By Forester W. Isen
This ebook is quantity I of the sequence DSP for MATLAB™ and LabVIEW™. the whole sequence includes 4 volumes that jointly conceal easy electronic sign processing in a realistic and obtainable demeanour, yet which still contain all crucial starting place arithmetic. because the sequence identify implies, the scripts (of which there are greater than 2 hundred) defined within the textual content and provided in code shape (available at www.morganclaypool.com/page/isen) will run on either MATLAB and LabVIEW. quantity I contains 4 chapters. the 1st bankruptcy offers a quick evaluation of the sector of electronic sign processing. this is often by way of a bankruptcy detailing many helpful signs and ideas, together with convolution, recursion, distinction equations, LTI structures, and so on. The 3rd bankruptcy covers conversion from the continual to discrete area and again (i.e., analog-to-digital and digital-to-analog conversion), aliasing, the Nyquist price, normalized frequency, conversion from one pattern fee to a different, waveform iteration at a variety of pattern premiums from saved wave facts, and Mu-law compression. The fourth and ultimate bankruptcy of the current quantity introduces the reader to many very important ideas of sign processing, together with correlation, the correlation series, the genuine DFT, correlation via convolution, matched filtering, uncomplicated FIR filters, and straightforward IIR filters. bankruptcy four, particularly, offers an intuitive or "first precept" realizing of the way electronic filtering and frequency transforms paintings, getting ready the reader for Volumes II and III, which supply, respectively, specified insurance of discrete frequency transforms (including the Discrete Time Fourier rework, the Discrete Fourier rework, and the z-Transform) and electronic filter out layout (FIR layout utilizing Windowing, Frequency Sampling, and optimal Equiripple concepts, and Classical IIR design). quantity IV, the end result of the sequence, is an introductory remedy of LMS Adaptive Filtering and functions. The textual content for all volumes includes many examples, and lots of priceless computational scripts, augmented by way of demonstration scripts and LabVIEW digital tools (VIs) that may be run to demonstrate numerous sign processing thoughts graphically at the user's monitor. desk of Contents: an summary of DSP / Discrete indications and ideas / Sampling and Binary illustration / remodel and Filtering rules
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Extra info for DSP for MATLAB and LabVIEW, Volume I: Fundamentals of Discrete Signal Processing (Synthesis Lectures on Signal Processing)
USEFUL SIGNALS, SEQUENCES, AND CONCEPTS 17 The following function will generate n periods of the sequence y: function nY = LVMakePeriodicSeq(y,N) % LVMakePeriodicSeq([1 2 3 4],2) y = y(:); nY = y*([ones(1,N)]); nY = nY(:)’; To illustrate use of the above, we will generate a sequence having three cycles of a cosine wave having a period of 11 samples. , are composed of sinusoids forming a harmonic (or overtone, as used in music) series. A periodic wave, then, is a superposition of sinusoids having frequencies of 1, 2, 3 ...
4. USEFUL SIGNALS, SEQUENCES, AND CONCEPTS 19 index zero. For example, the sequence [1,2,3,4] that has corresponding sample indices [3,4,5,6], when folded, results in the sequence [4,3,2,1] and corresponding indices [-6,-5,-4,-3]. To illustrate the above ideas, we can, for example, let x[n] = [1,2,3,4] with corresponding sample indices n = [3,4,5,6], and compute x[−n] using MathScript. 9 EVEN AND ODD DECOMPOSITION Any real sequence can be decomposed into two components that display even and odd symmetry about the midpoint of the sequence.
For example, we can write a script similar to the above one that inserts a delay Del (a number of samples valued at zero) before the cosine sequence. The reader should run both of the calls given in the script below to verify the shift invariance property. function LVScDelCosine(A,N,F,Del) % LVScDelCosine(1,128,3,0) % LVScDelCosine(1,128,3,30) t = [0:1:N-1]/N; x = [zeros(1,Del),A*cos(2*pi*F*t)]; y = 2*x; ﬁgure(14); subplot(2,1,1); stem(x); subplot(2,1,2); stem(y) We now provide a script that will implement a simple LTI system based on scaling and delaying an input signal multiple times and adding the delayed, scaled versions together.