Exercise · ZW-CONTINUOUS-FOURIER-TRANSFORM-004 · ★★☆ Intermediate
If \(x(t)\) is real, what symmetry does \(|X(j\omega)|\) satisfy?
Choose one option.
Show answer
- B. It is even in \(\omega\)
Explanation
For real signals, the spectrum magnitude is even in frequency, while the phase is odd. The option describing odd symmetry refers to the phase, not the magnitude.
Review the concept: Continuous Fourier transform
The continuous Fourier transform \(X(j\omega)\) is a frequency-domain representation of an aperiodic continuous-time signal \(x(t)\), assigning to each frequency \(\omega\) its spectral content.
\[X(j\omega)=\int_{-\infty}^{\infty}x(t)e^{-j\omega t}\,dt\]
More practice problems: continuous fourier transform
- ZW-CONTINUOUS-FOURIER-TRANSFORM-001 By definition, what is the kernel of the forward continuous Fourier transform?
- ZW-CONTINUOUS-FOURIER-TRANSFORM-002 What factor multiplies the integral in the inverse Fourier transform?
- ZW-CONTINUOUS-FOURIER-TRANSFORM-003 What is the Fourier transform of δ(t)?
- ZW-CONTINUOUS-FOURIER-TRANSFORM-005 What is the value of X(j0) for integrable x(t)?
- ZW-CONTINUOUS-FOURIER-TRANSFORM-006 Compute the transform of x(t)=e^-atu(t) with a>0.
- ZW-CONTINUOUS-FOURIER-TRANSFORM-007 If X(jω) is the transform of x(t), what is the transform of x(t-2)?
- ZW-CONTINUOUS-FOURIER-TRANSFORM-008 Compute the transform of the convolution y(t)=x_1(t)*x_2(t) if X_1(jω)=(1)/(1+jω) and X_2(jω)=(2)/(…
- ZW-CONTINUOUS-FOURIER-TRANSFORM-009 What is the transform of x(t)=(d)/(dt)e^-tu(t)?
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