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Signal Processing

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    $\begingroup$ Be careful comparing expressions in continuous-time and continuous-frequency to their counterparts in discrete-time and discrete-frequency. There are scaling issues both in the independent variable ($t$ and $n$ or $\omega$ and $k$) and in the dependent variable ($x(t)$ and $x[n]$ or $X(\omega)$ and $X[k]$). To make a good direct comparison, you might want to review the Riemann integral. That's a good way to compare the integrals and dirac impulses in the continuous-time/frequency domain to the summations and kronecker impulses in the discrete-time/frequency domain. $\endgroup$ Commented Jun 6, 2023 at 17:59