DSP for MATLAB and LabVIEW: Fundamentals of discrete frequency transforms
This book is Volume II of the series DSP for MATLABâ„˘ and LabVIEWâ„˘. This volume 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). 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 MATLABâ„˘ and LabVIEWâ„˘. The text for all volumes contains many examples, and many useful computational scripts, augmented by demonstration scripts and LabVIEWâ„˘ Virtual Instruments (VIs) that can be run to illustrate various signal processing concepts graphically on the user's computer. 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, preparing the reader for the present volume (Volume II). Volume III of the series covers digital filter design (FIR design using Windowing, Frequency Sampling, and Optimum Equiripple techniques, and Classical IIR design) and Volume IV, the culmination of the series, is an introductory treatment of LMS Adaptive Filtering and applications.
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4-pt DFT amplitude bins butterﬂy chapter circular convolution column vector complex conjugate complex correlator complex exponential complex plane Compute the DFT contour convert convolved decimation-in-time deﬁned DFT coefﬁcients difference equation Digital Signal Processing Direct Form domain sequence DTFT DTMF equivalent evaluate the z-transform Example Figure ﬁlter ﬁnite ﬁrst following code Form coefﬁcients Fourier Transform frames frequency response Goertzel Algorithm harmonic IDFT basis vector impulse response input arguments inverse DFT LabVIEW Laplace Lattice linear chirp linear convolution LTI system m-code magnitude and phase MathScript MATLAB matrix method multiplied Norm Freq Normalized Frequency number of samples obtained original sequence output padded pairs performed periodic sequence radian real and imaginary reconstructed result row vector sample rate sequence of length sequence x[n shown in Fig sinusoid speciﬁed steady-state test signal transfer function unit circle values waveform window Write a script z-plane z-transform