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How do the alpha & beta parameters referenced in this implementation of a software based digital phase locked loop relate to the loop bandwidth, in Hz? The loop filter equations gleaned from the code appear to be:
$$f_n=f_{n−1}+ \beta\epsilon_n \tag 1$$
$$\phi_n = \phi_{n-1} + f_n + \alpha\epsilon_n \tag 2$$
where $f_n... |
I'm studying MUSIC algorithm for far-field DOA estimation. I found that when the antenna spacing $d$ is larger than half wavelength $(\frac{\lambda}{2})$, the algorithm fails and the spatial spectrum shows multiple peaks.
In 5G beyond and 6G wireless communications/localizations, mmWave or even higher THz band can be u... |
Problem and backgroud
Two objects $A$ and $B$ are colliding and produce audio response $x_{AB}(t) = x_A(t) + x_B(t)$, where $x_A(t)$ and $x_B(t)$ are audio produce by these two objects individually.
In another word, I just apply impulse on $A$ and $B$ and get their response.
My project is only interested in the vibrati... |
I have an EEG csv data set of 268 samples. In every sample, there's data for 6 EEG channels, and every channel has 896 data points (256 Hz, 3.5 s).
At first, I interpolated and filtered the data one by one.
ch_names = ['A1', 'A2', 'F3', 'P3', 'F4', 'P4'] # channel names
sfreq = 256 # sampling frequency, in hertz
c... |
I'm using the following two functions to calculate the frequency response of an impulse response: numpy.fft.rfft and scipy.signal.freqz, but I get different results. Let's simplify the problem using a small number of FFT.
import numpy as np
import scipy.signal as signal
h = np.array([1,2,3])
H1 = np.fft.rfft(h, n=4)
w,... |
I have a signal $x(t)$ with bandwidth $B_x$, and I am taking its cosine to create $y(t) = cos(x(t))$. After checking the spectrum with FFT, it seems that $y(t)$ is also bandlimited. But, is there a way to prove it? If so, what is the bandwidth?
I have tried applying the integrals from the Fourier series definition, but... |
Maybe this is a trivial question, but I couldn't find an answer yet. Is there some discrete wavelet transformation which works with overlapping wavelets (half on half)? In other words, is there some smooth $f:\mathbf{R}\to\mathbf{C}$ with support in $[-1,1]$ such that such that $$\{t\mapsto\sum_{i=\infty}^\infty f(2^... |
For a given input sinewave with amplitude $A = 2000$ and frequency $f = 53405\,\text{Hz}$ (at $-3\,\text{dB})$,
From my understanding, the CIC filter gain should be $5^3=125$, and $-3\,\text{dB}$ magnitude response is at the frequency of about $f = 53405\,\text{Hz}$, so at least I should get a result around $2000*125/2... |
I am learning the Fourier transform from examples and one particular statement in the comment,
According to the Fourier Transform theory, FFT result is sized N/2+1 for 1D FFT...
in the below link to the example
https://www.intel.com/content/www/us/en/developer/articles/technical/use-onemkl-with-opencv-for-fft-calcula... |
I assume that fixed-point arithmetic can handle most of the traditional linear DSP tasks. As far as I know, there is a restriction for the FFT length with respect to the fixed point bit-depth.
Is there any common knowledge regarding other DSP applications that the fixed point can not handle? I assume that non-linear ap... |
I have this received signal in passband
$$
\begin{split}
r(t)=&\Re\left\{\tilde{x}_1(t)e^{j2\pi f_1t}+\tilde{x}_2(t)e^{j2\pi f_2t}\right\}\\
=&\Re\left\{e^{j2\pi f_1t}\underbrace{\left[\tilde{x}_1(t)+\tilde{x}_2(t)e^{j2\pi (f_2-f_1)t}\right]}_{\tilde{r}(t)}\right\}
\end{split}$$
Suppose the power spectral density (PSD)... |
What is the diversity gain in $4\times2$ vs $2 \times 2$ MIMO system. Is it $10 \log \left( N_{t} - N_{r} \right)$?
|
I'm studying a system's transient characteristics with awgn added to an input signal and I need to calculate $\text{SNR}$ before and after filtration.
