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2 votes

Why do singularities on the imaginary axis affect the Fourier transform differently than the Laplace transform?

The Laplace transform of a function $f(t)$ is defined as: $$F(s) = \int_{0^-}^{\infty} e^{-st} f(t) \, dt,$$ where $s$ is a complex variable $s = \sigma + j\omega$, and the region of convergence (ROC) ...
Ahsan Yousaf's user avatar
  • 1,573
2 votes

How does the shape of a frequency domain function (Fourier Transformed time domain function) change when a time shift is applied in the time domain?

Note that what you plotted is not the frequency spectrum $S_c(j\omega) =|S_c(j\omega)|e^{j\phi (\omega)}$, but the magnitude spectrum $|S_c(j\omega)|$ The shape of the magnitude spectrum is unchanged: ...
Jdip's user avatar
  • 6,300
1 vote

What are some good questions for a graduate level signal processing course?

How would you compress image using the KLT concept? Should be done by building a matrix of patches and applying PCA. The equivalence of the weighted least squares and Mahalanobis based distance. Show ...
Royi's user avatar
  • 19.8k
1 vote

Is there a Fourier Transform generalization that lets you analyze arbitrary complex frequencies?

So Gideon Genadi Kogan provided the following solution: We can consider a laplace transform of $f(t)$ that is $\int_{0}^{\infty} e^{-st} f(t) dt $ For each term in the expansion this would be ...
Sidharth Ghoshal's user avatar
1 vote

integration property of fourier series

I am sure my answer is way too late. I would rather establish the integration property by using the analysis equation instead. Also, you should remember that you need the integral of $x(t)$ to be ...
Carlos Bispo's user avatar
1 vote

DFT-like transform using triangle waves instead of sin waves

re earlier comment: hmmm... I'm not as advanced when it comes to orthogonality... Honestly, I don't understand what the implication of orthogonality is. Does it ultimately mean that it takes more CPU ...
thomasm5's user avatar

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