This is quite a broad question and it indeed is quite hard to pinpoint why exactly Fourier transforms are important in signal processing. The simplest, hand waving answer one can provide is that it is ...

Let's say you had a spinning wheel. How would you describe how fast it is spinning? You'd probably say it's spinning at X revolutions per minute (rpm). Now how do you convey in what direction it's ...

The Hough transform and the Radon transform are indeed very similar to each other and their relation can be loosely defined as the former being a discretized form of the latter. The Radon transform ...

Stochastic sampling doesn't have anything to do with sampling stochastic waveforms. It simply means that instead of sampling at regular intervals, the waveform is sampled randomly. Recall that in a ...

The two primary factors that describe a window function are: Width of the main lobe (i.e., at what frequency bin is the power half that of the maximum response) Attenuation of the side lobes (i.e., ...

The simplest answer if you're dealing with short recordings is to listen to it and detect "pops" (short spiked sound) in the playback. However, a more robust solution is to analyze the frequency ...

What you have here is the equivalent of a moving-average filter. Specifically, it is a filter of order 1, whose impuse response is $$h(n)=\delta(n)+\delta(n-1)$$ Taking its $Z$-transform, we get $... View answer Accepted answer 16 votes Analog filters are stable if the poles are in the left half of the s-plane (figure on the left) and digital filters are stable if the poles are inside the unit circle (figure on the right). So ... View answer Accepted answer 15 votes Independent component analysis (ICA) is used to separate a linear mixture of statistically independent and most importantly, non-Gaussian† components into its constituents. The standard model for a ... View answer Accepted answer 15 votes Yes, you can add AWGN of variance$\sigma^2$separately to each of the two terms, because the sum of two Gaussians is also a Gaussian and their variances add up. This will have the same effect as ... View answer Accepted answer 14 votes Given an image$I(m,n)$with$m,n$integers, the interpolation of that image at any arbitrary point$m',n'$can be written as $$\tilde{I}(m',n')=\sum_{m=\left\lfloor m'\right\rfloor-w+1}^{\left\... View answer Accepted answer 12 votes Filters always have an inherent "roll-off" in their frequency response, because you can't practically realize a pass-band that's a perfect rectangular function. For a low-pass filter, the point where ... View answer Accepted answer 12 votes Detecting different components: If you're trying to detect the different components, there probably are other approaches to do them than detecting the contours. Here's an example in Mathematica. An ... View answer 12 votes There's no single algorithm that will magically detect trails in a random image. You will need to implement a machine learning based routine and "train" it to detect trails. Without going into too ... View answer Accepted answer 10 votes The Remez exchange algorithm is a generic iterative procedure to approximate any function optimally in the L^\infty sense (i.e., give the best worst-case approximation or in other words, minimize ... View answer 10 votes It's fairly straightforward to do it using image processing. The following is a proof of concept in Mathematica. You'll have to translate it to MATLAB. First, trim the axes and keep only the image ... View answer Accepted answer 9 votes This can be solved fairly straightforwardly with simple template matching. I don't know exactly how you have it set up, so I'll just describe the algorithm generally and use illustrations. Observe ... View answer Accepted answer 9 votes If the "VS" is pretty much the same (save for some badge overlays as in the second example), you can use straightforward cross-correlation to detect the presence of the template in your video frame. I ... View answer 7 votes One approach that I'm aware of is to "load" the diagonal of \widehat{\mathbf{R}} by some value \sigma_d^2 in order to stabilize the covariance matrix and make the adaptive vectors more robust to ... View answer Accepted answer 7 votes You can approach the problem using the state transition matrix by solving the standard non-homogeneous ODE in the first equation. The solution to \dot{x}(t)=A x(t) + B u(t) is$$x(t)=x_0 e^{At}+\... View answer 6 votes Endolith is correct in that, if you actually start with the Fourier series, and see how it is extended to the Fourier transform, then things start beginning to make a lot of sense. I give a brief ... View answer 6 votes The relation that you have results from the Wiener-Khinchin theorem (WK). The WK theorem primarily relates the autocorrelation of the input and its power spectral density (PSD) as a Fourier transform ... View answer 6 votes You are making a wrong assumption on the process. In ICA, the number of mixtures must be at least as many as the number of components. The paper you cite does in fact, acknowledge this: These ... View answer 5 votes A necessary condition for BIBO stability is the existence of the$L^1$norm (or$\ell^1$norm for discrete systems) of the impulse response. From the wiki article you cited, For a continuous time ... View answer Accepted answer 5 votes I'm not entirely satisfied by Itamar Katz's answer, so here's my explanation. The DFT of an$N$length complex signal,$x[n]=e^{\imath 2\pi f n/N}$is$\$X[k]=\mathcal{F}\{x[n]\}=\frac{e^{\imath 2\pi ...

While your approach is theoretically correct (and needs to be slightly modified for non-monotonic functions), it is extremely hard to calculate the inverse of a generic function. As you say you'll ...

Papoulis introduced a generalization of the sampling theorem , of which derivative sampling approach is one case. The gist of the theorem, quoting from  is: In 1977, Papoulis introduced a ...