mws_gen_fft_spe_ppttranspair

mws_gen_fft_spe_ppttranspair - Numerical Methods Fourier...

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Unformatted text preview: Numerical Methods Fourier Transform Pair Part: Frequency and Time Domain http://numericalmethods.eng.usf.edu For more details on this topic Go to http://numericalmethods.eng.usf.edu Click on keyword Click on Fourier Transform Pair You are free to Share – to copy, distribute, display and perform the work to Remix – to make derivative works Under the following conditions Attribution — You must attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work). Noncommercial — You may not use this work for commercial purposes. Share Alike — If you alter, transform, or build upon this work, you may distribute the resulting work only under the same or similar license to this one. Chapter 11.03: Fourier Transform Pair: Frequency and Time Domain Major: All Engineering Majors Authors: Duc Nguyen http://numericalmethods.eng.usf.edu Numerical Methods for STEM undergraduates http://numericalmethods.eng.usf.edu 5 9/4/2010 Lecture # 5 http://numericalmethods.eng.usf.edu 6 ) ( ) ( ) ( 1 1 1 t Sin b t Cos a a t f + + ≈ ) 2 ( ) 2 ( ) ( ) ( ) ( 2 2 1 1 2 t Sin b t Cos a t Sin b t Cos a a t f + + + + ≈ ) 2 ( ) 2 ( ) ( ) ( ) ( 2 2 1 1 4 t Sin b t Cos a t Sin b t Cos a a t f + + + + ≈ Example 1 = < ≤ ≤ < = ) ( 2 for for ) ( T t t t t f π π π π ) 4 ( ) 4 ( ) 3 ( ) 3 ( 4 4 3 3 t Sin b t Cos a t Sin b t Cos a + + + + http://numericalmethods.eng.usf.edu 7 Frequency and Time Domain The amplitude (vertical axis) of a given periodic function can be plotted versus time (horizontal axis), but it can also be plotted in the frequency domain as shown in Figure 2. Figure 2 Periodic function (see Example 1 in Chapter 11.02 Continuous Fourier Series) in frequency domain. Frequency and Time Domain cont. Figures 2(a) and 2(b) can be described with the following equations from chapter 11.02, ∑ ∞ −∞ = = k t ikw k e C t f ~ ) ( (39, repeated) where { } ∫ − × = T t ikw k dt e t f T C ) ( 1 ~ (41, repeated) http://numericalmethods.eng.usf.edu 8 http://numericalmethods.eng.usf.edu 9 For the periodic function shown in Example 1 of Chapter 11.02 (Figure 1), one has: 1 2 2 2 2 = = = = π π π π T f w { } ∫ ∫ − − × + × = π π π π 2 1 ~ dt e dt e t T C ikt ikt k Frequency and Time Domain cont. Frequency and Time Domain cont. Define: ∫ ∫ − − − + − × = × ≡ π π π 1 1 dt e ik e ik t dt e t A ikt ikt ikt or [ ] − + = − + − = − − − − 2 2 2 1 1 1 1 k e k e k i e k e ik A ik ik ik ik π π π π π π http://numericalmethods.eng.usf.edu 10 http://numericalmethods.eng.usf.edu 11 Also, ( ) π π π π π π 2 2...
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This note was uploaded on 06/12/2011 for the course EML 3041 taught by Professor Kaw,a during the Spring '08 term at University of South Florida.

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mws_gen_fft_spe_ppttranspair - Numerical Methods Fourier...

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