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I'm trying to calculate symbol error probability of variant of pulse position modulation considering only AWGN channel. The decoder is maximum likelihood so the implementation of the detector is by using vector correlators. $$ \arg \max_{x} <y,x>. $$ Attached is the waveforms vector representation of the transceiver & ...
I have data that is sampled at 12 kHz. The downsample function in software such as MATLAB only allow you to downsample by an integer factor, i.e. from $12\to{6,4,3,2,1,\ldots}$ kHz. How would I downsample by a non-integer factor, say, from $12\to{10,9,8,7,5,...}$ kHz (pseudocode/description is fine)? You can assume tha...
I found a very interesting piece of code for MDFT polyphase filter bank here. Unfortunately, there doesn't seem to be a paper describing the theory. Does anyone know some reference for the code? I'm especially interested in these 3 topics: What are the data in the channels exactly? Are they supposed to be real, imagin...
Hey guys so I have an input sequence that are real values that represent intensity of a column of an image. I also have the transfer function in the Z domain of a 2nd order high pass filter. I have the following transfer function using the bi-linear transform estimate. Say my input signal is defined as x[n] = 27, 588,...
Question Considering that $1\over{2\pi}$ is the frequency of $\cos x$ and also of $\cos x - 2\cos 2x$, what is the frequency of $\cos x - \sqrt 2\cos\sqrt 2 x$? Thoughts Perhaps "frequency" isn't the interesting quantity. I think the period is infinite. That would make the frequency zero. Maybe what I want to know is b...
What are the formulas for signal and noise power gain of digital filters (FIR and IIR)? For a FIR, I've seen in Harris' windowing paper that the DC gain is the sum of the filter weights. $$ G = \sum_{i=0}^{N-1} w_i $$ For a FIR, I've seen that the noise gain is the square root of the sum of the square of the weights. ...
How does one choose the proper windowing function to apply in an FFT? What are the benefits of larger sizes and smaller ones? Which would be the best for pitch estimation? Also which window function would be best for pitch estimation?
Does anybody know if natural waterfalls generate pink noise or brownian noise? I have tried to search about this but the matches are non-scientific and contradictory. For example Livescience.com mention Brownian noise to resemble big waterfall. Soundonsound.com magazine says Pink noise to occur in nature, e.g. waterfa...
I've been reading about Super Resolution Image reconstruction (Reconstruction of high resolution image from multiple low resolution aliased images contain sub pixel shifts), and i want to know why SR is possible? this document explains why SR is possible, but i didn't understand completely! please can you explain more ...
I want to extrapolate a signal X of length 11, using the weiner filter coefficients W of length 7. The procedure I am using is as follows: Compute the autocorrelation matrix upto lag 8 . Using Levinson recursion, invert the autocorrelation matrix A. Multiply the matrix of cross-correlations with the inv(A) to get W Ob...
So I have discrete pixel values in the image and each row or column would make a signal. I would like to filter some of the rows or columns to remove high frequency components from them. Should I use the Z transform (difference equations) or work with the FFT of the data to perform the filtering?
Wigner transform and continuous wavelet transform are both some kind of time-frequency representation of a signal. What are the similarities and differences between them? Could you give some comparison between them? Let's restrict ourselves in 1D signal at the moment.
if we pad any signal with enough zeros we can get the same result as linear convolution whilst using the fft function we compute circular convolution. Why?
I'm currently trying to develop an algorithm to control the camera characteristic of a camera (the camera characteristic can be controlled to adopt it to the different lightning situation which can occur) In this case I need a good measurement of the exposure/lightning on the current image taken (i.e., if it's under/ov...
I have been working on a Harmonic Product Spectrum Algorithm. Now, all the literature I've read about the subject tells me to downsample an N amount of times. How does one determine what this N value should be? Here is my implementation of Harmonic Product Spectrum so far. Feel free to tell me if I have gone wrong some...
I build application witch will be transform piano sound to musical notes. I found some pitch detection algorithms with implementations (mainly based on autocorrelation or fft), but chord recognition, of course is not working. What is best method for instrument as piano(both hands + chords)? Is there any implementati...
