Questions tagged [signal-analysis]

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3
votes
2answers
112 views

Dealing with echoes / dead-spots in digital transmissions

I'm looking at communicating digital data through the air as soundwaves. To illustrate the problem, I generate a 10-cycle 2kHz wave, play it out through my MacBook's speakers and pick it up on my ...
3
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2answers
732 views

Fourier Transform of infinite sum

I'm looking at last year's exams, and I found an exercise I can't solve: (Roughly translated) Consider $x(t)=\sum\limits_{k=1}^{+\infty}\left(\frac{1}{2}\right)^k \cos(k2\pi t)$ the input to a LTI ...
3
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2answers
222 views

What is the autocorrelation of a Dirac pulse?

What is the autocorrelation of $x(t) = \delta(t)$? Can you explain to me how to calculate it?
3
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2answers
4k views

How does transition width of a low-pass filter affect a message which is well within the pass-band?

I'm taking a communication systems course and we use GNURadio in the lab. In an exam, we had a simple question where we were asked to demodulate a Dual Side Band (with carrier) AM signal in GNURadio. ...
3
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1answer
146 views

Trying to write a signal “unsmoothing” algorithm

Up front: I'm just a hobbyist, and I know zero about signal processing; I'm trying to write a simple(?) javascript algorithm and hoping I don't need a PhD in DSP to make progress on it. I have an ...
3
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2answers
2k views

Frequency Analysis (DFT / FFT) of a Signal Without a Constant Sampling Frequency (Non Uniform Sampling in Time Domain)

I'm a stack exchange user for some time and now I'm registering to ask a simple question (I think!). I have a vibration signal with an amplitude and time (sampling frequency not constant) in a $...
3
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1answer
938 views

what are the Pros and Cons of ESPRIT and MUSIC algorythms?

On wikipedia there are only 2 lines about ESPRIT: Estimation of signal parameters via rotational invariant techniques (ESPRIT)... MUSIC doesnt have an entry in the music disambiguation page, other ...
3
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2answers
804 views

FFT of SIN waves with different phase delays

I have come across a peculiarity of FFTs which has got me somewhat baffled. I've simply summed up 101 sine waves and taken the FFT using this matlab script : ...
3
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1answer
2k views

What is the reason for filtering out the negative frequencies of a signal?

I am reading this tutorial. Quoting the lines from the topic "Analytic signals and Hilbert transform filters": the corresponding analytic signal $ z(t)=x(t) + j {\cal H}_t\{x\}$ has the property ...
3
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2answers
1k views

How to identify useful elements of audio recording and ignore lulls?

I assume this is a relatively simple DSP task, but I'm having trouble finding any information on how to approach my problem. Hopefully someone with more experience and brain power can help me out: I ...
3
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2answers
2k views

Effects of DC offset on a signal

What are some of the reasons why DC offset is considered undesirable for a timeseries signal other than wastage of power during transmission ? Specifically, How does it cause spectral leakage and out ...
3
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1answer
80 views

Variance of an Implicit Function of Kalman State Vector

Given a state vector given by $ x = {[r, v, a]}^{T} $ (Range, Velocity, Acceleration) the Time to Hit is the the time which holds the following: $$ r + v {T}_{tth} + \frac{a {T}_{tth}^{2}}{2} = 0 $$ ...
3
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1answer
7k views

Concept of Orthogonality and Orthonormality

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 ...
3
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1answer
48 views

Given 1 recording of my voice, how can I process it to sound like 2 independent recordings of my voice played in unison?

I have one recording of my voice $x[n]$ singing a song. One thing I could do is independently record me singing the song again to obtain $y[n]$. Then, $z[n] = \frac{1}{2}\left(x[n] + y[n]\right)$ ...
3
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1answer
160 views

Square wave FFT results show frequency that seems too low?