Here is my code to generate input and output:
K0=1.2;
b=[0 K0];
a=[1 K0-1];
N=10000;
n=1:N;
uinp=[1 ones(1,N-1)];
sn=0 ; % SNR on input signal
levs=0 ; ... |
I have multiple physiological signals (EMG - muscular electrical activity) that are all of different length (one may even be 2/3 times longer than the smallest one). These signals are from 2 types of muscular activity, all sampled at 1000Hz. So, say I have:
10 EMG signals from activity A, with an average lenght of 1.... |
If I have a biquad filter with known $a_1, a_2, b_0, b_1, b_2$ coefficients, how do I calculate the corresponding lattice/ladder coefficients?
I have found information on deriving the lattice coefficients for all pole filters but not ARMA filters - am I missing something simple?
|
I am about to design a low-pass filter with a zero/pole placement method in such a way that rejected frequencies are placed at $500\,\text{Hz}$ and their multiples.
Are there any simple instructions to do it Matlab?
Expected freq. response fo LPF with rejection exact freqs ...
|
I'm an electrical department student studying signals and systems.
The RMS value of the general AC electrical signal is 6.31V, and the first harmonic value is 6.30932V(rms). (THD is approximately 1.5% at this time.)
How much does the std value of the white noise added to the signal affect the THD value of the signal?
W... |
TR 38.901 Section 7.7.2 mentioned that the TDL-A, TDL-B, and TDL-C channel models are constructed for NLOS scenarios. In TS 38.101-4 Annex B.2.1, in Table B.2.1.1-1 (picture is attached), delay profiles for NR channel models are mentioned where TDLA300 corresponds to 12 taps and 300 ns delay spread.
My question is -- w... |
I am trying to find the frequency difference ($\Delta f= f_1 - f_2$) between two complex sinusoidal signals using Matlab. The two signals are:
$$r_1 (t)= A~ e^{j 2 \pi f_1 t}= A \cos(2 \pi f_1 t)+j A\sin(2 \pi f_1 t)$$
$$r_2 (t)= A~ e^{j 2 \pi f_2 t}= A \cos(2 \pi f_2 t)+j A\sin(2 \pi f_2 t)$$
where $f_1=150\, \text{KH... |
EKF filter normally has a predict + update step, I am curious - how do you evolve the covariance of the state without one of the steps?
In essence I want to evolve the state of an object using an IMU and I want to track the covariance at each update to get an estimate on what the error could be. I do not have a seconda... |
Using the Exponential Sine Sweep (ESS) method and my test equipment, I am trying to find the impulse response (IR) of a room which contains a great deal of sound absorbing material. Ultimately I want to calculate the reverberation time (RT60) using the IR. Of course, I know there are similar questions, but I'm asking b... |
I have a IQ signal with a bandwidth of $200\,\text{MHz}$.
I do I*cos(2*pi*1000e6*t)-Q*sin(2*pi*1000e6*t), but my signal doesn't shift to carrier frequency 1000e6 on the power spectrum. I cant find the problem. I do this with Python.
|
The transfer function and the input output data of the system are known. The transfer function is given by $$G(s) = \frac{K}{(Js+b)(Ls+R)+K^2}$$
How are the parameters of the transfer function determined using the LMS algorithm?
Should the number of weights of the LMS algorithm always be same as the number of parameter... |
I am trying to solve a problem based on a real world measurement.
