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Questions tagged [signal-processing]

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

2139 questions
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What's the difference between $\mathbb{R}^2$ and the complex plane?

I haven't taken any complex analysis course yet, but now I have this question that relates to it. Let's have a look at a very simple example. Suppose $x,y$ and $z$ are the Cartesian coordinates and we have a function $z=f(x,y)=\cos(x)+\sin(y)$.…
Cancan
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3 answers

An explanation of the Kalman filter

In the past 3 months, I've been trying to understand the Kalman filter. I have tried to implement it, I have watched YouTube tutorials, and I have read some papers about it and its operation (update, predicate, etc.). However, I still am unable to…
xsari3x
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3 answers

How do I exactly project a vector onto a subspace?

I am trying to understand how - exactly - I go about projecting a vector onto a subspace. Now, I know enough about linear algebra to know about projections, dot products, spans, etc etc, so I am not sure if I am reading too much into this, or if…
Spacey
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54
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Real world application of Fourier series

What are some real world applications of Fourier series? Particularly the complex Fourier integrals?
Namit Sinha
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39
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10 answers

Rapid approximation of $\tanh(x)$

This is kind of a signal processing/programming/mathematics crossover question. At the moment it seems more math-related to me, but if the moderators feel it belongs elsewhere please feel free to migrate it. I'm working on a project where I have…
MattyZ
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36
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2 answers

Correct way to calculate numeric derivative in discrete time?

Given a set of discrete measurements in time $x_t, t \in \{0,\Delta t, 2\Delta t,\ldots,T-\Delta t,T\}$, what is the correct way to compute the discrete derivative $\dot x_t$. Is it more correct to take the difference with the previous value: $$\dot…
CodeFusionMobile
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23
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4 answers

Fourier transform of $\left|\frac{\sin x}{x}\right|$

Is there a closed form (possibly, using known special functions) for the Fourier transform of the function $f(x)=\left|\frac{\sin x}{x}\right|$? $\hspace{.7in}$ I tried to find one using Mathematica, but it ran for several hours without producing…
Vladimir Reshetnikov
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21
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3 answers

What does the Fourier Transform mean in the context of images?

This is clearly a very important equation with tonnes of properties that I see come up a lot in image processing literature, but I don't understand why this equation is important, and what it is saying. What does it really mean and why is the…
water
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2 answers

What is the sum over a shifted sinc function?

What is the sum of a shifted sinc function: $$g(y) \equiv \sum_{n=-\infty}^\infty \frac{\sin(\pi(n - y))}{\pi(n-y)} \, ?$$
DanielSank
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19
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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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13 answers

Adjustable Sigmoid Curve (S-Curve) from $(0,0)$ to $ (1,1)$

I feel like this is such a simple question but I am at such a loss. I currently have a set of values that I would like to weigh by an S Curve. My data ranges from $0$ to $1$ and never leaves those bounds, but nearly every version of a Sigmoid I see…
pure_bordem
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16
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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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14
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2 answers

Is there a way to relate prime numbers and the Fourier transform?

According to what I know about Fourier transforms, any continuous periodic signal can be represented as a combination of sine and cosine functions. To me, this looks analogous to the fundamental theorem of arithmetic (every integer $\ge 2$ can be…
user63152
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5 answers

Extracting exact frequencies from FFT output

Say I pass 512 samples into my FFT My microphone spits out data at 10KHz, so this represents 1/20s. (So the lowest frequency FFT would pick up would be 40Hz). The FFT will return an array of 512 frequency bins - bin 0: [0 - 40Hz) - bin 1: [40 -…
P i
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12
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2 answers

The definition of NMSE (normalized mean square error)

Many papers use the NMSE function without ever explicitly defining it. I have always assumed that $$MSE(x,y)=\frac 1N \sum_i (x_i-y_i)^2$$ and $$ NMSE(x,y)=MSE(x,y)/MSE(x,0) = \frac{\| x-y\|_2^2}{\| x\|_2^2}$$ where $y$ is the approximation to $x$.…
Gummi F
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