Fourier analysis techniques Fourier transforms- part 2
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The document discusses various Fourier analysis techniques, including applying Fourier series to electric circuits and exploring Fourier transforms for both periodic and aperiodic signals. It outlines the method for calculating DC and AC dissipations, as well as how Fourier transforms can represent nonperiodic functions with a focus on their applications in circuits and systems. Additionally, it addresses the absence of a fundamental frequency concept in aperiodic signals, highlighting key transformation facts.
Fourier analysis techniques Fourier transforms- part 2
- 2. Contents • Applying Fourier series concept to general electric circuits • Finding DC and AC dissipations • Fourier Transforms Concept • Fourier Transform Pairs • Examples of Fourier Transform • Application to circuits and systems (Please not that Fourier transforms in not in HEC Approved curriculum so it will not be part of final exams)
- 3. Applying Fourier series concept to general electric circuits As we know that thus And total power is given by
- 5. Example 15.7 The DC term is not given so the Average DC power voltage is 0v. The v1, v2, v3 and v4 can be calculated by putting n=1, 2, 3 and 4 in above equation. We get; And the total voltage for first 4 terms is then expressed as; 1ꙍ=2, 3ꙍ=6, 5ꙍ=10, 7ꙍ=14
- 7. Example 15.8
- 8. Fourier Transforms (Derivation for aperiodic signal)
- 9. Inverse Fourier Transforms (Derivation for aperiodic signal) Multiply and divide by T and the apply condition for T Fourier Transform Pair
- 10. Fourier Transform Usage • Fourier transform is used to represent a general, nonperiodic function by a continuous superposition or integral of complex exponentials. The function is continuous w.r.t frequency and is defined for every instant. • The Fourier transform can be viewed as the limit of the Fourier series of a function with the period approaches to infinity, so the limits of integration change from one period to (−∞,∞).
- 11. Fourier Transformation Facts • Just like Laplace transformation, the Fourier Transform (FT) pairs are used for quick conversion and reducing mathematical steps • The end result of FT results an equation that contains frequency component ꙍ • Inverse Fourier Transform (IFT) converts all the terms to the time domain relations, containing a variable (t) • There is no concept of fundamental frequency and its harmonics for an aperiodic signal • The aperiodic signal contains frequencies as real numbers and may have both rational as well as irrational values, concluding a real valued set,
- 13. Example 15.12
- 14. Thanks • http://eedmd.weebly.com/ca2/ • MS Teams: EE-201 Circuit Analysis II (Code: kv0slqu) • http://slideshare.com/jazzofizia/