When I was studying spatial frequency and entropy, it occured to me that "is there a relationship between entropy and frequency?". As you can see, if we consider only horizontal line, the frequency of (a) is lower than (b). Intuitively, I think that magnitude of frequency is proportional to entropy. But Google said not...
I would like to do research on automatic music composition. At the lowest level , I would like to start from discrete frequency levels as states. Here I would like to know the mathematical tools I can use for this? I have heard of markov chains and chaos theory etc used in this purpose. But one professor recently told ...
I want to remove the background from image. Let's say I have this background: . Then I put pen drive and tippex on it. . Is it possible to remove the background image from second image? If so, then how can I do it? I'm using the AForge.NET Framework. UPDATE I want to remove background like in this research paper. Is ...
I have a signal that I want to make it sound like a whisper. This is probably better than using a voice conversion system, but I was just want to do some experimenting before. I was thinking maybe try to reduce the frequency of the signal? Maybe downsampling? Does anyone have a idea how to get closer to a whisper/unvoi...
In continuous time it was possible; $$ u(t){\longrightarrow} \boxed{\quad\textrm{system}\quad} {\longrightarrow} y(t)\implies \delta(t)=\frac{du(t)}{dt}{\longrightarrow}\boxed{\quad\textrm{system}\quad}{\longrightarrow} \frac{dy(t)}{dt}=h(t) $$ Does the same apply for discrete time system i.e. $$ \delta[t]=\frac{du[t]}...
Let $\Omega > 0$ and denote by $\mathcal{B}_\Omega$ the subspace of $L^2(\Bbb R)$ consisting of signals that are bandlimited to $(-\Omega, \Omega)$. Denote $\mathcal{L}_{\Omega} : L^2(\Bbb R) \rightarrow L^2(\Bbb R)$ the ideal lowpass filter that projects signals $x \in L^2(\Bbb R)$ into $\mathcal{B}_\Omega$: i.e., $\...
I'm trying to port some MATLAB code to Python and am running into some strange behaviour. I am implementing a 5th order Butterworth bandpass filter. The sampling rate is 30 Hz. Running MATLAB R2012b, Spyder 2.2.0 with Python 2.7, SciPy 0.12.0 on Windows 7 x64. In MATLAB: [b,a] = butter(5, [0.75*2/30, 5.0*2/30], 'bandpa...
I tried to apply a Gabor filter with a specific scale (according to my values of lambda and sigma, so it is (7x7) and for 4 orientations (0, $\frac{\pi}{4}$, $\frac{\pi}{2}$ and $\frac{3\pi}{4}$) to a input gray scale image. In my code, three steps are achieved: Create a Gabor Filter Read an RGB image, then convert i...
Suppose you have N samples of a sinusoid of frequency $f_0$. $$ x[n] = A\sin[2\pi (f_0/f_s)n ] $$ Suppose you take an M-point FFT (where M may be greater than N) of your N samples of x. What will the amplitude of the peak of the spectrum be? Reference: http://www.designnews.com/author.asp?section_id=1419&doc_id=236273&...
I've recently come across this YouTube video that shows a PCM stream being played back via the 1-bit internal "PC Speaker", and after hours of googling I've come to think this is done via Sigma-Delta modulation. So far, what I gather from the process is that it takes the original digital signal, oversamples and approxi...
I want to create a microphone array that can be connected to my laptop. Previous discussions in stack exchange and other forums suggested me to get a USB audio interface. I would want to do a lot of real time signal processing on the sound arriving at the microphones (To be precise, I want to calculate the time delay o...
Suppose,I have an input of length of lenght 100. data=[x0...x99]; I take a window of lenght 11 from x0 to x10. windowed data=[x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10], now, I compute 7 wiener coefficients which are [w0 w1 w2 w3 w4 w5 w6]; next I will move by window one sample forward, new windowed data= [x1 x2 x3 x4 x5 x6...
