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There's no need to use numerical methods here. The most straightforward way to compute the output is to see that the filter's impulse response is given by $$h(t)=\sum_{k=1}^Nr_ke^{s_kt}u(t)=\sum_{k=1}^Nh_k(t)\tag{1}$$ where $N$ is the filter order, $u(t)$ is the unit step function, and $r_k$ are the coefficients of the partial fraction expansion of $H(s)$: ...


3

A plot of the normalized impulse responses, for the n = 2 through 10 Butterworth low pass filters, are given by H.J. Blinchikoff, A.I. Zverev, "Filtering in the Time and Frequency Domains", Wiley-Interscience, John Wiley & Sons, NY, ©1976, p. 113. This is shown below. They do not give the h(t) expressions in the book, at least where I have looked thus ...


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Given a complex time-domain signal is it always implied that this is a QAM-demodulated form of a real time domain signal? No, we generally use complex baseband to describe all kinds of signals, or even passband systems (e.g. frequency-selective or time-variant channels). So, any bandlimited signal has an equivalent complex baseband, and it's not implied ...


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My updated answer to OP's update To do this specifically for the case of the FFT of a product of two sinusoids, you must choose a sampling rate or modulation frequency such that the upper sideband of the "positive" frequency component aliases to be on top of the lower sideband of the "negative" frequency component. For instance using a carrier frequency of ...


1

If you want to have a "numerical grasp" and you're not afraid of getting a little bit dirty, you can check the numbers with LTspice. I don't know how well you know to work with it, so I'll just explain it, feel free to ignore all the redundant info. Here you can download the archive, out of which you only need Filter.asy and filter.sub. Create a new ...


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Frequency domain analysis has much broader application (more numerous to list) than just analyzing sinusoidal components of a signal. Frequency domain analysis appears as a mathematical tool whenever the equivalent operations in the time domain can be simplified, and vice versa. For example, convolution in one domain is multiplication in the other which can ...


1

I think you are looking for a "peak" detectors. They are not filters in the conventional sense. Typically the output is increased when the incoming sample is either above a certain threshold or above the current output and decreased if it's smaller. The increase and decrease are often just simple exponential with time constants determined by your application....


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The problem with the filters you want, e.g., 3dB/octave or 1 dB/octave, is that they are not simple filters: they are carefully designed by some very clever people, including at least one person here, e.g., robert bristow-johnson, and the aforementioned JOS III. So it is very helpful to look first at Pink (1/f) pseudo-random noise generation and all the ...


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1) g1 assumes that there is a non-zero mean and that always needs to be subtracted off for the correlation calc to make sense. g2 assumes that the mean is zero. g2 is incorrect if the mean is not zero. 2) the mean is taken over the whole sample because the autocorrelation calc has the underlying assumption that the process is stationary so the mean doesn'...


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These terms refer to the general duality properties of these two domains. It should be obvious that higher frequency components mean faster changes in time and lower rise/fall times. In most natural systems, some of these fundamental properties oppose each other: Shorter rise time means more overshoot and higher settling times and vice versa; lower ...


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In the absence of noise and other distortions in the channel and in the transmission system, the received signal in a passband transmission system has the form $$r(t)=I(t)\cos(2\pi f_ct+\phi)-Q(t)\sin(2\pi f_ct+\phi)\tag{1}$$ where $I(t)$ and $Q(t)$ are the in-phase and quadrature components, respectively. After demodulation you're left with the two ...


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One common use of the IQ data from an SDR is to feed them to an FFT. The upper and lower halves of an FFT result indicated different relationship between the (real) cosine and (imaginary) sine components of the complex FFT result. The direction of rotation of each complex component tells the rest of the signal chain whether the complex component is an upper ...


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I think you can do a dft for a single frequency fine. Just sum over your window of a whole compression and rarefaction multiplied by the sine of the frequency your looking for, then do it for the cosine, then the amplitude is the hypotenuse if they were graphed on xy axis, and the phase is the angle.


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Why not using the tsa in Matlab ?


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