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You are really close! Change your signal and steering vectors to be complex. Specifically for the steering vectors, these coefficients are meant to act as phase shifts. Using a real sinusoid will introduce a phase shift term in the opposite angle direction, which you don't want. Doing this alone you will see an improvement in your pseudospectrum. In regards ...


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You're almost there; you just need to connect a few dots. Let your $\frac{10}{5 + i 2 \pi f} = G(f)$. Then $g(t) = 10 u(t) e^{-5 t}$. Now we get into that exponent part. Your $h(t) = g(t - t_0)$ is correct, but you're applying it incorrectly. You need to apply it to the part that I've labeled as $g(t)$: $h(t) = g(t - t_0) = 10 u(t - t_0) e^{-5 (t - t_0)}...


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The principal idea behind my recommended approach is to identify characteristic points in your cycle. You can then make a mapping from time within the cycle (as it is occuring) and the location of that point within your representative cycle. Once you have a set of mapping points, create a best fit function. This will then give you a mapping function of ...


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You may be able to use a modified transform to compute change in a time stretch parameter (I will use $\zeta$) versus time (t). Your success in being able to do this depends on the cross correlation properties of your pattern with time stretched versions of itself. Let me explain: First notice that the Fourier Transform is a correlation over all possible ...


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Hello check this source To begin with, let’s remember what the fundamental frequency is and in what tasks it may be needed. The fundamental frequency, which is also referred to as F0, is the vibration frequency of the ligaments when pronouncing voiced sounds. When pronouncing unvoiced sounds, for example, by whispering or uttering hissing and ...


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Wifi uses OFDM, which uses symbols that can transport many bytes at once. That means you can't have arbitrary long packets, but always need to use the next multiple of a symbol duration.


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A more general expression states that for $ M \geq N$: $$ \sum_{n= N}^{n = M} c = (M-N+1) \cdot c $$ where the derivation simply relies on fact that the epxression has (M-N+1) terms : $$ \sum_{n= N}^{n = M} c = \{ c + c + ... + c\} = (M-N+1) \cdot c $$ And when applied for your particular case (with $N = -M$) it becomes: $$ \sum_{n= -M}^{n = M} c = (M-(-...


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For instance, from $-3$ to $3$, you have $-3,\,-2\,-1,\,0\,1,\,2,\,3$, hence $2\times 3+1$ terms. More generally, the sum from $-M$ to $M$ is composed of $2M+1$ terms: indices with $m$ strictly negative (a total of $M$), those which $m$ strictly positive (a total of $M$), plus one at zero ($1$). If all terms are the same constant $c$, the total is $(2M+...


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From what I can glance : The chattering seems to be high-frequency compared to your signal of interest, it should not be hard to filter this chattering noise. You simply need to identify the frequency band of your signal and the frequency band of this noise. Could your perform an FFT to analyze the frequencies of your noise? Then design a filter that will ...


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Looking at documents like Lecture notes on Distributions, Hasse Carlsson, or Convolution dans l'espace $\mathcal{D}'_+(\mathbb{R})$, convolution of distributions can be defined under some technical conditions. However, when one of the operand has a compact support, as $\delta(t)$ does, the convolution is well-defined. From Wikipedia:Distribution-Convolution:...


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Well, by definition of the $\delta$ distribution, you have: $\int_{-\infty}^{\infty} f(t) \delta(t-T)\, \textrm{d}t = f(T)$ The autocorrelation of a function $g(t)$ can be computed via: $\int_{-\infty}^{\infty} g^{*}(t)g(t + \tau)\, \textrm{d}t$, with $g^*$ as the complex conjugate of $g$. Since $\delta(t)$ is real-valued, this is conjugation can be ...


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