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zen barcode ssrs LINE SPECTRUM in Software
LINE SPECTRUM Decoding Denso QR Bar Code In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. Draw QR Code In None Using Barcode printer for Software Control to generate, create QR Code image in Software applications. A plot showing each of the harmonic amplitudes in the wave is called the line spectrum. The lines decrease rapidly for waves with rapidly convergent series. Waves with discontinuities, such as the sawtooth and square wave, have spectra with slowly decreasing amplitudes, since their series have strong QR Code ISO/IEC18004 Scanner In None Using Barcode scanner for Software Control to read, scan read, scan image in Software applications. Denso QR Bar Code Creation In Visual C# Using Barcode printer for VS .NET Control to generate, create Quick Response Code image in Visual Studio .NET applications. FOURIER METHOD OF WAVEFORM ANALYSIS
Encode QR Code In .NET Framework Using Barcode drawer for ASP.NET Control to generate, create QR image in ASP.NET applications. Generate Quick Response Code In VS .NET Using Barcode printer for .NET framework Control to generate, create QRCode image in .NET applications. [CHAP. 17
QR Generation In Visual Basic .NET Using Barcode drawer for .NET Control to generate, create Quick Response Code image in .NET applications. Barcode Creation In None Using Barcode printer for Software Control to generate, create bar code image in Software applications. high harmonics. Their 10th harmonics will often have amplitudes of signi cant value as compared to the fundamental. In contrast, the series for waveforms without discontinuities and with a generally smooth appearance will converge rapidly, and only a few terms are required to generate the wave. Such rapid convergence will be evident from the line spectrum where the harmonic amplitudes decrease rapidly, so that any above the 5th or 6th are insigni cant. The harmonic content and the line spectrum of a wave are part of the very nature of that wave and never change, regardless of the method of analysis. Shifting the origin gives the trigonometric series a completely di erent appearance, and the exponential series coe cients also change greatly. However, the same harmonics always appear in the series, and their amplitudes, c 0 j 1 a0 j 2 or c0 jA0 j and and cn p a2 b2 n ! 1 n n n ! 1 14 (15) Bar Code Encoder In None Using Barcode generation for Software Control to generate, create bar code image in Software applications. UPC Code Maker In None Using Barcode generator for Software Control to generate, create UPCA Supplement 2 image in Software applications. cn jAn j jA n j 2jAn j
Painting EAN13 In None Using Barcode creation for Software Control to generate, create EAN13 image in Software applications. Making Code 39 In None Using Barcode creation for Software Control to generate, create Code 39 Full ASCII image in Software applications. remain the same. Note that when the exponential form is used, the amplitude of the nth harmonic combines the contributions of frequencies n! and n!. UPC  E0 Printer In None Using Barcode generation for Software Control to generate, create UPC E image in Software applications. ECC200 Decoder In C# Using Barcode decoder for .NET Control to read, scan read, scan image in Visual Studio .NET applications. EXAMPLE 17.4 In Fig. 178, the sawtooth wave of Example 17.1 and its line spectrum are shown. Since there were only sine terms in the trigonometric series, the harmonic amplitudes are given directly by 1 a0 and jbn j. The 2 same line spectrum is obtained from the exponential Fourier series, (13). Printing Barcode In ObjectiveC Using Barcode drawer for iPhone Control to generate, create bar code image in iPhone applications. UPC  13 Encoder In VB.NET Using Barcode creation for Visual Studio .NET Control to generate, create GS1  13 image in .NET applications. Fig. 178 Matrix Barcode Printer In VS .NET Using Barcode encoder for .NET Control to generate, create Matrix Barcode image in .NET framework applications. Recognizing Data Matrix In None Using Barcode reader for Software Control to read, scan read, scan image in Software applications. WAVEFORM SYNTHESIS
Encoding Barcode In None Using Barcode drawer for Microsoft Word Control to generate, create barcode image in Microsoft Word applications. UPCA Supplement 5 Encoder In Java Using Barcode creation for Java Control to generate, create UPC A image in Java applications. Synthesis is a combination of parts so as to form a whole. Fourier synthesis is the recombination of the terms of the trigonometric series, usually the rst four or ve, to produce the original wave. Often it is only after synthesizing a wave that the student is convinced that the Fourier series does in fact represent the periodic wave for which it was obtained. The trigonometric series for the sawtooth wave of Fig. 178 is f t 5 10 10 10 sin !t sin 2!t sin 3!t 2 3 These four terms are plotted and added in Fig. 179. Although the result is not a perfect sawtooth wave, it appears that with more terms included the sketch will more nearly resemble a sawtooth. Since this wave has discontinuities, its series is not rapidly convergent, and consequently, the synthesis using only four terms does not produce a very good result. The next term, at the frequency 4!, has amplitude 10/ 4, which is certainly signi cant compared to the fundamental amplitude, 10/. As each term is added in the synthesis, the irregularities of the resultant are reduced and the approximation to the original wave is improved. This is what was meant when we said earlier that the series converges to the function at all points of continuity and to the mean value at points of discontinuity. In Fig. 179, at 0 and 2 it is clear that a value of 5 will remain, since all sine terms are zero at these points. These are the points of discontinuity; and the value of the function when they are approached from the left is 10, and from the right 0, with the mean value 5. CHAP. 17] FOURIER METHOD OF WAVEFORM ANALYSIS
Fig. 179 EFFECTIVE VALUES AND POWER The e ective or rms value of the function f t 1 a0 a1 cos !t a2 cos 2!t b1 sin !t b2 sin 2!t 2 q q 1 a0 2 1 a2 1 a2 1 b2 1 b2 c 2 1 c 2 1 c 2 1 c 3 0 2 2 1 2 2 2 1 2 2 2 1 2 2 2 3

