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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### How to use polynomial to describe this?

I hava a stupid question. I would like to use a 7$^{th}$ order Polynomial to describe this figure. But if I use the matlab function $polyfit(x,y,7)$, Runge's phenomenon will come up. Currently I have no idea to solve that, anybody has good idea…

Yunhua Hu

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### Can we extract the signal back after convolution with orthogonal code?

Assume we have a random signal $h$ convoluted with another signal $s$ which is assumed to be Walsh code represented by one column of Hadamard-matrix, i.e.,
$$s = \begin{bmatrix} 1\\ -1\\ -1\\ 1\end{bmatrix}$$
which means that all code of Walsh are…

New_student

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### Is this linear algebra?

For noiseless data, we can define two $(N-L)\times L$ matrices, $Y_1$ and $Y_2$, defined by
\begin{align}
[Y_2] &= \begin{bmatrix}
x(1) & x(2) &\cdots& x(L)\\
x(2) & x(3) &\cdots& x(L+1)\\
\vdots & \vdots & \vdots & \vdots\\
x(N-L-1)&…

Mark Fisher

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### Convolution of rectangular pulse with sinusoid

I have the following convolution
$$ 3 \mbox{rect} \left(\frac{t}{10}\right) \circledast \frac{1}{2}[ \delta(t - 20) + \delta(t+20)] $$
How can I compute it?

Jafar Eldeni

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### Spectrum of a sinusoid multiplied by the cardinal sine

I think it'd be easier to understand if i gave an example; let's say we have this function:
$$\cos(200 \pi t) \cdot \mbox{sinc} (5t)$$
What would the correct procedure to calculate the spectrum of the signal be?
Usually if it were a simpler function…

Jafar Eldeni

- 53
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### 2-D Dirac Delta Function of Functions

I need to calculate the Radon transform of $f(x,y)=cos(2\pi y)$ using the projection-slice theorem.
After doing the 2-D polar Fourier transform, I get two 2-D delta functions which then need to go through a 1-D inverse Fourier transform. Those…

TinyRick

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### Can someone explain this sinc function equation?

$ \frac{A}{2}(e^{jω\frac{T}{2}}-e^{-jω\frac{T}{2}})+\frac{A}{2}sinc(\frac{ωT}{4π})(e^{jω\frac{T}{4}}-e^{-jω\frac{T}{4}})=Ajsinc(\frac{ωT}{2π})+Ajsinc^2(\frac{ωT}{4π})$

ripmsn

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### Extract trajectory from recurrence plot

Let's say I have a time series in a vector $v$, and I compute its recurrence(-like) plot $R(i,j)=\left \| v(i)-v(j) \right \|$.
Is there any standard way of extracting $v$ knowing only $R(i,j)$ ??
See wikipedia page…

user655870

- 159
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### Fourier Transform of $y(t)=x(t-c)\sum_{n=-\infty}^{\infty}\delta(t-nT)$

I struggle to understand the solution of an exercise and would be grateful for your help.
We have the following signal :
$$y(t)=x(t-c)\sum_{n=-\infty}^{\infty}\delta(t-nT)$$
The Fourier Transform of $x(t-c)$ is $$e^{-2\pi i f c} \hat{x}(f)$$
The…

Ryukyu

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### Fourier coefficients of $1-|t|$ with $t \in [-1,1]$

I'm asked to find the fourier coefficients $c_k$ of the following signal:
What I did:
(For simplicity, let $ a := \pi i k$. And obviously, the period $T=2$)
$$c_k= \frac{1}{T}\int_{0}^{T}x(t)e^{-2 \pi i k t/T}=\frac{1}{2}\int_{-1}^{0}(1+t)e^{-2…

Ryukyu

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### Solving integral of rectangular function

I am learning how to calculate convolution of basic signals, such as rectangular ones. Specifically, the definition of such a signal is:
$$
\operatorname{rect}_T (t)=
\begin{cases}
1 & |t|\leq \frac{T}{2} \\
0 &…

user929304

- 1,354
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### Convolution of non-periodic function with another function

We're given a signal $X_a(t)=X_b(t)*[4\cdot \text{sinc}(4t)]$, with $X_b(t)$ being a non-periodic function.
We have to find the periodicity of $X_a(t)$, and the period if it's periodic.
Are there any properties for non-periodic functions that can be…

sdds

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### Checking the periodicity of a signal

We're given this signal:
$X_a(t) = x(t)\cdot rect(\frac{t}{100})$, where $x(t) = cos(3t)$
And we have to check if it's periodic or not, and find the period if it is.
Now, for $cos(3t)$, the period $T_A$ is $\frac{2π}{ω_1} = \frac{2π}{3}$.
For…

sdds

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### eigen functions of finite filters

In the context of DSP (Digital Signal Processing) denote
$$H=\{h|h:\mathbb Z \rightarrow \mathbb C\}$$
as the set of filters. one can prove that the functions $$\omega\in\mathbb R:e^{i\omega x}\in H$$
are eigen functions of every filter (that keeps…

Nathan Sikora

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### Confused about region of convergence in $z$ transform.

If $X_1(z)=\dfrac{z}{z-2}$ and $X_2(z)=\dfrac{z}{z+2},$
then what will be the difference between ROCs of $X_1$ and $X_2?$

engr

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