# 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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### Analysing the modes of a signal with Laplace transform

If I have a linear dynamical system (assume continuous time for the time being) I can create the transfer function, let's say: $$\frac{1}{(s+a_1)(s+a_2)}$$ and the pole-zero map (this one is for e.g. ...
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### Using 2D Parseval-Plancheler theorem to solve an equation

In the context of a digital communications problem I have to solve the following equation with respect to $\tilde{\tau}$: \begin{eqnarray*} &&Im\Big\{\Big(\int\limits_0^{T_0}r^{*}(t)g(t-\tilde{...
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### Quality of a signal (cascaded)

This question extends my previous one Quality of a signal to the case of two cascaded signals. We have a signal x(t) that is transformed (T1) into v(t) that is transformed (T2) into y(t). We want to ...
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### Quality of a signal

Let's consider a signal y(t) that is an output of a linear transformation with the addition of noise. $$y ( t ) = Ax ( t − \theta) + m ( t )$$ The hypothesis on the signals x(t), y(t) is that they ...
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### FFT butterfly diagram

I got confused in the FFT butterfly diagram. Can someone please help me understand it? If I have the vector $x = (-3, -2, -1, 0, 1, 2, 3, 4)$, and I want to apply FFT to it using the Butterfly ...
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### DFT of a sequence while ignoring some of its elements

I sample a signal at a certain frequency for a finite amount of time to get a sequence $$(x_n)_{n=1}^N = (x_1, x_2, ... , x_N)$$ with the intention of analyzing its power spectral density by ...
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### Unknown normalization

I am trying to do BPP imaging and have been trying to replicate the algorithm in "Photoplethysmographic imaging of high spatial resolution" however I've ran into a problem. They say they normalize ...
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### Negative autocorrelation values

Autocorrelation is informally defined (Wikipedia article) as "the similarity between observations as a function of the time lag between them". I create the following time series in MATLAB: ...
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### Estimate original matrix from matrix multiplication result

Let $A$ be $m \times n$ real matrix. Let $B$ be $n \times k$ real matrix. Let $C= A \times B$ ($m \times k$ matrix). Now, the question is: given $C$ and $A$, give an estimate for $B$. Possible ...
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### Calculation of an FIR filter in Matlab.

I have been researching FIR filter design with regard to my signal processing assignment and am having a lot of difficulty trying to understand how the frequency response and ultimately the magnitude ...
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### Conceptual Question : Relationship between entropy and a technique for source coding

I want to encode the messages to a sequence of 1s and 0s (subsequently called "bits"). This is called "source coding". Shannon's source coding theory states that the entropy of a source that emits a ...
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### Convert floating point number to short int [closed]

This is the transfer function of a FIR filter $$H(z) = -0.125 + 0.25z - 0.125z^2$$ How to convert the coefficients to short int? Is it correct if I just multiply ...