# Questions tagged [math]

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### DFT of pure sinusoidal wave

I'm writing a program in which you can synthesize waves by adding to a sound's Fourier transform, and then inverse the transform to get the modified sound. In order to do this, I need to know what to ...
55 views

### SNR for the magnitude of a complex signal

The SNR for a complex valued signal is presented by Dilip Sarwate in: https://dsp.stackexchange.com/a/42359 Following the same steps I would like to estimate the SNR for the magnitude of a complex ...
29 views

### I don't understand how the zeros are found of this 2nd order feed-forward filter

I realized someone asked a question about the exact same section of a book, which can be found here: Question about zeroes of simple 2nd order FIR filter. While the answer to this question looks ...
66 views

### Coordinate system in digital image processing

I am trying to understand image coordinate system where I read that it is reversed (http://www.ece.northwestern.edu/local-apps/matlabhelp/toolbox/images/intro28.html) SO if f(x,y) is actually f(y,x) ...
48 views

### Summations in Z-Transform

I'm currently working on a problem that involves a Z-Transform. Basically, the essence of the problem is that if: \begin{equation} H\left(z\right) = \sum_{n=0}^{N-1}h\left(n\right)z^{-n} \end{equation}...
40 views

I am writing a synthesizer. One part of the synthesizer specification says that different sources can specify an attenuation to be applied to a signal, and that these attenuations should be summed. ...
53 views

### Fourier Transform of an Exponential Sine Sweep

The Exponential Sine Sweep (ESS), according to Farina , can be described by the following formula: $$x(t)=\sin\left(\frac{2\pi f_1 T}{R}\left(e^{\frac{t R}{T}} -1\right) \right)$$ where, $t$ - ...
71 views

### Problem with natural logarithmic function in fixed point notation

I am facing a problem with natural logarithmic function in fixed-point notation. Let's say $$x = 0.54, \qquad\text{then}\qquad \ln(x) = -0.616186, \qquad\text{a negative number} \tag{1}$$ Then in ...
63 views

### FFT algorithm gives wrong signs on my output numbers

I was told from another stack exchange (stackoverflow and computer science stack exchange) to post here - so hopefully now i can get some help from people who understand the algorithm, but if this is ...
93 views

### Why Cramér spectral representation and not DTFT for stochastic process

In a lot of time-series analysis references I find (written by mathematicians or statisticians rather than engineers), I find the following signal decomposition for a stochastic process, termed the &...
2k views

### What is the first derivative of Dirac delta function?

Could you please help me in a simple way, what is the first derivative of a Dirac delta function? I found this answer: The informal answer is a positive Delta function immediately followed by a ...
37 views

49 views

### Rearranging exp terms

I have some problems rearranging exp terms to receive a cos or sin. I guess the solution is silly but I‘m not able to spot my mistake. I know the solution (since i looked it up with wolfram alpha) ...
29 views

### Equation Derivation: Help with intermediate steps

As per the attached image above, I don't know how the equation in the first line transformed to the form in second line. I tried solving it by multiplication but the result was different.
495 views

### Laplacian of Gaussian Approximation and Gaussian Blur as the Solution of Heat Equation

While I was reading SIFT paper(Lowe, 2004), I came across the method that he apply "heat diffusion equation" to Gaussian function to derive that $$\frac{∂G}{∂σ} = σ∇^2G$$ I searched Wikipedia and ...
86 views

### How to measure the distance between two circle-like-lines over 360 degree

I am looking for a slim and with that quickly programmable image processing strategy to measure the distance between two circles over 360°. It is important to notice that the circles are not perfect, ...
101 views

### How to prove Line Spectral Pair coefficient properties?

I am trying to understand the definition of LSP coefficients from http://www.dspcsp.com/pdf/lsp.pdf. We take the polynomial $a(x)$ of degree $M$ from the denominator of the LPC system function, and ...
67 views

### Explicit a succession using z inverse transform

Is it possible to explicit $y(n)$ of this mathematical succession in recursive form using z inverse transform?: $y(0) = 1 \\ y(n+1) = 2y(n) + 3$ I can't write ...
39 views

### Relationships between $f(t)$ signal and $f(t) \times \sin(\omega t)$ signal

Let's assume that there is a signal $f(t)$, $0\le t \le T$. Then, is there any special meaning of the signal $g(t) =f(t) \times \sin(\omega t)$? Like AM transmission. What is shown/heard when we play ...
272 views

### NMSE of complex numbers

Actually I am doing an RF measurement and this includes phase and power. i generate a list of powers ranging for example from (-50 to 40) dBm, while the phase rotate to make it for example spiral ...
178 views

### MLE parameter estimation — confusion regarding some terms in the pdf of complex normal r.v (Part 2)

This question is based on the application of the pdf which was an earlier question of mine asked here Confusion regarding pdf of circularly symmetric complex gaussian rv If $v \sim CN(0,2\sigma^2_v)$ ...
73 views

### MLE formulation — confusion regarding the terms in the equation (Part1)

If $v \sim CN(0,2\sigma^2_v)$ is a circularly complex Gaussian random variable which acts as the measurement noise in this model $$y_n = x_n + v_n \tag{1}$$ where $x \sim CN(0,2\sigma^2)$, then is ...
70 views

### What kind of math is introduced in this answer related to DSP?

What kind of math is introduced in this answer: https://dsp.stackexchange.com/a/40225/30897 It smells like standard linear algebra course (which I haven't studied, yet), but is it only that? Thanks!
100 views

### How does the assumption that symbols are equi-probable hold

If I draw a number uniformly between zero and one, what is the probability that they are equal? Mathematically, it should be zero but I don't recall why? Can somebody please help in explaining why the ...
Suppose I have a sequence $x[k]$ with $\mathcal{Z}$-transform $$X(z) = x_{0} + x_{1}z^{-1} + x_{2}z^{-2} + \ldots + x_{N-1}z^{N-1}$$ I know that for real-valued $x[k]$ the $\mathcal{Z}$-transform ...
I have a function $y$ defined as $$y(t) = \left\{\begin{array} ~t~ \mbox{ where} |t| \le 3\\ 0~ \mbox{ otherwise} \end{array} \right .$$ With a system defined as $$G(t) = ty(t),$$ is it BIBO ...