Questions tagged [math]
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178 questions
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When buffering a wrapper process at one length, and an internal process at another length, what is the logic behind the delay caused?
In an audio (or likely any data transfer context) processing scenario, at times it is necessary for an internal process which takes a fixed amount of data N to be wrapped by an external process which ...
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Efficient Computation of Modified Autocorrelation
How can I determine the array $D$, where $$D[k]=\frac{\displaystyle\sum_{n=0}^{N/2-1} y[n] \cdot y[n+k]}{\sqrt{\left(\displaystyle\sum_{n=0}^{N/2-1} y[n]^2\right) \cdot \left(\displaystyle \sum_{n=k}^{...
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How can I determine the "almost-period" of a sum of sinusoidals?
I have a sum of sinusoids $$g(x)=\sum_{i=1}^N a_i \cos(2\pi \cdot f_i \cdot x).$$ For all $i$, $\frac{f_{i+1}}{f_i}=2^{\frac 1{12}}$ (like with MIDI). Because the ratio between the periods of adjacent ...
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Does weights in Space-Time Adaptive Processing follow any distribution?
Does weights in Space-Time Adaptive Processing follow any distribution? If yes, does the distribution depend of the type of clutter, antenna pattern, grazing angles etc.
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Frequency aliasing mathematical formula in Understanding Digital Signal Processing by Lyons
I am reading through the second chapter of Richard Lyons' "Understanding Digital Signal Processing", and I am at the point where the frequency aliasing is explained.
Now, as regards to what ...
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Does there exist a Nyquist-Shannon sampling theorem between two *discrete* domains? Not continuous to discrete
I'm new to signal processing so this might be a dumb question, but that's good if it is because it would have a simple enough answer. But googling around has not helped me so far.
I found on paper ...
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Explanation math expression to form a cluster
Could someone please explain to me, in simple terms, the mathematical expression from the paper "Ammar, H.A., Adve, R., Shahbazpanahi, S., Boudreau, G., and Srinivas, K.V., 2021. Distributed ...
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Hypergeometric functions in Wireless communication: Seeking guidance for Performance analysis
I am transitioning from pure mathematics to wireless communications and am particularly intrigued by the mathematical challenges in analyzing Nakagami-m fading channels. These channels are widely used ...
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What mathematical space are we using in communication theory?
In just about every communication theory paper I've come across, there is no mention of what mathematical space(s) we are working in. Let's suppose the kind of paper I'm thinking about mentions ...
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Fraction and inverted fraction: a name for it?
(I hope this question is in scope here. I use this function in a DSP related module.)
Is there a name for a calculation that on a call with unsigned integer ...
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Why can Euler's identity be used to express a sinusoid with a single exponential?
I'm unsure how 4.1.5 is used to express the value in 4.1.4... any advice or tips?
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What are the essential mathematical topics required to build a strong foundation for learning Digital Signal Processing (DSP)?
I'm looking for a detailed breakdown of the key areas of mathematics that are fundamental to understanding and mastering DSP concepts. It will be great if anyone can suggest me a good book or a course ...
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Fourier uncertainty principle
When working on DSP of audio signals, I personnaly "experience" the Fourier uncertainty principle in this way:
When doing a STFT / a spectrogram, you have to choose a tradeoff between time-...
- 549
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Showing analytically that sampling exactly 1 period of a sinusoid yields a spectrum with no lobes in the DFT
The DTFT of a discrete sinusoid $f[k] = \sin(\omega_0 k)$ is
$$F(\Omega)=i\pi(\delta[\Omega-\omega_0] + \delta[\Omega+\omega_0]), \: \: \: \Omega \in [-\pi, \pi)$$
The DTFT of a rect function $w[k] = ...
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Complex cross-correlation: conjugate first or second argument?
If I understand correctly the definition of cross-correlation, the complex conjugate is not applied to the same argument depending on whether we're working with deterministic signals or with ...
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