Questions on the mathematical aspects of signal processing. Please consider first if your question might be more suitable for http://dsp.stackexchange.com/
0
votes
1answer
170 views
Summability of a sinc function power 'p', where 1<p<2
We know that a sum of the form
$\sum_{n=0}^{\infty} \left|\frac{sin(a\pi n)}{a\pi n}\right|$ where $a$ is not an integer, is unbounded and tends to infinity. But what about the expression
...
0
votes
1answer
487 views
LTI: How to derive the impulse response of this system?
Well, i transform g and x into the frequency domain.
u[n] = 1, n ≥ 0
u[n] = 0, n < 0
\begin{aligned}
x[n] & = u[n] \\
h_1[n] & = (\frac{1}{2})^n u[n] \\
g[n] & = (\frac{1}{2})^n u[n] \\
...
1
vote
1answer
809 views
LTI: How to calculate the step response of this impulse response?
i need to evaluate the convolution sum of x[n] * h[n].
x[n] is the step function u[n].
I know how the output should look like but i don't know how i can calculate it.
I think the lower border is 0, ...
1
vote
1answer
1k views
How to sketch the following discrete time signal?
i need to sketch y[n] where * denotes the convolution operator and delta is the unit impulse.
I know how to sketch x[n-1] and delta[n-2] but i have problems with the convolution.
In my script i only ...
1
vote
1answer
352 views
How can I increase/decrease (frequency/pitch) and phase using fft/ifft
How can I increase/decrease (frequency/pitch) and phase using fft/ifft
I think I have the basic code but I’m not sure what to do next
PS: It's done in Octave/matlab code
Example I have a signal that ...
0
votes
1answer
83 views
Signal processing and SNR
I am working on a problem where we measure some ripple over a huge constant. The problem is from electronics. You can think of as 100V DC always constant and we have a ripple of +/- couple mV over ...
5
votes
2answers
328 views
Which time-frequency coefficients does the Wavelet transform compute?
(I asked this on Stack Overflow a while ago and didn't get a satisfying answer, so I'm trying again here.)
The Fast Fourier Transform takes O(N log N) operations, while the Fast Wavelet Transform ...
0
votes
0answers
78 views
Extracting the power of a frequency range in a signal
I have a heartrate signal which is a few hours long. I need to preform a spectral analysis to get the ratio high frequency (0.15Hz-0.4Hz) to low frequency (0.04Hz - 0.15Hz) changes in heartrate within ...
0
votes
1answer
318 views
Aliasing in DFT: mathematical expression
The Fourier transform of a sinc function is the top hat function. So, if $\{y_k\};\ k\in\{0,1,...,n-1\}$ are samples of the sinc function, sampled $T$ apart, the discrete Fourier transform is
...
3
votes
1answer
61 views
Given a set of 2D points (x,y) (cloud of points), find the points that, when connected, will contain all other points
Given a set of 2D points I have to find the points that when connected will form a polygon that contains all the points in the set.
A quick example: imagine you have a set ...
1
vote
0answers
89 views
What is the difference between various kalman filters?
What is the difference between additive and multiplicative kalman filters, as well as some other kinds?
I'm also looking for reference texts and articles that describe the algorithms, so ...
4
votes
1answer
281 views
Fourier Transforms
I'm having a terrible time trying to understand Fourier transforms. I'm very visual so leaving the $X,Y,Z,t$ domain is not working form me :)
I'm trying to figure out the basics at the moment. ...
0
votes
2answers
3k views
MATLAB interpretation of Xcorr2 - Cross Correlation function
I have two vectors of matching lengths. They are readings from two different sensors (one is from a smartphone and the other is from a wiimote) of the same hand movement. I am trying to find the time ...
1
vote
1answer
727 views
Mathematics of a leading signal for a sine wave
Taken from elsewhere on the web : -
"The derivative of a sine function is
d SIN(ω*t) / dt = ω * COS(ω t)
where ω = angular frequency = 2 π *frequency
and this derivative leads the original function ...
3
votes
4answers
90 views
How much noise will the average of N noisy signals have?
