6
votes
Accepted
For unit step $g(t) = u(t)$, why does $G(z) = \frac{z}{1-z}$, whereas $G(s) = \frac{1}{s}$?
Answer to the updated question:
You wonder why there are several mappings from the continuous domain to the discrete domain, and why we don't just use the optimal mapping $z=e^{sT}$.
Let's see how we ...
- 88.8k
3
votes
Accepted
Why dft sine plot is so strange
There are two things you can try, depending on what you're aiming for.
If you want to see a sharp peak at frequency $\omega = 1$, as in the code in your question, then you need to increase the DFT ...
- 14.9k
2
votes
Accepted
What is the rationale behind the "same" mode of discrete convolution?
I think that the only reason why the same mode exists is because sometimes it is convenient if the output has the same length as the input (assuming that the input ...
- 88.8k
2
votes
Why does the griffin lim algorithm work?
Sound is just the combination of multiple sin waves at different frequencies and phases. These phases determine how those sin waves combine together, i.e. if frequencies are resonant or eliminate each ...
- 121
1
vote
Practical Implications of DFT Eigenvector Formulations
The unitary scaling convention for the DFT is identical in scaling with its inverse and preserves energy across the transform or inverse transform:
$$ \begin{align}
\mathcal{DFT}\Big\{x[n]\Big\} & ...
1
vote
Accepted
Calculating the main lobe width of Dirichlet kernel
There's no analytical solution for the general case. However, it's quite straightforward to compute that value using a few iterations of Newton's method. I've done that and the plot below shows the ...
- 88.8k
1
vote
Proper audio noise and artifact detection approach
That's a tough problem to solve. There are commercial solutions for this type of measurements (e.g. Audio Precision (ap.com), Listen, Inc. (https://www.listeninc.com/). They do an ok job but tend to ...
- 42.5k
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