For a periodic function f(t) that has odd symmetry, how does the calculation of its complex Fourier coefficient cn simplify?
Explanation
When a function has odd symmetry, its complex Fourier coefficients cn become purely imaginary, because the an components (the real part of 2*cn) are zero. The calculation can be simplified to integrating over half the period using a sine function, as shown in Eq. [32].
Other questions
What is the relationship between the period T of a periodic function's fundamental frequency and its radian frequency ω0?
What does the Fourier series coefficient a0 represent?
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If a periodic function f(t) possesses even symmetry, where f(t) = f(-t), which coefficients in its trigonometric Fourier series are guaranteed to be zero?
If a periodic function f(t) possesses odd symmetry, where f(t) = -f(-t), which coefficients in its trigonometric Fourier series are guaranteed to be zero?
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What is the Fourier transform of a unit impulse function located at t = t0?
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What is the relationship between a linear system's impulse response h(t) and its system function H(jω)?
What is the relationship between the system function H(jω) derived from Fourier transform analysis and the sinusoidal steady-state transfer function G(ω)?
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What is the frequency of the first harmonic of a sinusoid also known as?
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What is the integral expression used to calculate the cosine coefficient 'an' for the trigonometric Fourier series of a function f(t) with period T?
In a line spectrum for a Fourier series, if a harmonic component has both a sine term (coefficient bn) and a cosine term (coefficient an), what represents the total amplitude of that component?
For a function with both half-wave and even symmetry, how can the coefficient 'an' for odd harmonics be calculated more efficiently?
For a function with both half-wave and odd symmetry, which set of coefficients is guaranteed to be zero for all n?
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If f(t) is an odd function of time, what are the characteristics of its Fourier transform F(jω)?
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What is the Fourier transform of the signum function, sgn(t)?
What is the Fourier transform of the unit-step function, u(t)?
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What is the Fourier transform of the convolution of two time functions, f(t) * g(t)?
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Integrating a Laplace transform F(s) from s to infinity corresponds to what operation in the time domain?
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Examine the square wave in Figure 18.4b. What type of symmetry does this waveform possess?
What type of symmetry does the triangular waveform shown in Figure 18.4c possess?
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