Suppose I am trying to obtain a complex signal $S(x)$, but only know its magnitude squared,
$|S|^2$ and its imaginary part $\text{Im}(S)$, to fully reconstruct the signal, I need to determine its real part or its phase. I'm wondering if this problem has ... |
I am working on this project in which I am using Short Time Fourier Transform (STFT) for feature extraction before applying classification model. I have a time series sensor data, applied signal processing on it to remove noise peaks and then applied STFT for feature extraction. The code that I have used to implement S... |
I am trying to convolve an image with the code above using Convolution Theory and numpy's Fourier transform. However, my output seems to be slightly different than the result from scipy. I am not sure why my values are slightly off.
The inputs image is a numpy array, and the kernel input is a normalised 3x3 kernel.
Any... |
I am reading the book "Detection of Signals in Noise" by Robert N McDonough, A D Whalen. In chapter 10, they compute the gradient of the log-likelihood for the time of arrival. See attached picture.
I do not understand why the integral
\begin{equation}
\int_{-T/2}^{T/2} m(t-\hat{\tau}) \frac{\partial}{\partial \hat{\ta... |
I am looking to ways to store data points in the format $\left( x, y \right)$ where $x$ goes from $0$ to $255$, while $y$ can be either $0$ or $1$: (e.g. $\left[ 0, 1 \right]$ $\left[ 1, 1 \right]$ $\left[ 2, 0 \right]$ etc...). See graph below.
This is basically a clock (each "$x$" value is one clock cycle) recording ... |
I am trying to form a range-doppler map using dechirped signals. I wanted know if there are any resources that provide and explain the steps taken to form the range-doppler map.
If there are or you could provide a simple flowchart to form the range-doppler map that would be very helpful. Thank you!
|
I have an acceleration measurement for a full day with sampling rate 10.24 Hz. I have divided the signal into 30 minute intervals because I want to compare the amplitude spectra for each 30 minute interval to other data I have for 30 minute intervals of the day.
I have not used any windowing, overlap or derating of the... |
Sorry for asking this basic question, but I am new to signal processing and have this doubt for a long time.
I have been studying signal modelling and have
$$H(z) = B_q(z)/A_p(z)$$
where $A_p(z)$ represents the poles of the Filter's Transfer function.
When we increase poles, $A_p(z)$ increases in terms and the signal a... |
i am currently attempting system identification using the LMS algorithm. The input and the output data are available and are very noisy and consists of multiple frequencies. The input and the output data are shown below.
The LMS algorithm fails to converge, i.e., adapt to the desired output signal. See images below.
... |
I have two signals $x_1(t)$ and $x_2(t)$ both with a baseband bandwidth of $W$ Hz. $x_1(t)$ is transmitted over carrier frequency $f_1$ Hz, and $x_2(t)$ over carrier frequency $f_2=f_1 + \frac{W}{2}$ Hz. The received signal can be written as
$$
\begin{split}
r(t)=&\Re\left\{x_1(t)e^{j2\pi f_1t}+x_2(t)e^{j2\pi f_2t}\rig... |
I have created a 2D matrix with L as the number of samples and K as the number of chirps. Now I am trying to plot the Range-Doppler response which doesn't correspond to the correct range and velocity values defined in the parameters.
The formula to calculate the 2D matrix is correct because it's taken from one of the ... |
I am having trouble finding the frequency function that takes me from $X_t$ to $Y_t$ in the system stated in the title. $X_t$ and $Y_t$ are stationary stochastic processes and $e_t$ is zero mean white noise. If I didn't have $-18$ and the white noise it would be $H(f)= 0.4 + 0.9e^{-i2\pi f}$, but with them I am not rea... |
I'm trying to familiarize myself with the FFT modules on Python. I'm thus doing some tests with simple functions, and I'm having troubles with the simplest one : the FFT of a sine. It is extremely noisy, and the full spectrum is very dependent on the sampling rate, with some sampling rates resulting in fairly big spect... |
We have a signal constellation with decision regions given in the figure below and symbols are equally likely to be transmitted.
Now we have to find the average probability of error for a transmission system using this signal constellation, and the equations for the probability are as follows:
The part I'm confused... |
ARMA basically is an AR model which considers past inputs to the filter as well. But what is the benefit of taking past inputs to the filter if we are considering real-time processes which are all stochastic and we don't know the input signal among the noise that is coming to the input of filter?
|
I don't understand what stationarity of random process mean.
