# Tagged Questions

**1**

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**0**answers

86 views

### Relationship between Fourier series & DFT

Sources like http://www.dsprelated.com/dspbooks/mdft/Relation_DFT_Fourier_Series.html explain the equivalence between FS and DFT.
However, isn't there a flaw? When I integrate over the continuous ...

**1**

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**1**answer

185 views

### Bandwidth approximation for a nonlinear problem

Can anyone please help me with this problem.
I must let you know from the beginning that it's not an easy one.
"Two functions are given: $u, y \in L^{2}(-\infty,\infty), y(t)=\frac{u(t)}{u(t)+b}$ ,
...

**2**

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**2**answers

350 views

### Understanding Discrete Cosine Transformation

I'm currently working on some software and a key component is 2D DCT. But my question is more general, as I'm trying to understand the DCT in general, let's say from engineers point of view.
For ...

**51**

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**4**answers

2k views

### How Does My Radio Work?

Bear with me for a moment while I invoke the real world; the main question at the end is purely mathematical.
I live in an area with $n$ AM radio stations and $m$ FM radio stations.
AM station ...

**1**

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**0**answers

271 views

### Generalized fourier transform and convolution?

Let $a(t)$ and $b(t)$ be two equal length sequences indexed by time index $t$.
We know that $a(t) * b(t)$ corresponds to $A(\omega) \odot B(\omega)$ in the frequency domain where $A(\omega)$ and ...

**3**

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**1**answer

162 views

### Levelset of band limited function

In a practical application problem I encountered such a question: Given a subset of a N*N Cartesian grid, how to determine if it is a sublevel-set of a band-limited (discrete) function? Here ...

**2**

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**1**answer

1k views

### Complete formulas book for Communication System engineer

I'm looking for a formulas book.
I'm currently student in Communication Systems and we have several courses involving mainly complex analysis, fourier analysis, signal processing, information theory ...

**4**

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**5**answers

530 views

### What is a rigorous statement for “linear time-invariant systems can be represented as convolutions”?

In Signal Processing books, a fundamental theorem is that linear time invariant systems can be represented as a convolution with a distribution. Could you give a mathematically rigorous statement of ...

**3**

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**4**answers

812 views

### Decomposing a 1-d signal into arbitary basis functions

Hi all,
The short-time fourier transform decomposes a signal window into a sin/cosine series.
How would one approximate a signal in the same way, but using a set of arbitrary basis functions instead ...