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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)}... 3 It is very strange phenomena that one object is completely dropped out of attention of researchers. It is Urysohn operator. First of all Urysohn is equivalent to multiple parallel Hammersteins and Urysohn followed by static nonlinearity is a model of any deterministic dynamic object, it maps any given input to any provided output. I obtained Ph.D. in ... 3 I think the jitter to SNR formula is based on a gaussian jitter. You use "rand" which yields uniformly distributed numbers. You should use randn() instead which yields numbers distributed according to a gaussian distribution. 2 Not sure to understand what you are asking, Microwaves wavelengths range between 300 MHz (1 m) and 300 GHz (1 mm) which is indeed of the same order of magnitude as the probe. 1GHz corresponds to a wavelengths of about 30 cm and is also in the Microwave range. Are you saying that it is possible to measure a frequency of 1GHz with a probe while it is ... 2 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 ... 2 The easiest is Urysohn adaptive filter: http://www.ezcodesample.com/UAF/UAF.html It can build nonlinear model by few lines of code. The theoretical details can be found here http://www.ezcodesample.com/NAF/index.html The site has downloadable coding sample. Besides UAF, the other common methods are: Kernel LMS, Voltera LMS, Neural networks, Point cloud. ... 2 Obviously, you might need to use the given frequency somehow to solve the problem. Guessing alone will usually not suffice. Since this is a homework type problem, and since you still need to learn a lot of basics, I'll give you a few hints to get you started. First, the frequency domain behavior can be obtained from a (stable) transfer function by ... 2 What you are trying to archive is very hard if at all possible. The pinnacle of research today (including my own) is striving for good results on such tasks. DCASE challanges engage with similar tasks with some interesting results, though the make assumption which cannot be generalized to your case. In DCASE2019 task 3, for example, they assume up to 2 ... 2 Zero padding does not increase the frequency resolution— it just interpolates more samples in frequency but does not give you any more information. The frequency resolution in Hz of an non-windowed (rectangular window) Fourier Transform is 1/T where T is the length of your time domain waveform in seconds. You must have a longer data sample in order to get ... 1 Zero pad your FFT (append zeros) such that you get more samples of the Discrete Time Fourier Transform (DTFT). The DTFT would give you the sidelobes and roll-off that you want to see (specifically for your diagram you would zero pad an input that is all ones, or an input that is any constant value). 1 So, you have numerically solved a second order differential equation and plotted its result. Now it seems to be a damped sinusoidal response of the type $$y(t) = K e^{-\alpha t} \cos(\omega_0 t + \phi)$$ for some constants$\alpha$,$\omega_0$and$K$. And you want to compute the damping parameter$\alpha$. A crude approximation to$\alpha$can be ... 1 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 ...