We can capture frequency response, phase response and reverb in recording of impulse response. Then we can use it to simulate audio system and/or space by convolving it with dry audio signal. Is there similar technique for measuring and simulating non-linear distortion? I thought of measuring how the amplitude of outpu...
I am new to signal processing, and was reading about filters. I came upon the Sobel filter which has the following forms, $\textbf{G}_x = \begin{bmatrix}+1 & 0 & -1\\+2 & 0 & -2\\+1 & 0 & -1 \end{bmatrix} * \textbf{A}$ and $\textbf{G}_y = \begin{bmatrix}+1 & +2 & +1\\0 & 0 & 0\\-1 & -2 & -1 \end{bmatrix} * \textbf{A}$ ...
I have a program which takes in data from an oscilloscope, and due to reflections in the medium, we will get random signals at random intervals. The two grey windows at the right bottom show the original data (below red line), and after FFT forward and backward (above red line). The data set is originally 10,000 point...
I don't quite understand why the textbooks say it is impossible to implement an ideal low pass filter. If I was to take the FFT of a discrete signal x[n], with Matlab's fft function I'd be returned with a complex sequence X[n] which represents the magnitude of each frequency from 0 to n/2 and is repeated. If I was to t...
Suppose you have N samples of a sine wave of frequency $f_0$ sampled at $f_s$. $$ x[n] = A\sin[2\pi(f_0 /f_s)n] $$ How do you get a delta function in the frequency domain (i.e. all of the energy is in the center one bin of the FFT)? Does the number of samples (N) need to be a prime number of cycles of $f_0$? If so, wh...
I have designed a simple 3-state $[x\ \dot{x}\ \ddot{x}]$ Kalman filter which is updated by measurements for $x$ and $\dot{x}$. The filter is tracking a peak on a surface in the $x/\dot{x}$ plane. At each iteration, I detect a number of peaks on the surface, each with an $x/\dot{x}$ measurement pair. I need to select t...
In Harris Corner detection, is there any particular reason why this function is chosen: $R=det(M)-k*trace(M)^2$ We want to a function to evaluate how fast E(u,v) fluctuate accross different direction, but can't we use other function such as: $R=1-(\lambda_1+\lambda_2)^2$
MATLAB has a spectrogram function for the time-frequency analysis of a single signal. It also has a cpsd function for estimating the cross-frequency spectrum for two signals. However, cpsd averages across windows, collapsing the time axis into a single estimate. Is there a function in this same family that does not av...
fdesign.arbmagnphase is a MATLAB built-in function that will create a filter that best fits the frequency-response that it is given. I'd like to implement a similar function in Python. What algorithms are used to synthesize filters based on an arbitrary frequency response?
Goal: For a particle moving uniaxially, to estimate position ($d$) and velocity ($v$) from noisy acceleration ($a$) and very noisy position (GPS) measurements using a Kalman filter. Catch: The accelerometer has a DC offset, i.e. its zero is not zero but some number $\Omega$ such that the "true" acceleration $a^{true}$ ...
Please explain me the concept of Orthogonality and Orthonormality. I understand that the mathematical definition of orthogonality between two vectors is that their dot product is zero. It means that there is no correlation between the two vectors. And in case of Orthonormality the vector length would be 1. I am unable ...
How can I find out frequency and peak value of a signal's fundamental? Please do consider the following: The peak value of some harmonics might be higher than that one of the fundamental The frequency of the harmonic is not an integer (e.g. 3.45 Hz) I have information about where to search for the frequency (3.45 +- ...
I am asked to find a pair of sequences, each one of which contains three distinct values and where the convolution is an all-zero sequence. I've came to the conclusion that one of the sequences must be infinite but just can't think of any examples...
If I have a time domain array of N samples, and swap the final half with initial half, then perform an FFT, what will be the effects on the frequency domain? Will the frequencies' magnitudes remain the same as the ones in the frequency domain of the original array? What if instead of swapping halves, I just circle 1/10...
