1. Hülya Yalçın ©1 Fourier Series

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12. Hülya Yalçın ©12 Nice Java Applet http://www.falstad.com/fourier/ Fourier series java applet

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29. Hülya Yalçın ©29 Well, there are also -Fourier Transform -Discrete Fourier Transform - etc How all these things are related?

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39. Hülya Yalçın ©39 Going from Fourier Series to Fourier Transform

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57. Famous Fourier Transforms Sine wave Delta function

58. Famous Fourier Transforms Gaussian

59. Famous Fourier Transforms Sinc function Square wave

60. Famous Fourier Transforms Sinc function Square wave

61. Famous Fourier Transforms Exponential Lorentzian

62. FFT of FID

65. Effect of changing sample rate

67. Lowering the sample rate: Reduces the Nyquist frequency, which Reduces the maximum measurable frequency Does not affect the frequency resolution

68. Effect of changing sampling duration

70. Reducing the sampling duration: Lowers the frequency resolution Does not affect the range of frequencies you can measure

71. Effect of changing sampling duration

73. Measuring multiple frequencies

75. Hülya Yalçın ©75 Trigonometric Fourier series: example

76. Hülya Yalçın ©76 Complex Exponential Fourier Series

77. Hülya Yalçın ©77 Complex Exponential Fourier Series

78. Hülya Yalçın ©78 Symmetry Properties for real signals

79. Hülya Yalçın ©79 Amplitude and phase spectra

80. Hülya Yalçın ©80 Fourier Transform

81. Hülya Yalçın ©81 Recap: Fourier Series

82. Hülya Yalçın ©82 Spectral content of aperiodic signals: the Fourier transform

83. Hülya Yalçın ©83 Example: rectangular pulse

84. Hülya Yalçın ©84 Inverse Fourier Transform

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86. Hülya Yalçın ©86 Properties of Fourier Transform

87. Hülya Yalçın ©87 Properties of Fourier Transform: Linearity

88. Hülya Yalçın ©88 Properties of Fourier Transform: Time-shift

89. Hülya Yalçın ©89 Multiplication by a complex exponential Multiplication by a cosine

90. Hülya Yalçın ©90 Convolution in time-domain

91. Hülya Yalçın ©91 Parseval’s Theorem

92. Hülya Yalçın ©92 Duality Example

93. Hülya Yalçın ©93 Generalized Fourier Transform

94. Hülya Yalçın ©94 Fourier Transform of cosine

95. Hülya Yalçın ©95 Fourier transform of a periodic signal

96. Hülya Yalçın ©96 Bandlimited and timelimited signals

97. Hülya Yalçın ©97 Frequency response of LTI systems

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106. Hülya Yalçın ©106 Some useful links http://www.falstad.com/fourier/ Fourier series java applet http://www.jhu.edu/~signals/ Collection of demonstrations about digital signal processing http://www.ni.com/events/tutorials/campus.htm FFT tutorial from National Instruments http://www.cf.ac.uk/psych/CullingJ/dictionary.html Dictionary of DSP terms http://jchemed.chem.wisc.edu/JCEWWW/Features/McadInChem/mcad0 08/FT4FreeIndDecay.pdf http://jchemed.chem.wisc.edu/JCEWWW/Features/McadInChem/mcad0 08/FT4FreeIndDecay.pdf Mathcad tutorial for exploring Fourier transforms of free-induction decay

107. Hülya Yalçın ©107 Review: vectors

108. Hülya Yalçın ©108 Vector Spaces

109. Hülya Yalçın ©109 Signal Spaces

110. Hülya Yalçın ©110 The space of periodic signals

111. Hülya Yalçın ©111 Complete orthonormal sets of functions

112. Hülya Yalçın ©112 Fourier Series

113. Hülya Yalçın ©113 Fourier Coefficients

114. Hülya Yalçın ©114 Convergence of Fourier Series

115. Hülya Yalçın ©115 Trigonometric Fourier Series

116. Hülya Yalçın ©116 Trigonometric Fourier Series

117. Hülya Yalçın ©117 Trigonometric Fourier Series

118. Hülya Yalçın ©118 Symmetry Properties

119. Hülya Yalçın ©119 Trigonometric Fourier series: example