I have created an open source plotting package for a low cost oscilloscope - see link here: GitHub Plotting Software But during my testing I have one result that may be wrong: a noisy 7 kHz square ...
3
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1answer
468 views

PSD from autocorrelation in MATLAB

I am trying to simulate a simple stochastic process defined by the equation: \begin{equation} \frac{1}{v}\frac{db}{dt} +\Gamma_0 b= \sqrt{\sigma}R(t), \end{equation} where $R(t)$ is a zero-mean white ...
3
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2answers
193 views

Contradiction while using the convolution sum for a non-LTI system

In a recent quiz, we were given the following problem: The cascaded LTI systems $\mathcal{T}_1$ and $\mathcal{T}_2$ respectively have impulse responses $h_1[n]=\delta[n+3]$ and $h_2[n]=\delta[5−n]$....
3
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1answer
105 views

Maximum of cross-correlation not moving

I already asked this question here yesterday, but it was very poorly worded I think. I made a much more detailled post explaining my problem of stackoverflow, as it might also be a code problem. Here ...
3
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1answer
265 views

Gaussian Equivalent of Convolving an Image 50 Times with a Box Filter

I have a image that I'm convolving 50 times with a box filter, and I like to replace this with a single gaussian filter. Because both box filter and gaussian filter are separable I can just study the ...
3
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1answer
430 views

Parseval's Theorem for discrete series

I need to use Parseval's Theorem to find \begin{equation} S\:=\:\sum _{n=-\infty }^{\infty }\:\left[\left(\frac{\sin\left(\frac{\pi }{4}n\right)}{2\pi n}\right)\left(\frac{\sin\left(\frac{\pi \:}{6}n\...
3
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1answer
465 views

Determination of periodicity in data and finding mean

I have to find whether there is any pattern (I mean periodicity or close to periodicity) and if there is, for one cycle i have to perform numerical integration to determine mean. In the first picture ...
3
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2answers
81 views

Proving conditions for controllability

Let's say I have the following LTI system: $$\dot{x}(t) = \mathbf{A} x(t) + \mathbf{B} u(t)$$ I need to somehow show the following is true or false (proof): This system is controllable if and only ...
3
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2answers
3k views

An explanation of parts of the MUSIC Algorithm for someone without a background in signal processing?

I've been looking at every tutorial and paper I can find, but I keep losing the intuition behind what's going on when they get into the matrix operations. There is a step in which the signal vector ...
3
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2answers
82 views

Need to calculate $\frac{E\left[|x(n)|^4\right]}{E\left[x^2(n)\right]}$

I need to calculate $\frac{E\left[|x(n)|^4\right]}{E\left[x^2(n)\right]}$ in real time, where $x(n)$ is complex. For $E\left[|x(n)|^4\right]$ I plan to take the absolute, raise it to the power $4$ ...
3
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2answers
2k views

Morlet wavelet time and frequency resolution

I want to calculate Morlet time and frequency resolution. the Morlet wavelet function is define as : $\psi(t)=\frac{1}{\sqrt{\pi f_b}}e^{j2\pi f_c}e^{-t^2/f_b}$ Note: I know the answers, but I don't ...
3
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1answer
3k views

Large Laplacian Spatial Filter on EEG?

I want to know that why large laplacian spatial filtering is done on EEG signals? I tried a lot but could not find material on LLSF. And what is meant by spatial filter ( in context of Digital Signal ...
3
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4answers
7k views

what does the statement “band limited signal of 5 KHz” mean

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 ...
3
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1answer
165 views

How to match two signals that have similar shape but are scaled and expanded?

I have two signals A and B in time domain as follows: Visually both signals look very similar; however the X and Y axis range are different for both the signals. Signal B is basically a "stretched" ...
3
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1answer
66 views

Compare two signals, find times when they are affected by the same processes

I have two (noisy) signals $S_1(t)$ and $S_2(t)$. They contain information on three distinct events occurring in a physical system. Event $A$ affects only $S_1(t)$, event $B$ affects both $S_1(t)$ and ...
3
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1answer
74 views

What is the signal-noise model of laser induced fluorescence?

The following image is an example of a fluorescence signal trace from the photomultiplier tube detector (PMT). Each spike represents one fluorescently labeled cell. This signal model is definitely ...
3
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1answer
400 views

Cross-correlation, sharp peak at 0?

First of all, I have to stress that I am not a professional of coding, no more than a professional of signal processing. I am a chemist that happen to be working on a project involving both. So in ...
3
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1answer
255 views

Efficient FFT (or SFFT) for adjacent parts of signal with overlap?

Imaging we have a signal $x$, which is segmented to 50% overlapped vectors $x_1,x_2,..,x_m$ , and we intent to compute FFT of each segment. Is there anyway that we can reduce computation of FFT of ...
3
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1answer
55 views

How to differentiate the product signal $f(t)\theta(t)$, where $\theta(t)$ is Heaviside's unit step function?

