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

**11**

votes

**1**answer

### Creating intuition about Laplace & Fourier transforms

I've been reading up a bit on control systems theory, and needed to brush up a bit on my Laplace transforms. I know how to transform and invert the transform for pretty much every reasonable function, I don't have any technical issue with that. My…

jpaquim

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votes

**2**answers

### Is the convolution an invertible operation?

I have a signal $f(x,y)$, which is discrete. I convolve this signal with a kernel $h(x,y)$:
$y(x,y) = f(x,y) \star h(x,y)$ (where $\star$ is the convolution operator)
Can I obtain $f(x,y)$ given only $y(x,y)$ and $h(x,y)$ ?
Note: Even though this…

dynamic

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votes

**2**answers

### What is spectral leakage?

Can someone, please, explain in simple words what spectral leakage is?
I am interested in the case where a window is used to reduce the truncation error of a Fourier transform of a finite signal.
Maybe someone can also add a simple example to…

henry

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votes

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### Smooth sawtooth wave $y(x)=\cos(x-\cos(x-\cos(x-\dots)))$

Consider an infinite recursive function
$$y(x)=\cos(x-\cos(x-\cos(x-\dots)))$$
$$y=\cos(x-y)$$
Plotting the function $y(x)$ implicitly we get a smooth sawtooth-like wave:
Was this function studied before? For example, its derivative, Fourier…

Yuriy S

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votes

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### Sampling theorem.

Let us consider
\begin{equation}
\hat{f}(x)=\sum_{n\in \mathbb Z}\left\langle\hat{f},e^{i n x}\right\rangle_{L^2[-\pi,\pi]} e^{i n x} \ \ \ \ \ \ \ \ (1)
\end{equation}
where $\langle g, h\rangle_{L^2[-\pi,\pi]}=\int_{-\pi}^\pi g(x) \overline{h(x)}…

Mark

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**10**

votes

**1**answer

### Connection between SVD and Discrete Fourier Transform for Denoising

Denoising signals (in particular, 2D arrays, such as images) can be done by removing the high frequency components of the discrete Fourier transform (which is related to convolution with a Gaussian kernel) or by removing the smallest singular…

user3658307

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**10**

votes

**2**answers

### Integration of sawtooth, square and triangle wave functions

Context
After a discussion about how to plot the results of a frequency modulation between two signals on Stack Overflow, I understood that I need to find the time-integral of the following wave functions before using them in the general FM formula…

Mark Anderson

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votes

**2**answers

### What are the limitations /shortcomings of Fourier Transform and Fourier Series?

I am fond of Fourier series & Fourier transform.
But every approach has some outcomes and some shortcomings. It's limitations lead to innovation of new approach. So, can anybody explain about
The limitations/ shortcomings of the Fourier…

pandu

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**9**

votes

**0**answers

### Matrix performing local differintegral analysis being its own inverse. Coincidence?

I found a curious matrix
$$T = \begin{bmatrix}1&2&1\\1&0&-1\\1&-2&1\end{bmatrix}$$
This matrix (or actually $\frac 1 2 T$) performs
Local mean value (integral) estimation.
Local derivative estimation by central midpoint distance.
Local second order…

mathreadler

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votes

**1**answer

### Why is the plot of $f(t)=\frac{\partial}{\partial t}\left\{\sin(\sin(\pi t))\right\}$ so similar to a triangle wave?

I was playing around the other day and I found that the function
$$t\to f(t), f(t)=\frac{\partial}{\partial t}\left\{\sin(\sin(\pi t))\right\}$$
seemed to be very close to the triangle wave. Is there some intuitive explanation for this?

mathreadler

- 24,082
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**9**

votes

**2**answers

### Usage of inverse Laplace transform

At my current study level in college, use of inverse Laplace transform is not mentioned well - textbooks say "use tables." So, can anyone show me how to use inverse Lapalce transform? And also proof?
Edit: I am not asking how to use tables to solve…

La Ventana

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**9**

votes

**3**answers

### Removing noise when the signal is not smooth

Suppose we have (an interval of) a time series of measurements:
We assume it can be explained as a "simple" underlying signal overlaid by noise. I'm interested in finding a good algorithm to estimate the value of the simple signal at a given point…

hmakholm left over Monica

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**9**

votes

**2**answers

### Is Fourier series always used for periodic signals and Fourier transform for aperiodic signals only?

I want to ask basic question. In our mathematics classes ,while teaching the Fourier series and transform topic,the professor says that when the signal is periodic ,we should use Fourier series and Fourier transform for aperiodic signals.
My…

sagar

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**9**

votes

**4**answers

### Looking for a Calculus Textbook

I want to start signal processing and I need a book that satisfies my mathematical requirements: I am in the third grade of high school and I don't know any useful thing about limit, differential, ...
Please help me.

reza

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**9**

votes

**2**answers

### compare lines and recognize similar ones

how can I find similar patterns in a line if I got a "template-line"?
In this example, if I got the template (red), how can I find out that there are two occurences in the green one? The lines don't match exactly and the min/max values can be…

swalkner

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