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

**92**

votes

**14**answers

### 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

- 2,507
- 5
- 21
- 28

**53**

votes

**13**answers

### Real world application of Fourier series

What are some real world applications of Fourier series? Particularly the complex Fourier integrals?

Namit Sinha

- 711
- 1
- 7
- 13

**49**

votes

**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

- 1,204
- 2
- 13
- 20

**35**

votes

**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…

Bitrex

- 2,163
- 3
- 20
- 32

**32**

votes

**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

- 451
- 1
- 4
- 8

**22**

votes

**3**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

- 45,303
- 7
- 151
- 282

**19**

votes

**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

- 191
- 1
- 1
- 4

**17**

votes

**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

- 1,139
- 7
- 20

**13**

votes

**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

- 169
- 1
- 5

**13**

votes

**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

- 2,024
- 2
- 16
- 30

**12**

votes

**12**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

- 173
- 1
- 1
- 7

**12**

votes

**1**answer

### Prove of the Parseval's theorem for Discrete Fourier Transform (DFT)

If $x[k]$ and $X[r] $ are the pair of discrete time Fourier sequences, where $x[k]$ is the discrete time sequence and $X[r]$ is its corresponding DFT. Prove that the energy of the aperiodic sequence $x[k]$ of length $N$ can be expressed in terms of…

Cheung

- 347
- 1
- 4
- 9

**11**

votes

**3**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

- 309
- 1
- 2
- 10

**11**

votes

**2**answers

### Waves of differing frequency are orthogonal - help me understand

I know that sinusoidal waves of different frequencies are orthogonal to each other. For instance:
# Shows that 1Hz and 2Hz waves are orthogonal
import numpy, scipy
x = numpy.linspace(0, 1, 1000)
wave_1hz = scipy.sin(1 * 2*scipy.pi*x)
wave_2hz =…

caleb

- 395
- 1
- 3
- 9

**11**

votes

**2**answers

### Speech processing pre-emphasis: how does it work?

In speech processing, the original signal usually has too much lower frequency energy, and processing the signal to emphasize higher frequency energy is necessary. To perform pre-emphasis, we choose some value α between .9 and 1. Then each value in…

Nate Glenn

- 301
- 2
- 12