(Inspired by this question on the photography site)
Say you have N copies of the same signal, each with a layer of noise on top. You average these copies together in an attempt to reduce the effect ...
1
vote
2answers
307 views
Barker sequence
Hi I am learning about Barker sequence. I have a problem, because I do not know, why for example 5, in Barker Code looks like this: +++-+. What is the base of this code. I am looking for some ...
0
votes
1answer
557 views
Frequency Swept sine wave — chirp
I am experiencing what I think is really simple confusion.
Take $y(t) = \sin(2 \cdot \pi \cdot t \cdot\omega(t))$
and $\omega(t) = a \cdot t+b$ for $t \in [0,p)$ and let $\omega(t)$ have a periodic ...
2
votes
2answers
168 views
Easy question about finite energy due to convergence
The infinite-length sequence $x_1[n]$ defined by
\begin{multline}
x_1[n]=
\begin{cases}
\dfrac{1}{n}& \text{if $n \geq $1},\
0& \text{if $n \leq $0}.
\end{cases}
\end{multline}
has an energy ...
0
votes
4answers
236 views
What probability distribution is this?
This image show a histogram (200 bins) of accumulated distances from a radar distance meter (very noisy).
The peak around 7 meters is an object. At thought this looked kind of like a normal ...
0
votes
3answers
928 views
How to sketch a sinc function by hand?
I have to do this for an upcoming exam, but cannot find anywhere (in the textbook or online) how to do this.
I only really need to know a couple points to plot it... when x = 0, and then the earliest ...
2
votes
1answer
436 views
Rigorous definition of convolution with the unit doublet
The unit doublet is a symbolic object whose convolution with a differentiable function is supposed to give the derivative:
$$(x * u_1)(t) = \frac{dx(t)}{dt}$$
See also: ...
6
votes
4answers
1k views
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 ...
1
vote
1answer
2k views
Calculating the Savitzky-Golay Coefficients
I am working on a signal-smoothing algorithm for personal interest. I understand the basic concept of the Savitzky-Golay algorithm but I would like to understand how the coefficients were discovered. ...
2
votes
1answer
117 views
5
votes
3answers
314 views
How can I interpret “energy” in signals?
I am learning about various signal processing methods in my university course, and I can't seem to grasp what 'energy' in signals represent. I mean, I know that it is the integral of the absolute ...
1
vote
2answers
511 views
Sensor fusioning in Kalman filter
I'm interested, how is the dual input in a sensor fusioning setup in a Kalman filter modeled?
Say for instance that you have an accelerometer and a gyro and want to present the "horizon level", like ...
2
votes
2answers
1k views
How do I apply a Gaussian Blur (low-pass filter) to an image made up from a set of points?
I have an image encoded in the form of a list of points, like so:
...
3
votes
1answer
924 views
Wiener filter: A good tutorial
I am interested in image analysis and am looking for an approachable tutorial to the Wiener filter. At some point I am interested in implementing such a filter but I would like to have a deeper ...
2
votes
2answers
244 views
Encoding a Discrete Signal to an Artificial Neural Network?
What might be some potential methods to encode a 100-point signal (curve) for input to a Artificial Neural Network?
Example: we have a large number of 100-pt 'curves' ranging from flat-line to ...
2
votes
0answers
90 views
Analysing an optics model in discrete and continuous forms
A discrete one-dimensional model of optical imaging looks like this:
$I(r) = \sum_i e_i P(r - r_i)$
Here, the $e_i$ are point light sources at locations $r_i$ in the object and $P$ is a point spread ...
1
vote
2answers
72 views
Preserving the extrema of one function after applying another
Suppose we have some function $f(x)$ with local extrema at $x_1, x_2, \dots$, and a second function $g(x)$ which is continuous, strictly increasing and non-zero everywhere over the range of the $x_i$. ...
4
votes
2answers
297 views
Simple lowpass frequency response
Okay, so hopefully this isn't too hard or off-topic. Let's say I have a very simple lowpass filter (something that smooths out a signal), and the filter object has a position variable and a cutoff ...
