11

Your professor is right, and you're almost right too. The filter is clearly an FIR filter, but because its frequency response can be expressed as a geometric series, a recursive implementation is possible. If you write the transfer function as a rational function you get $$H(z)=2\frac{1-z^{-12}}{1+z^{-2}}\tag{1}$$ which is almost the same as you got, apart ...


3

Here is a potential starting point: it is considered that when a function behaves as a power law ($x(t) \sim t^\alpha, t> 0$), then its magnitude spectrum as well, with $|X(f)| \sim f^{-(1+\alpha)}$. One can see for instance: Computing Fourier transform of power law An Interesting Fourier Transform - 1/f Noise Sketches of a "proof" and ...


3

The integral is the Fourier transform of $g^2(t)$, so an inverse Fourier transform can recover $g^2(t)$. But without any further information you can't recover $g(t)$ from $g^2(t)$. So the problem is not the integral transform but simply the squaring operation.


2

Can I perform FFT on pieces of a very large signal, and then assemble the results to obtain the FFT of the total signal? This is the basis for the FFT algorithm, in that a large DFT can be more efficiently done as 2 DFT's each half the size (and so on and so on until the only thing left is 2 point DFT's). (The efficiency comes about since a DFT requires on ...


1

I post it as the answer, because the text does not fit into a comment format. First, I wonder what is a purpose of computing PSD for the signal acquired with the zero wind speed. You are correct in describing the data acquired when the inverter is turned on: the regular peaks separated by 0.25ms intervals betray the default switching frequency (4kHz) of the ...


1

You can get the sound pressure level from PSD, and the velocity is related to the sound pressure. According to the equation of motion, $$ \rho \frac{\mathrm{d}\vec{v}}{\mathrm{d}t} = -\nabla p \tag{1} $$ where $\rho$ is the density of the medium, $\vec{v}$ is the particle velocity, $\nabla=\frac{\partial}{\partial x}\vec{i}+\frac{\partial}{\partial y}\vec{j}+...


1

Quantifying a difference in the frequency domain can be useful if the information on how your signals differ is better expressed in the Fourier space. If this assertion is valid in your case, hereafter are hints on methodology, and basically the sort of you can find in Shazam to distinguish music from a short listening period. By the way, I think that I have ...


1

Below, the result of a simulation where I have the sum of two sine-waves with frequencies 100 Hz and 201 Hz, respectively: $$ x(t) = > \sin(2 \pi 100 t) + \sin(2 \pi 201 t) $$ The signal is periodic (with a period equal to 1 s) but it does not contain harmonics Yes it does. It is a 1 Hz periodic signal that only contains the 100th and 201st harmonics.


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