Tagged Questions

Questions on the mathematical aspects of signal processing. Please consider first if your question might be more suitable for http://dsp.stackexchange.com/

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Proof of Caratheodory's theorem about the unique determination of a linear combination of sinusoids

Following is a statement of Caratheodory's Theorem about a positivelinear combination of sinusoids :- Any positive linear combination of k sinusoids is uniquely determined by its value at time t =...
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Signal compression

I believe I have an extremely simple question but I can't seem to figure it out. This image shows $x[n]$ and I have to draw $y[n]=x[2n-4]$ by first doing a compression and then a time shift. The ...
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Relationship between DFT and FFT/DTFT

Question 1: Assume we already know $x(t):[0,2\pi]\to\mathbb{R}$'s Fourier series $x[n]_{n=-\infty}^\infty$. Perform DFT on $x[n]_{n=0}^N$. How is the result connected to $x(t)$? WHY? Question 2: ...
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Bases in compressed sensing (signal reconstruction)

I have been posting this kind of question in Cross Validated, but since this one deals almost entirely with mathematics, I will post it here. In signal reconstruction using compressed sensing, we ...
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Given one sine wave in time domain, how to find its frequency?

Given one sine wave in time domain, I want to find its frequency. Because I observe only a very small part of the sine wave ~1 cycle, FFT methods have a poor spectral resolution. Has there been work ...
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How do I compute “AUC” Area under the curve number, if all I have are my TPR and FPR values?

I am trying to rank my neural network, which is trained for binary classification. That is, given a set of input signals, it outputs either a 1 or a 0. I have a training set, where I have the actual ...
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Using FFT in matlab

I am not completely sure if this is where a MatLab question belongs, so if not, please direct me where I should ask. But onto my question. I am working on trying to deconvolution a signal with noise....
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Approximation of Saturation function

"Saturation" or "clipping" function: clip(x)=min(max(x, -1), 1) The context where I encountered this is LTI (linear time-invariant) system analysis (in classic ...
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What are Autoregressive Coefficients?

Can anyone explain what are Autoregressive Coefficients? What is their meaning that is. Consider a method: public double[] calculateARCoefficients(double[] inputseries, int order) When this method ...
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Max frequency of a signal?

Having $$f(x) = \cos(x) + \sin(10x)$$ How Can I know which is the max frequency of this signal? I need it to set the right Nyquist frequency ($2\cdot\max\text{frequency}$) I can use Matlab if it'...
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Sawtooth wave spectrum

Could a good soul help me? I heard that the fourier transform of a periodic signal is a pulse train, but for a sawtooth wave: what is the fundamental frequency of the spectrum? Thanks
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How do I find transfer function of a discrete-time system when its state-space form is given?

I read this and this Wikipedia pages, but both of them are explaining continuous-time systems. My question is about discrete-time case. For example, given the state-space equations of the second ...
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Find peak output value using transfer function

I have a filter with Transfer function $H(z)=(1-0.5z^{-1})(1+0.5z^{-1})$ designed for a sampling rate of 800 samples/s. How to find peak output if a sine of 200Hz and amplitude 4 is applied as input?
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Transfer Function from input to node.

From the IIR filter flow graph below i don't understand how the transfer function is calculated in every node: The circles contains 'X' inside are multiplications. The circles contains 'Σ' inside ...
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