Circuits, Signals, and Systems for Bioengineers: A by John Semmlow

By John Semmlow

Techniques resembling the move functionality and the Fourier and the Laplace transforms are vital instruments for bioengineers that frequently thought of borrowed from electric engineering. this article permits bioengineering scholars and bioengineers the power to foster a feeling of possession of those instruments by way of offering them with an exceptional origin within the options of linear structures analysis.Circuits, indications and structures for Bioengineers publications readers throughout the uncomplicated engineering suggestions that underlie organic platforms, clinical units, biocontrol, and biosignal research. fabric very important to their research and regularly taught in an electric engineering carrier direction can now be embraced via bioengineers. To additional improve the effectiveness of the ebook, instructive illustrations and MATLAB exercises and examples are supplied in the course of the e-book with extra fabric to be had on a CD-ROM. ?· interprets very important electric engineering instruments similar to Fourier remodel, Laplace remodel, analog modeling, structures modeling, and different linear structures research ideas for bioengineering scholars. ?· comprises MATLAB examples and difficulties. ?· contains CD-Rom with PowerPoint shows, additional examples, figures, and help exercises.

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Example text

Be sure to convert the sine into a cosine [recall Eq. 4: sin(w) = cos(wt - 90 degrees)] before expanding this term. 0 cos(2t - 30) This approach can be extended to any number of sinusoids. An example involving three sinusoids is found in Problem 4. 2 Complex Representation An even more compact representation of a sinusoid is possible using complex notation. A complex number combines a real number and an imaginary number. Real numbers are commonly used, whereas imaginary numbers are the product of square roots and are represented by real numbers multiplied by the -1.

8] To convert from a sine and cosine to a single sinusoid with angle q, start with Eq. 8. If a = Ccos(q) and b = Csin(q), then to determine C: a 2 + b 2 = C 2 (cos 2 q + sin 2 q ) = C 2 C = a2 + b2 [Eq. 10 shows the calculation for q given a and b: b C sin(q ) = = tan(q ) and . . a C cos(q ) q = tan -1 Ê bˆ Ë a¯ [Eq. 10] Care must be taken in evaluating Eq. 10 to ensure that q is determined to be in the correct quadrant on the basis of the signs of a and b. If both a and b are positive, q must be between 0 and 90 degrees; if b is positive and a is negative, q must be between 90 and 180 degrees (a calculator or MATLAB will not know this and will put any negative product in the fourth quadrant); if both a and b are negative, q must be between 180 and 270 degrees (calculators and MATLAB put positive arguments in the first quadrant even if they result from two negative numbers); and finally, if b is negative and a is positive, q must be between 270 and 360 degrees.

17 and Eq. 18. The term correlation implies this normalization. 7, which shows various pairs of waveforms and the correlation between them. Note that a sine and a cosine have no (zero) correlation even though the two are alike in the sense that they are both sinusoids (upper plot). Intuitively, we see that this is because any positive correlation between them over one portion of a cycle is canceled by negative correlation over the rest of the cycle. Mathematically, this is a demonstration that a sine and a cosine of the same frequency are orthogonal functions, functions that, by definition, are uncorrelated.

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