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Based on $$x(-t) \rightarrow {X}(-\omega) \hspace{1cm} (time-reversal)$$ $${x^*}(t) \rightarrow {X^*}(-\omega) \hspace{1cm} (conjugation)$$ if we were able to split a function $x(t)$ into real/imaginary parts and then further into even/odd functions, x(t) = {x_R^E}(t) + {x_I^E}(t) ...

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Here is what I found in this reference: The mel-cepstrum computed with $H_m[k]$ or $H'_m[k]$ will differ by a constant vector for all inputs, so the choice becomes unimportant when used in a speech recognition system that has trained with the same filters. And the two equations $H_m[k]$ and $H'_m[k]$ are: However, on page 328 of the mentioned reference, ...

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Normalizing the filterbanks by their widths is optional and totally up to you (similarly to the warping scale Mel/Bark). Depending on your application, you can start without normalization and see what results you are getting. Personally I prefer to keep it fixed and have one knob less for turning. There are more important parameters to tune, such as warping ...

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I think the answer to your question is "yes" and this is why: A Linear Time-Variant (or possibly time-variant) system is fully described (from the POV of output $y(t)$ in terms of input $x(t)$) by this convolution integral: $$y(t) = \int\limits_{-\infty}^{\infty} h(t,u) \, x(u) \, \mathrm{d}u$$ $h(t,u)$ is the (possibly time-variant) impulse response ...

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LTI means Linear Time-Invariant systems. The system has to satisfy two conditions. (1) Linear and (2) Time-Invariant. (1) Linear means, if the response of the system due to load Px and Py is Rx and Ry respectively, then for the load (Px+Py), the response of the system will be (Rx+Ry). (2) Time-Invariant means, the parameters of the system does not vary with ...

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First of all, I wouldn't worry too much about the speaker response since it is relatively flat and the microphone has a much bigger roll-off. Since you've captured the frequency response using sweep, why not to skip the whole part of designing the filter that mimics the frequency response and use the original impulse response? I don't know what kind of ...

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