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0
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1answer
897 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
207 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
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4answers
250 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 ...
1
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3answers
4k 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
782 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: ...
10
votes
5answers
4k 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
3k 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
134 views

Kalman gain over one

Short question: Can an element in the Kalman gain vector ever be over one?
5
votes
3answers
600 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
3answers
750 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 ...
3
votes
2answers
2k 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: ...
2
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0answers
123 views

Deriving Isosensitivity Functions in ROC space from elementary signal detection parameters

In signal detection, an observer is assigned the task of discerning the presence (or absence) of some signal with accompanying noise. There are four possible outcomes: a hit ($H$), a miss, a false ...
4
votes
1answer
1k 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
325 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 ...
3
votes
0answers
119 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 ...
1
vote
2answers
105 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
334 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 ...