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What's the difference between the Hough and Radon transforms?
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35 votes

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 ...

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What is the difference between Remez exchange and Parks-McClellan filter design?
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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 ...

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What are the advantages, if any, of derivative sampling?
3 votes

That's a very nice article that you linked to (I hadn't read it before), and in fact, the answer that you seek is in that very article in §2.3! I've reproduced below a portion of §2.3 that is relevant....

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Detection of a Circle in Noisy Image Data
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 ...

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Why does my stop-band filter attenuate other frequencies?
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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 ...

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Detecting Arabic verses spanning multiple lines
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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 ...

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Detecting a fixed template image out of a semi-constant frame of video
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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 ...

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Is Ideal LPF BIBO unstable?
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 ...

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Why is $y(n) = x(n) + x(n-1)$ a low pass filter?
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16 votes

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 $...

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How do I detect distinct objects when their edges touch each other?
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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 ...

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Why are there comb-like hills in a periodogram?
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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 ...

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What are the practically relevant differences between various image resampling methods?
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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\...

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What is the most lucid, intuitive explanation for the various FTs - CFT, DFT, DTFT and the Fourier Series?
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 ...

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Is it numerically more stable to implement filtering as multiplication or convolution?
2 votes

Why do you suppose things will be different? The theoretical concepts should translate to practical applications, with the only difference being that of floating point issues, which we can't escape. ...

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Detecting Trail in Forest Images
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 ...

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What is the physical significance of negative frequencies?
46 votes

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 ...

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What should be considered when selecting a windowing function when smoothing a time series?
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28 votes

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., ...

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How can one improve the robustness of adaptive beamformers to signal mismatches?
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 ...

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What is the relation between the PSDs of filter input and output called? $R_Y = |H|^2R_X$
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 ...

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Why is the Fourier transform so important?
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156 votes

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 ...

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Calculating the PDF of a waveform from its samples
5 votes

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 ...

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Can ICA be applied, when the number of mixture signal is less than number of source signal?
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 ...

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What are the advantages, if any, of derivative sampling?
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5 votes

Papoulis introduced a generalization of the sampling theorem [1], of which derivative sampling approach is one case. The gist of the theorem, quoting from [2] is: In 1977, Papoulis introduced a ...

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How do I find a system's impulse response from its state-space repersentation using the state transition matrix?
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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}+\...

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Are there alternatives to the bilinear transform?
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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 ...

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What are the proper pre-processing steps to perform Independent Component Analysis?
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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 ...

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What is meant by "stochastic sampling"?
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32 votes

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 ...

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What are good ways to detect signal clipping in a recording?
20 votes

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 ...

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How do I add AWGN to an I and Q representation of a signal?
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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 ...

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