What is the derivative (in the engineer's sense) of the causal function $f(t)\theta(t)$, where $\theta$ is the Heaviside unit step function? I've seen the formula $f'(t)\theta(t)+f(0)\delta(t)$, ...
3
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1answer
424 views

Occupied Bandwidth

I am pretty new in the field of Signal Processing. I am a structural engineering graduate student at the UT at Austin. I am currently working on a project that regards acoustic emission monitoring of ...
3
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3answers
2k views

How Do You Save / Convert an Image to Be in the Frequency Domain?

Quick Note: I don't believe this is a subjective question... however if it is I will gladly modify to be more objective In ImageJ, if I take the FFT of an image, how can I save this new frequency ...
3
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2answers
352 views

Is it correct to subtract two signals acquired over different times and trials to remove the common signal in them?

I have two signals that represent the response of a neuron under two different conditions. Signal 1 (S1): response to Stimulus A Signal 2 (S2): response to Stimulus A+B The response to stimulus A is ...
3
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1answer
1k views

Separating 'signal' from periodic 'noise'

I have data in which the signal we want is a few gaussian peaks superposed on a noisy background in which some of the 'noise' is periodic. Simply suppressing the associated fourier modes is effective ...
3
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1answer
248 views

Usefulness of Matrix Notation for Linear Periodically Time Variant Transformations

I am quit puzzled about a notation I found in Gardner's 1986 book titled Introduction to Random Processes. It is in the chapter on Cyclostationary Processes at section 12.4 which pertains to Linear ...
3
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2answers
1k views

Using Goertzel Algorithm in under-sampling

I plan to calculate a signal's phase using Goertzel Algorithm. I have 2 signals coming to microcontroller's ADC. Need to measure the phase difference between them. Signals are 15MHz sinusoids. Sample ...
3
votes
1answer
276 views

What is the general feature of a time domain signal that gives a step like spectrum?

I'm trying to study a nonlinear system by sending a pulsed signal into the system and look at the response spectrum. The signal I send to the system is something like and the response spectrum from I ...
3
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1answer
185 views

Noise rejection / feature extraction

I'm hoping someone could point me in the direction of some signal processing methods to clean up my data. I'm collecting physiological data from human muscle (lower leg; gastrocnemius) during walking/...
3
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1answer
1k views

Why do we read that Hilbert transform can be used for envelope detection?

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 ...
3
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0answers
97 views

How to compute (in non adaptative way based on MMSE FIR) the feedback and feedword filter for DFE equalization?

System Model Consider the single-input single-output (SISO) communication system in the figure below: where the information bit stream is encoded and mapped such that the output of the encoder is a ...
3
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0answers
540 views

Linear Frequency Cepstral Coefficients, is Filter bank needed?

I am working on my master thesis on acoustic pattern recognition and have a question to the calculation of cepstral coefficients. I understand the step with a filter bank in MFCC calculation, it is ...
3
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0answers
135 views

Preserve scale during PCA

I have two signals, I've done a Principal Component Analysis and separated my signals, I get one with noise and one with signal. . ...
3
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2answers
194 views

Detect repetitive units within signals

I have several signals that consist of repetitive units. In the figure you'll clearly see the variability of the signals, that increases top down. The first signal is super repetitive and units are ...
3
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0answers
239 views

Segment/Idenfication of signal from a spectrogram

I have the following Spectrogram of a signal: Essentially, in this signal, I know there is one point of interest (between 60-80) and between the the particular frequencies. I could, potentially ...
3
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2answers
397 views

How to Extract Nonorthogonal PCA Principal Components

My problem is essentially a 'blind source separation' problem. I have 3 non-orthogonal sources (or basis functions) and $N$ random linear combinations (mixes) of said sources. My problem is to obtain ...
3
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0answers
162 views

understanding discrete wavelets

I was reading section 4.3.3 from chapter 4 of "A Wavelet Tour of Signal Processing", "...Let $\bar{f}(t)$ be a continuous time signal defined over $[0,1]$. Let $f[n]$ be the discrete signal obtained ...
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2answers
2k views

Performing a Deconvolution

So I have the following data: ...

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