Fourier Series Hlya Yaln 1 Hlya Yaln 2
- Slides: 119
Fourier Series Hülya Yalçın © 1
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Nice Java Applet http: //www. falstad. com/fourier/ Fourier series java applet Hülya Yalçın © 12
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Well, there also -Fourier Transform -Discrete Fourier Transform - etc How all these things are related? Hülya Yalçın © 29
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Going from Fourier Series to Fourier Transform Hülya Yalçın © 39
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Famous Fourier Transforms Sine wave Delta function
Famous Fourier Transforms Gaussian
Famous Fourier Transforms Sinc function Square wave
Famous Fourier Transforms Sinc function Square wave
Famous Fourier Transforms Exponential Lorentzian
FFT of FID
FFT of FID
FFT of FID
Effect of changing sample rate
Effect of changing sample rate
Effect of changing sample rate Lowering the sample rate: Reduces the Nyquist frequency, which Reduces the maximum measurable frequency Does not affect the frequency resolution
Effect of changing sampling duration
Effect of changing sampling duration
Effect of changing sampling duration Reducing the sampling duration: Lowers the frequency resolution Does not affect the range of frequencies you can measure
Effect of changing sampling duration
Effect of changing sampling duration
Measuring multiple frequencies
Measuring multiple frequencies
Trigonometric Fourier series: example Hülya Yalçın © 75
Complex Exponential Fourier Series Hülya Yalçın © 76
Complex Exponential Fourier Series Hülya Yalçın © 77
Symmetry Properties for real signals Hülya Yalçın © 78
Amplitude and phase spectra Hülya Yalçın © 79
Fourier Transform Hülya Yalçın © 80
Recap: Fourier Series Hülya Yalçın © 81
Spectral content of aperiodic signals: the Fourier transform Hülya Yalçın © 82
Example: rectangular pulse Hülya Yalçın © 83
Inverse Fourier Transform Hülya Yalçın © 84
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Properties of Fourier Transform Hülya Yalçın © 86
Properties of Fourier Transform: Linearity Hülya Yalçın © 87
Properties of Fourier Transform: Time-shift Hülya Yalçın © 88
Multiplication by a complex exponential Multiplication by a cosine Hülya Yalçın © 89
Convolution in time-domain Hülya Yalçın © 90
Parseval’s Theorem Hülya Yalçın © 91
Duality Example Hülya Yalçın © 92
Generalized Fourier Transform Hülya Yalçın © 93
Fourier Transform of cosine Hülya Yalçın © 94
Fourier transform of a periodic signal Hülya Yalçın © 95
Bandlimited and timelimited signals Hülya Yalçın © 96
Frequency response of LTI systems Hülya Yalçın © 97
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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/Culling. J/dictionary. html Dictionary of DSP terms http: //jchemed. chem. wisc. edu/JCEWWW/Features/Mcad. In. Chem/mcad 0 08/FT 4 Free. Ind. Decay. pdf Mathcad tutorial for exploring Fourier transforms of free-induction decay Hülya Yalçın © 106
Review: vectors Hülya Yalçın © 107
Vector Spaces Hülya Yalçın © 108
Signal Spaces Hülya Yalçın © 109
The space of periodic signals Hülya Yalçın © 110
Complete orthonormal sets of functions Hülya Yalçın © 111
Fourier Series Hülya Yalçın © 112
Fourier Coefficients Hülya Yalçın © 113
Convergence of Fourier Series Hülya Yalçın © 114
Trigonometric Fourier Series Hülya Yalçın © 115
Trigonometric Fourier Series Hülya Yalçın © 116
Trigonometric Fourier Series Hülya Yalçın © 117
Symmetry Properties Hülya Yalçın © 118
Trigonometric Fourier series: example Hülya Yalçın © 119
- Fourier series multiplication property
- Fourier series
- Series de fourier
- Use of fourier series
- Series complejas de fourier
- Fourier series circuit analysis
- Formula series de fourier
- Fourier transform in image processing
- Single phase half wave controlled rectifier with rle load
- Line spectrum in signals and systems
- Fourier series
- Dirichlet condition for fourier series expansion
- Series de fourier
- Discrete time fourier series
- Half range cosine series solved examples
- Series representation
- Polar fft
- Series de fourier
- 4780/2
- Matlab fourier series coefficients
- Fourier series of even and odd functions
- Series fourier
- Fourier serires
- Fourier series and orthogonal functions
- Polar fourier series
- Www.google.com
- Wolfram fourier series
- Series de fourier
- Frequency domain
- Define discrete fourier transform
- Fourier series
- Fourier transform odd function
- Trigonometric form of fourier series
- Fourier series
- Orthogonal functions in fourier series
- Rectified sine wave fourier series
- Series fourier
- Fourier's theorem
- Frequency domain to time domain
- Orthogonality of trigonometric functions
- Fourier series formula
- Define fourier series of a function
- Fourier series
- Fourier transform of shifted delta function
- Fourier representation of signals
- Symmetrical waveform
- Fourier transform
- Serie de fourier del seno
- Fourier series of periodic function
- Função par e impar
- Duality of fourier transform
- Fourier sine series
- Half range fourier series formula
- Fourier transformation equation
- Heisenberg 1925 paper
- Shunt-series feedback example
- Taylor vs maclaurin
- Series aiding and series opposing
- Maclaurin series vs taylor series
- Maclaurin series vs taylor series
- Arithmetic sum formula
- Ibm p series servers
- Trasformata di fourier
- Fourier shell correlation
- Discrete time fourier transform
- Discrete fourier transform formula
- Fft decimation in frequency
- Fourier basis
- Matlab periodic function
- Inverse fourier transform
- Continuous fourier transform formula
- Trasformata di fourier
- Frequency
- Studio fourier
- Ft representation
- Transformata fourier
- Fourier transform formula
- Fourier transform table
- Koeffizienten mathe
- Contoh soal deret fourier fungsi genap dan ganjil
- Transformée de fourier dirac
- Sinc function fourier transform
- Even fourier
- Imagens
- Espectro bilateral
- Fourier image processing
- Fourier transform
- Fast fourier transform
- R fft
- Fourier transform
- Fourier's law heat transfer
- Hukum fourier konduksi panas
- Transformada directa de laplace
- Duality of fourier transform
- Fourier entrance
- Serie de fourier
- Inverse of fourier transform
- Cftft
- Jpeg fourier transform
- Rect t/2
- Application of discrete fourier transform
- System and signals
- Top hat function fourier transform
- Discrete fourier transform formula
- Sinc fourier transform
- Application of discrete fourier transform
- A function
- Laplace transform
- Fourier transform
- Relationship between laplace and fourier transform
- Jbj fourier
- Fourier transform of x
- Fourier transform spherical coordinates
- Fourier transform conclusion
- Perpindahan panas pada gambar terjadi secara
- Fourier analysis
- Transformada de fourier discreta
- Equation de la chaleur
- Overlap save method