inverse and pseudo-inverse -- FIR frequency sampling design formulas -- Whole-cycle mode filter formulas -- Odd length, symmetric (type I) -- Even length, symmetric (type II) -- Odd length, anti-symmetric (type III) -- Even length, symmetric (type IV) -- Half-cycle mode filters -- Odd length, symmetric (type I) -- Even length, symmetric (type II) -- Odd length, anti-symmetric (type III) -- Even length, anti-symmetric (type IV).

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This book is Volume III of the series DSP for MATLAB and LabVIEW. Volume III covers digital filter design, including the specific topics of FIR design via windowed-ideal-lowpass filter, FIR highpass, bandpass, and bandstop filter design from windowed-ideal lowpass filters, FIR design using the transition-band-optimized Frequency Sampling technique (implemented by Inverse-DFT or Cosine/Sine Summation Formulas), design of equiripple FIRs of all standard types including Hilbert Transformers and Differentiators via the Remez Exchange Algorithm, design of Butterworth, Chebyshev (Types I and II), and Elliptic analog prototype lowpass filters, conversion of analog lowpass prototype filters to highpass, bandpass, and bandstop filters, and conversion of analog filters to digital filters using the Impulse Invariance and Bilinear Transform techniques. Certain filter topologies specific to FIRs are also discussed, as are two simple FIR types, the Comb and Moving Average filters. The entire series consists of four volumes that collectively cover basic digital signal processing in a practical and accessible manner, but which nonetheless include all essential foundation mathematics. As the series title implies, the scripts (of which there are more than 200) described in the text and supplied in code form (available via the internet at http://www.morganclaypool.com/page/isen) will run on both MATLAB and LabVIEW. The text for all volumes contains many examples, and many useful computational scripts, augmented by demonstration scripts and LabVIEW Virtual Instruments (VIs) that can be run to illustrate various signal processing concepts graphically on the user's computer screen. Volume I consists of four chapters that collectively set forth a brief overview of the field of digital signal processing, useful signals and concepts (including convolution, recursion, difference equations, LTI systems, etc), conversion from the continuous to discrete domain and back (i.e., analog-to-digital and digital-to-analog conversion), aliasing, the Nyquist rate, normalized frequency, sample rate conversion, and Mu-law compression, and signal processing principles including correlation, the correlation sequence, the Real DFT, correlation by convolution, matched filtering, simple FIR filters, and simple IIR filters. Chapter 4 of Volume I, in particular, provides an intuitive or "first principle" understanding of how digital filtering and frequency transforms work.Volume II provides detailed coverage of discrete frequency transforms, including a brief overview of common frequency transforms, both discrete and continuous, followed by detailed treatments of the Discrete Time Fourier Transform (DTFT), the z-Transform (including definition and properties, the inverse z-transform, frequency response via z-transform, and alternate filter realization topologies including Direct Form, Direct Form Transposed, Cascade Form, Parallel Form, and Lattice Form), and the Discrete Fourier transform (DFT) (including Discrete Fourier Series, the DFT-IDFT pair,DFT of common signals, bin width, sampling duration, and sample rate, the FFT, the Goertzel Algorithm, Linear, Periodic, and Circular convolution, DFT Leakage, and computation of the Inverse DFT). Volume IV, the culmination of the series, is an introductory treatment of LMS Adaptive Filtering and applications, and covers cost functions, performance surfaces, coefficient perturbation to estimate the gradient, the LMS algorithm, response of the LMS algorithm to narrow-band signals, and various topologies such as ANC (Active Noise Cancelling) or system modeling, Periodic Signal Removal/Prediction/Adaptive Line Enhancement (ALE), Interference Cancellation, Echo Cancellation (with single- and dual-H topologies), and Inverse Filtering/Deconvolution/Equalization.

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