I have a signal with length of $N$. The sampling frequency is $f_s$. Window size is $w$ The noverlap size is set to $m$. And $nfft$ is selected for frequency resolutions. I am running a STFT with matlab spectrogram function. [S,F,T,P]=spectrogram(x,window,noverlap,nfft,fs) what is the effect of nfft , $f_s$ and...
What is computational complexity of continuous wavelet transform cwt ? What is computational complexity of wavelet packet transform wpt ? What is computational complexity of Stockwell transform transform wpt ? for the cwt : imagine I have a signal with length of $N$ and I scale vector is 0:1:s what will happen if I di...
When we implement the 1D-short time fourier transform, the formula is as such: $$ Sf[m,l]=\sum_{n=0}^{N-1}f[n]g[n-m]\exp\left(\frac{-i2\pi l n}{N}\right). $$ the window $g$ used is normally symmetric, why is this so? (Hint: Use the phase of Short time fourier transform.
I have to implement a complete receiver in digital communications. The transmitter gives me an output vector which has real and imaginary values. It uses 16psk for modulation. How would I demodulate that signal? I was assuming the output with constant amplitude with different phases, but the magnitude of the whole ve...
I have a half second audio data sampled at $44.1\textrm{ kHz}$. If I FFT it I get frequency components in $2\textrm{ Hz}$ increments. Now suppose I want the component of an arbitrary frequency, like $32.45\textrm{ Hz}$, how can I get it? Looking at the DFT formula from Wikipedia: $$ X_k = \sum_{n=0}^{N-1} x_n e^{-i 2 \...
A band limited signal of $5$ kHz is observed at the output node whose sampling frequency is $600$ kHz. What is the minimum order of the filter? Does it mean: a signal that is from $0$ to $5$ kHz on the frequency axis when drawn a signal from $-2.5$ kHz to $2.5$ kHz a signal with bandwidth of $5$ kHz centered anywher...
I am trying to code a simple algorithm in MATLAB that would be used to detect a single word. The goal would be to have a user record the word one time to act as a template, then make the user repeat the same word to try and detect it. Searching on this website has answered many of my questions, but I still have some i...
What this relation on picture mean? Why response for a digital low-pass filter exists on "-" side of x axis? Impulse starts at 0 as i can understand and goes to infinity... Please use phrases starting with "think of it this way..." or "it's like..."?
In this answer, Jim Clay writes: ... use the fact that $\mathcal F\{\cos(x)\} = \frac{\delta(w - 1) + \delta(w + 1)}{2}$ ... The expression above is not too different from $\mathcal F\{{\cos(2\pi f_0t)\}=\frac{1}{2}(\delta(f-f_0)+\delta(f+f_0))}$. I have been trying to obtain the later expression by using the standar...
I am trying to implement the symbol timing recovery loop and for that I have chosen two algorithm to compare my results one is feedforward and Gardner TED. One thing that is confusing me is smoothing of error after finding timing error and finding the right sampler. Should I use the sampler after matched filter or bef...
I am studying wavelets in image processing. I would like to learn how to downsample a matrix in columns using MATLAB. I have used the downsample(x,n) command to downsample the given matrix in rows. But how to do the same in columns? x = 1 2 3 4 5 6 7 8 9 10 11 12 y = downsample(x,2) y...
Here is a sinusoid of frequency f = 236.4 Hz (it is 10 milliseconds long; it has N=441 points at sampling rate fs=44100Hz) and its DFT, without zero-padding : The only conclusion we can give by looking at the DFT is: "The frequency is approximatively 200Hz". Here is the signal and its DFT, with a large zero-padding : ...
I need to record sound using 2 (or 4, eventually) microphones and then calculate the time delay of arrival of sound at the different microphone pairs. But first, I need a microphone array. And since I'm just starting out, I would like to connect just 2 mics first and calculate the time at which sound arrives at them. C...
Please help me understand the following MATLAB code for Ideal Low pass filter. I am unable to understand the Part2 in the below code. Please explain me why we are doing like this. I have read the Rafael C. Gonzalez's Digital Image Processing Using Matlab 2E which explains my question but I couldn't understand properly....
