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1answer
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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, ...
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1answer
2k 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 ...
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1answer
716 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 ...
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1answer
97 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 ...
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2answers
556 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
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1answer
514 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
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1answer
86 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 ...
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0answers
147 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 ...
5
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1answer
459 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. ...
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2answers
4k 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 ...
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1answer
1k 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 ...
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4answers
127 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 ...
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2answers
727 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
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1answer
833 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 ...
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2answers
202 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 ...
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4answers
249 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 ...
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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
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1answer
747 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: ...
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5answers
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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 ...
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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
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1answer
131 views

Kalman gain over one

Short question: Can an element in the Kalman gain vector ever be over one?
5
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3answers
533 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 ...
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3answers
715 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 ...
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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: ...
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0answers
120 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 ...
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1answer
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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
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2answers
304 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
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0answers
116 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 ...
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2answers
103 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
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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 ...