Exercise · ZW-CONTINUOUS-FOURIER-TRANSFORM-001 · ★☆☆ Basic
By definition, what is the kernel of the forward continuous Fourier transform?
Choose one option.
Show answer
- A. \(e^{-j\omega t}\)
Explanation
The forward kernel is the exponential with a negative sign in the frequency. The option with a positive exponential corresponds to the inverse transform.
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
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