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

# Questions tagged [signal-processing]

1906 questions

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### Find the non null complex Fourier coefficients

I'm doing my homework on signal processing in MatLab and I'm stuck on an exercise.
I'm given this signal $x(t)=1 + 2\sin(12\pi t+\frac{\pi}{4})\cos(21\pi t);$ and I have to get the non null complex Fourier coefficients using this expression…

Favolas

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### Examples of Multiplicative Noise

I understand the main idea behind a multiplicative noise in signal processing, but I'm struggling to see it expressed in a specific example. Could someone help me?
For example, if I have a system of ODEs to which I intend to implement a…

sam wolfe

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### Purpose of the $2 \pi$ in the following equation

I am figuring out how to calculate average power for continuous periodic signals, I have learned what the rest of the equation means however I need some guidance on why the $(t)$ on the LHS is equal to $(2\pi t)$ on the RHS.
There are some holes in…

Aztec warrior

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### How to integrate over spikes in the context of signal processing?

In this question, say I have to integrate from F=3 to F=4, wrt F. We encounter one spike in this range. How are these spike integrals defined and how do I evaluate it?

Ryder Rude

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### LTI: Is my calculation of the frequency response correct?

i am not sure if my computation is correct. Hope someone can have a look at it.
Here is my problem:
\begin{aligned}
H[e^{j\omega}] & = \sum_{m=0}^{\infty} (\frac{1}{2} e^{-j\omega})^n = \frac{1}{1-0.5e^{-j\omega}}\\
H[e^{j\omega}] & =…

madmax

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### What does the phase data of a Fourier transform represent?

I have written some software which can perform additive synthesis given a set of partials; that is, the frequency, phase and amplitude of a set of sinusoids.
The idea is to perform an FFT on some audio data and use additive synthesis to invert the…

Doddy

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### Complex Exponential Sequence (Discrete-time exponentials) factor equalling 1?

I'm reading page 10 of Schaum's ouTlines "Signals and Systems" by Hwei P. HSU, and I don't understand why this factor in the complex exponential sequence equals 1.
Consider the complex exponential sequence with frequency ($\Omega_{0} + 2\pi k$),…

Andres Kiani

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### Find period of signal $y(t)=\sum_{n=-\infty}^{+\infty}{e^{-|6t+n|}}$

There is a continuous time signal
$$y(t)=\sum_{n=-\infty}^{+\infty}{e^{-|6t+n|}}$$
I want to calculate it's period ($T$) however I didn't find any easy way to calculate it. Is there any formula to convert this signal to a periodic signal form? Is it…

Amin

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### nth generalized derivative (of a generalized function: delta function) formula

I'm reading page 8 of Schaum's ouTlines "Signals and Systems" by Hwei P. HSU, and I'm not understanding where this formula for the nth generalized derivative (of a generalized function) comes from:
If $g(t)$ is a generalized function, its $n$th…

Andres Kiani

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### What does applying Z-transform to an equation mean?

I have read the Wikipedia page on Z-transform and came across one section I couldn't manage to understand.
I am now referring to the section called "Linear constant-coefficient difference equation"
Suppose signal $x$ is mapped to signal $y$ via some…

Nathan Sikora

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### Remove general drift from data? (Spectral Analysis)

I am working on separating a song from a moving source. The recordings all have a drift since the sound source itself is moving. This means that the information that I am interested in (the higher frequencies) has a drift with a low frequency. I…

Grilbor

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### Expressing a matrix product of a matrix and a hadamard product as a hadamard product of matrix products

I have a matrix $\mathbf{X}\in\mathbb{C}^{N\times K}$ which undergoes a transform (specifically the ZCA whitening transform) represented by $\mathbf{W}\in\mathbb{C}^{N\times N}$ to form $\mathbf{Y} = \mathbf{W}\mathbf{X}$. Now the issue is that most…

Karn Watcharasupat

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### Find k that satisfies $\cos{(\omega fx)}=\cos{(\omega k x)}$

For which frequency k>f is
$\cos (\omega fx_1)= \cos (\omega kx_1)$
only at point $x_1$.
Like k = 9
$\cos (\omega*1*0.1)= \cos (\omega * 9 * 0.1) \approx 0.809$
I need at general solution.

Hulla

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### The science of pearson product moment correlation coefficient

I need to compare two sound signals for similarity, I took cross-correlation of both the signals and I got a cross-correlation signal, now I intend to use pearson correlation coeff formula to get the coeff out of it, by looking to the below formula…

Firdous

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### Summability of a sinc function power 'p', where 1

We know that a sum of the form
$\sum_{n=0}^{\infty} \left|\frac{sin(a\pi n)}{a\pi n}\right|$ where $a$ is not an integer, is unbounded and tends to infinity. But what about the expression
$\sum_{n=0}^{\infty} \left|\frac{sin(a\pi n)}{a\pi…

Ahmed

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