This preview shows pages 1–3. Sign up to view the full content.

iv Signals and Systems with MATLAB Computing and Simulink Modeling, Third Edition Copyright © Orchard Publications 6.8 Solutions to End of Chapter Exercises. ............................................................... 6 25 MATLAB Applications Pages 6 12, 6 15, 6 30 7 Fourier Series 7 1 7.1 Wave Analysis. ........................................................................................................ 7 1 7.2 Evaluation of the Coefficients. ................................................................................ 7 2 7.3 Symmetry in Trigonometric Fourier Series. ............................................................ 7 6 7.3.1 Symmetry in Square Waveform. .................................................................... 7 8 7.3.2 Symmetry in Square Waveform with Ordinate Axis Shifted. ....................... 7 8 7.3.3 Symmetry in Sawtooth Waveform. ................................................................ 7 9 7.3.4 Symmetry in Triangular Waveform. .............................................................. 7 9 7.3.5 Symmetry in Fundamental, Second, and Third Harmonics. ....................... 7 10 7.4 Trigonometric Form of Fourier Series for Common Waveforms. ......................... 7 10 7.4.1 Trigonometric Fourier Series for Square Waveform. .................................. 7 11 7.4.2 Trigonometric Fourier Series for Sawtooth Waveform. .............................. 7 14 7.4.3 Trigonometric Fourier Series for Triangular Waveform. ............................ 7 16 7.4.4 Trigonometric Fourier Series for Half Wave Rectifier Waveform. ............ 7 17 7.4.5 Trigonometric Fourier Series for Full Wave Rectifier Waveform. ............. 7 20 7.5 Gibbs Phenomenon. .............................................................................................. 7 24 7.6 Alternate Forms of the Trigonometric Fourier Series . ......................................... 7 24 7.7 Circuit Analysis with Trigonometric Fourier Series. ............................................ 7 28 7.8 The Exponential Form of the Fourier Series. ....................................................... 7 31 7.9 Symmetry in Exponential Fourier Series. ............................................................. 7 33 7.9.1 Even Functions. .......................................................................................... 7 33 7.9.2 Odd Functions. ........................................................................................... 7 34 7.9.3 Half-Wave Symmetry . ................................................................................ 7 34 7.9.4 No Symmetry . ............................................................................................. 7 34 7.9.5 Relation of to ................................................................................ 7 34 7.10 Line Spectra. ......................................................................................................... 7 36 7.11 Computation of RMS Values from Fourier Series. ............................................... 7 41 7.12 Computation of Average Power from Fourier Series . .......................................... 7 44 7.13 Evaluation of Fourier Coefficients Using Excel® . ............................................... 7 46 7.14 Evaluation of Fourier Coefficients Using MATLAB® . ....................................... 7 47 7.15 Summary. .............................................................................................................. 7 50 7.16 Exercises . .............................................................................................................. 7 53 7.17 Solutions to End of Chapter Exercises . .............................................................. 7 55 MATLAB Computing Pages 7 38, 7 47 C n C n

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Signals and Systems with MATLAB Computing and Simulink Modeling, Third Edition v Copyright © Orchard Publications Simulink Modeling Page 7 31 8 The Fourier Transform 8 1 8.1 Definition and Special Forms . ............................................................................... 8 1 8.2 Special Forms of the Fourier Transform. ............................................................... 8 2 8.2.1 Real Time Functions. ................................................................................. 8 3 8.2.2 Imaginary Time Functions. ........................................................................ 8 6 8.3 Properties and Theorems of the Fourier Transform. ............................................. 8 9 8.3.1 Linearity. ..................................................................................................... 8 9 8.3.2 Symmetry. ................................................................................................... 8 9 8.3.3 Time Scaling. ............................................................................................ 8 10 8.3.4 Time Shifting. ........................................................................................... 8 11 8.3.5 Frequency Shifting . .................................................................................. 8 11 8.3.6 Time Differentiation . ............................................................................... 8 12 8.3.7 Frequency Differentiation . ....................................................................... 8 13 8.3.8 Time Integration . ..................................................................................... 8 13 8.3.9 Conjugate Time and Frequency Functions. ............................................. 8 13 8.3.10 Time Convolution. ................................................................................... 8 14 8.3.11 Frequency Convolution. ........................................................................... 8 15 8.3.12 Area Under ........................................................................................ 8 15 8.3.13 Area Under ...................................................................................... 8 15 8.3.14 Parseval’s Theorem. .................................................................................. 8 16 8.4 Fourier Transform Pairs of Common Functions. ................................................. 8 18 8.4.1 The Delta Function Pair. ......................................................................... 8 18 8.4.2 The Constant Function Pair. ................................................................... 8 18 8.4.3 The Cosine Function Pair. ....................................................................... 8 19 8.4.4 The Sine Function Pair. ............................................................................ 8 20 8.4.5 The Signum Function Pair. ....................................................................... 8 20 8.4.6 The Unit Step Function Pair . ................................................................... 8 22 8.4.7 The Function Pair. ................................................................... 8 24 8.4.8 The Function Pair . .............................................................. 8 24 8.4.9 The Function Pair .
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}