Some methods #1 YData = YData / max(abs(YData)); #2 maxYdataAbs = abs(max(YData)); minYdataAbs = abs(min(YData)); YData = YData / (0.5*(maxYdataAbs + minYdataAbs)); I am not happy with neither one. Assume that you have the following data. Only one or two sharp peaks. I am not happy with #1 or #2. I am not sure anymo...
I am on a project of vehicle type Identification (MUV,jeep,Sedan,etc) from images and Here is what I have done up-to now on matlab. I am working only on the sideview of images. Input Image : Masked image Then I detected the corners easily Now I got a matrix C with 40 corner coordinates thus I got a matrix of C=[...
I am not very good at mathematics I was doing some image processing so I came to know about FFT and IFFT I was learning about them but the mathematics involved seems to be too dense So can someone tell me about what are FFT and IFFT and their general application in short in LayMan's Language So that again when I go to ...
I want to write continuous wavelet transform codes manually by matlab. And I want to use complex morlet function. Here are some background: Continuous wavelet transform definition: $C(S,T;f(t),\psi (t))=\frac{1}{\sqrt{S}}\int_{S}^{b}f(t)\psi^{\ast }(\frac{t-T}{S})$ S is scale vector.for example 1:60;$T$ is time slid. ...
I'm trying to find the fundamental frequencies present in a piano recording using MATLAB. These are the steps I've followed; Find the envelop of the signal Find the note onsets perform FFT between each onset Harmonic product spectrum. It's when I try to implement the HPS algorithm that I face a "dimensions don't agre...
Please suppose the following: The frequency of a signal's fundamental has been estimated using FFT and some frequency estimation methods and is lying between two bin centers The sampling frequency is fixed Computational effort is not an issue Knowing the frequency, what is the most accurate way to estimate the corres...
I've often seen i my DSP book, that when they record a sound, they use a sample rate at 10khz or 8 khz, which makes sense since the fs is 2 times bigger than the sampling signals max freq. What i don't understand is why they only take 205 samples, rather than 10000 samples or 8000 samples, wouldn't each sample be "unpe...
Can you please explain in simple terms what do the input parameters indicate in the ordfilt2 function in matlab? B=ordfilt2(A,Order,Domain) I have seen people use this function as J = ordfilt2(I, 9, true(5)) or J=ordfilt2(I,25,ones(3,3)) But I do not understand what each input does to the image I to give J as output.....
I need to convert 150 Frequency domain samples to the time domain. The problem is, I have been provided with 250 time domain samples for comparing my results. How am I supposed to relate the 150 samples to 250 samples? I can't find any relationship like interpolation/decimation between the two. Does this have anything...
I have researched a bit into DSP filters for the problem of finding the angular velocity from X/Y acceleration measured by a rotating accelerometer. Essentially I need more help in picking the best type of filter. An example of the type of data I can measure can be seen in this image (ignore the y-axis as values are s...
Text present in captured images is high frequency or low frequency component?Why?
I'm building my own MIDI synth. I have to create a decent sounding tone for every note on the piano keyboard (A-1 through C7, or MIDI 21 through 21+88=109) I've been using a basic ring resonator, where I create a ring of the right size (for example, sampling at 44.1 kHz the ring for A440 a.k.a. concert pitch would be 4...
Is there an example of an eigenfunction of a linear time invariant (LTI) system that is not a complex exponential? Justin Romberg's Eigenfunctions of LTI Systems says such eigenfuctions do exist, but I am not able to find one.
I'm trying to combine two filters into a single filter command for a homework problem and was looking for advice. I don't necessarily need an explicit answer as long as someone can point me in the right direction. In the following code, assume that 'y' is a sound file that has been pre-loaded (10kHz). Also, both the h...
In a problem I'm working on, I have a signal that is sampled 256 times for 3.5 microseconds. After performing a Discrete Fourier Transform on the data, what is the frequency step between the calculated values of Cn? The prompt states that this is also called the bandwidth of each point in the power spectrum. How can I ...
