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For an example analysis, I’ve picked up the low-shelf filter in Robert Bristow-Johnson’s Audio EQ Cookbook. In the book, the transfer function is given as; $$H(s) = A\frac{s^2 + \frac{\sqrt{A}}{Q}s + A}{As^2 + \frac{\sqrt{A}}{Q}s + 1}$$ Since the analysis is going to be done by hand, the asymptotic approximation method of Bode plot analysis can be followed. ...


3

The resonant frequency is related to the "significant frequency" (which is the shelf midpoint frequency) by a factor of $\frac{1}{\sqrt{A}}$ for the lowShelf and the reciprocal of that for the highShelf.


3

You are looking at harmonics of the fundamental. There's a lot of literature available to read on the topic.


3

I think the word/phrase you are looking for is "discontinuity" / "discontinuity in the source signal". Although a jump is always a discontinuity, a discontinuity is not always a jump. When it isn't a jump, it is known as a pluggable discontinuity, i.e. you can define a value to plug a hole. The sinc function at zero is an example of this. So to be more ...


3

It is the time of maximum constructive interference of the derivatives of the harmonics. That's a physics term, but widely known.


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Phasor Alignment : The individual frequency component phasors of the square wave are aligning, but I don't think this is a well-defined (or previously-defined) term.


2

You have designed a bandpass filter, i.e. it does not allow any frequency far way from the resonance to pass. As far as I understand, you want a filter, that does not change the signal in the stopband, but has a resonance at some frequency. So, you actually want a parallel connection of your bandpass filter and an allpass filter. In Z-Domain, let the ...


2

Assuming that you are not changing the phase too much, you are basically turning sinusoids to narrow-band noise. If there is a room frequency response node that strongly attenuates a sinusoid, the total power of narrow-band noise centered at the same frequency will not be attenuated as much. It will survive with a dip in its spectrum. Room modes or frequency ...


2

I can help with some of your multiple questions. First, a cascade of n buffered RC low pass filters (LPFs), a so-called n-th order synchronous LPF, has the impulse response and step response shown in the screenshot below: This is a screenshot from my paper 1 referenced at the bottom. All R values are the same and all C values are the same. Buffering simply ...


2

The question is not very specific so this will also be just a general answer. The stability of a composite linear-time-invariant (LTI) system composed of smaller LTI systems cannot be deduced from the stability of the component systems if the composition introduces feedback. Instead, you should test the stability of the full composite system. The system is ...


1

You seem to have 3 problems 1 - You have a phase wrap. It happens when the phase goes past 180 degrees. The phase will wrap back to -180 degrees. You can fix this by unwrapping the phase. 2 - Your phase is in normalized radians instead of being in radians or degrees. This is not a problem per se but when you try to unwrap the phase, you should be aware that ...


1

The question is, if we are given a range of resonant frequencies (the "dangerous" range around the resonant frequency), can we decide whether "the window would break", so to speak, based on the DFT alone, without a physics model (and therefore regardless of the problem, i.e. a window, a vibrating wire, etc.)? No. There is a whole lot of ...


1

Is it possible for a neural network to 'detect'/'pick out' these frequency values? Yes, that sounds generally possible. There's the Universal Approximation Theorem that says that a sufficiently large Neural network¹ can approximate any continuous function on anything isomorphic to $\mathbb R^N$ (and your FFT output is that), including things like map this ...


1

This may be a better question for https://physics.stackexchange.com/ but I'll give it a shot. I assume you show the FFT of the time waveform at the sensor. In order to get the actual frequency response you would need to divide by the FFT of the hammer response. Since the hammer is reasonably smooth, we can eyeball this. It also looks like your measurement ...


1

First of all, like Cal-linux mention in their comment, I would strongly suggest intermodulation distortion for the frequencies that are not multiple integers of the fundamental. Now, regarding the sweep tone artefacts. Since you are talking about high frequencies we are talking about a high-frequency driver. Nowadays, most high-frequency drivers are domes ...


1

For lowpass and highpass filters, Q factor is not well defined. What is defined is the cutoff frequency and bandwidth. Q factor is useful for bandpass or bandstop (notch) filters as it shows the selectivity of the BPS. Quantitatively Qf is the ratio of the center frequency of the pass-band to the bandwidth of the pass-band. Assuming the system has only a ...


1

Given the formula for second order sections: $$ s_k = \omega_c e^{\frac{j(2k+n-1)\pi}{2n}}\qquad k = 1,2,3,\ldots, n \qquad s = i\omega $$ $$ H(s)=\frac{G_0}{\prod_{k=1}^n (s-s_k)/\omega_c} $$ Use k = 1 for the resonance section, add $Q$ in the normal way i.e. calculate $H_{k=1}^2 = H_{k=1}(s) \overline{H_{k=1}(s)}$ where $s = i\omega$ and the denominator ...


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