How do you calculate the noise equivalent bandwidth for an IIR or FIR filter?
I am doing a project on image classification and I don't know where to get the data-set collection for cars and bikes.Any suggestions to sites for this purpose is welcome.Also please suggest the general size of images to act as a database. Thanks and regards in advance.
I was reading about active sonar and couldn't quite understand how the echos are recognized. My doubt is, when the sound signal is reflected back, it is greatly attenuated and distorted due to many factors. Do they use MFCC(which I think is only good for audible range) for identifying the echo or are there any other be...
I'm working on my own implementation of the discrete Haar wavelet transform, I understand the wavelet theory and how to construct the Haar matrix of size N to perform the transform, but obviously there is a problem using the Haar matrix in application - it's simply too big. I am working on an application that applies t...
Here I have a MATLAB code for Ideal Low pass filtering an Image. In the below code they have used D=sqrt(U.^2+V.^2); which finds some distances. Then this distance matrix D is compared with the cut-off frequency to create a filter function H ( H=double(D<=P); ) that has be multiplied with the fourier transformed image ...
I have a device (whose behaviour I can't change) which does the following signal processing: The incomming signal contains two frequencies $f_1$ and $f_2$. One has a huge amplitude, the other a smaller one: $x_1 = X_{01} \cdot cos(2\pi f_1 \cdot t)$ $x_2 = X_{02} \cdot cos(2\pi f_2 \cdot t)$ with (for example): $f_1 = ...
We can often read that Hilbert transform is useful for envelope detection (e.g. Hilbert transform to compute signal envelope?) I have done some tests with various soundfiles, and x[n] -> absolue value -> 1-pole low pass filter -> envelope or x[n] -> Hilbert transform -> absolute value -> 1-pole low pass filter -> enve...
Given a an IIR lowpass-filter in z-space: $ H(z) = \frac{\sum_{i=0}^P b_{i} z^{-i}}{1+\sum_{j=1}^Q a_{j} z^{-j}} $ How to calculate it's 3dB cut-off frequency? I about evaluating it's fourier transform (as long it exits) and take it's magnitude: $\frac{1}{\sqrt{2}} = \frac{|H(e^{j\omega_c)}|}{|H(e^{j0})|}$ This is then...
When I calculate the cross correlation between two vectors with the following code a = [1 2 3 4 5]; b = [6 9 8 9 10]; % correlation using convolution conv(a,conj(flipdim(b,2))) % correlation using FFT ifft(fft(a,9).*conj(fft(b,9))) fftshift(ans) when I use the FFT i need to fftshift the output in order to get the cor...
My knowledge of wavelets is less than epsilon. Bear with me. If I have a signal of two well separated sinusoids (15 and 48 Hz) plus some random noise, I can clearly make out the two in a spectrogram (the two stripes in my picture); t=0:0.002:1; % fs = 500 Hz x=4*sin(2*pi*15*t)+2*cos(2*pi*48*t); xn = x + randn(size(x)...
I'd like to do a fade out of a sound in a few seconds, but in a "spectral way", with a special curve : (here x-axis is time, y-axis is frequency from a few hz to 20khz). All the part "to be removed" has to be removed ! Do you know how to do this ? (an EQ / simple IIR/FIR filter won't work for this, etc.)
This question follows from: Synthesizing harmonic tones with Karplus Strong I am attempting to generate a full soundbank of 88 notes. As far as I can see my three options are: Using samples Using something like Karplus Strong (as linked above) Synthesising each harmonic and combining them (1) does not give much flexi...
I've been googling for a while and came across the audio cookbook and Bjorn's blog explaining it further Link Here. Background info: I've modified the rtl-sdr open source code to tune to a VOR station (transmits heading, typically used for aircraft). I tune to 113.1 MHz which is the the frequency the nearby VOR station...
I want to model a "negative dispersion" in waveguides. Is it possible to design an all pass filter with inverted phase response? (e.g. -pi at 0 and pi at Nyquist)? I feel :) this could be possible in complex domain (but don't know how). I could use a Hilbert transformer to complexity real signal at first.
I have a guitar music signal and I want to detect the onset points via energy. This is the signal example: This is the energy plot: My question is what would be the best method defining the threshold and consequently finding the peaks. I reckon I will have to set a window length and a window step (I am thinking 1000 ...
What is currently the most accurate Voice Activity Detection algorithm with high levels of background noise? I would also appreciate if it does not require any manual calibration. Bonus points for examples. EDIT: I am referring to accuracy as yielding the lowest amount of false positives and negatives.
I am working on a project that requires me to detect and track a human in a live video from a webcam connected to a Beagleboard xm. I have completed this task using Opencv in pixel domain. The results on the board are very accurate but extremely slow. Many people have suggested me to leave pixel domain and do the same ...
Does some have an example of what a Wiener filter (that can be used directly with scipy.signal.wiener) can be useful for, in sound processing (it seems that such adaptive filters can be useful for noise reduction, etc.) ? I tried with various (noisy + sinusoids) soundfiles (read into an array x) with the command y = wi...
I am working and researching on Image watermarking/steganography and I'm stuck at a point and want to know which technique is better in image processing for data hiding. Bit Plane Complexity Segmentation OR CDMA Spread spectrum. Can some experts give their opinion on both techniques and which one is better and why? lik...
I am new to the field of image compression. While going through various texts, I read about how transforming the image to another domain using, for example, the wavelet transform, or the DCT, makes it suitable for lossy compression. I have been trying to play around with wavelet transforms on a sample bmp in MATLAB. Us...
Given the signal shown below, what is the best way to remove the steps and local maximas it contains. The signal contains some steps which can last up to 100 Samples before they return to about the same value as before the step (Marked with red circles). There are also some peaks which last only for one sample which sh...
I am struggling to implement a mathematical morphology toolset in an image processing package. I base my implementation on what I saw in MATLAB, and on several papers on the subject. There seems to be abundant literature on morphological operation optimization through structuring element (strel) decomposition. For ins...
If i have two images of the same scene, reference image and a shifted image, the shift can be in x or y directions, i want to estimate the shift using the shift property of the fourier transform. S1 = fftshift(fft2(im1)); % Fourier transform of the reference image S2 = fftshift(fft2(im2)); % Fourier transform of the i...
My question here is in regards to implicit information/terminology. Basically, whenever we say that "a shift in time means a change of phase in fourier space", is it implicit that the shift is always circular? Are there any exceptions to this? Caveats? etc?
Could you please clearly explain what is the difference between correlation and convolution that is done by a filter on an image? I mean in terms of signal processing definition I know that convolution describes the output of an LTI system, that is if an LTI system produces an output due to convolution with an input s...
I have a question regarding Discrete Fourier Transform and Discrete Time Fourier Transform. Suppose that we have a sequence $x(n)= \{1,2,3,3,2,1\}$. So is it possible to reconstruct the Discrete Time Fourier Transform $X(e^{j\omega})$ from the Discrete Fourier Transform $X(k)$ ? And how? In my opinion , it is possible,...
Question 3.1 d from Chapter 3 of Oppenheim's Signals & Systems I have $$x[n]=(-1)^n{u[-n]-u[-n-8]}$$ $$h[n]=u[n]-u[n-8]$$ and the question asks for $y[n]$ which is the convolution of $x[n]$ and $h[n]$ namely $$y[n]=x[n]\star h[n]$$ I'm stuck with the limits on the sum $$\sum_{k=-\infty}^{\infty}{\left((-1)^{k}(u[-k]...
As I understand, the overall colour average can be obtained by summing the individual r, g, b values of all pixels within and image and dividing by the number of pixels to produce a new tri-vector. What are the applications of such techniques?
I have to compute an HSV histogram of a colored image. Is it same as an H-S histogram? I have found H-S histogram computation code everywhere. What is the method to change an H-S histogram to an HSV?