I know they're statistical properties that are time invariant but I don't have intuition for it and I don't get what that has to do with random process joint probability density function intuitively.
|
I am using cross-correlation for the purposes of image stabilisation. The images which I'm processing can sometimes be rather large. The contents of the image are often repeating patterns. For these reasons I'd like to leverage the Fast-Fourier transform in order to speed up computation time.
Currently, I am using the ... |
Assume that we got a sine wave function
$$u(t) = A\sin(2\pi \omega(t)t)$$
Where the frequency $\omega(t)$ changes over time $t$ and $A$ is the amplitude.
Assume that we apply that $u(t)$ signal onto a transfer function $G(s)$ and we receive the output $y(t)$ in the time domain.
Then our goal is to create the bode plot ... |
In the Non-maximum suppression algorithm, each pixel has a total of 4 directions since there are 8 neighboring pixels. But why there is not 8 directions instead, please? I see below there are 8 directions not only 4:
|
We have a DAC capable of being driven with IQ data (thus the bandwidth is $-f_s/2$ to $f_s/2$), and the task is to create an "arbitrary" BPSK waveform at IF. I think that means generating this waveform:
$$
y(t) = e^{j\left( 2 \pi f_c t + \phi(t) \right )}
$$
where $y$ is complex (the I and Q portion), $f_c$ is the carr... |
I'm working on a little audio/embedded systems project, and I'm using synthesis to generate waveforms and feeding them into DAC and speakers. Currently, I am able to produce sine waves of individual frequencies, and they sound decent.
Now I'd like multiple frequencies to play together, so that it sounds like a music ch... |
I am working through the proof that the DFT is symmetric from Lyons - Understanding Digital Signal Processing
I don't quite understand the use of the $N$ variable. My understanding is that in $X(N-m)$, it indicates the number of points of the DFT (e.g. we calculate the DFT for 16 frequencies, a 16-point DFT).
$m$ indic... |
According to this tutorial, by exploiting quadrature sampling with IQ signals, we then have the benefit that each ADC operates at half the sampling rate of standard real-signal sampling (This conclusion in the link is right below the Figure. 18). Why is that? It seems the bandwidth of the signal is the same.
|
I want to design a sinc filter in the time domain (a bandpass filter in the frequency domain).
I wrote test code in python to investigate, and would appreciate help understanding it and answer my question.
Here is my script in python:
import numpy as np
from matplotlib import pyplot as plt
fs=1200
ww = np.linspace(-4,... |
Since this question is book-oriented, I will kindly ask you to accompany it with a book that is considered by many researchers the bible of Digital Communication: Proakis - Digital Communications, one from the 4th ed, and another from the 5th ed.
Let
$$ x(t) = \text{Re}[x_l(t) e^{j2\pi f_0 t}]$$
be a filtered white Gau... |
We know that $Z^{-1}\left(\frac{z}{z-a}\right) = a^nu[n]$ if $|z| > |a|$.
In addition, $Z^{-1}\left(\frac{1}{z-a}\right) = a^{n-1}u[n-1]$ if $|z| > |a|$. This is the delayed version of the first one.
In acausal case, $Z^{-1}\left(\frac{z}{z-a}\right) = -a^nu[-n-1]$ if $|z| < |a|$.
But, I am confused about $Z^{-1}\left... |
We know that
$$x(t) \star h(t) = y(t) $$
and
$$X(\omega)H(\omega) = Y(\omega).$$
But in real world, $X(\omega)$ and $H(\omega)$ are DFTs. So to prevent circular convolution, we do zero padding before FFT.
When I want to get $H(\omega)$ from $Y(\omega)/X(\omega)$, I think circular convolution problem will be occurred.
... |
I'am getting Transfer function from FEM Model of Simply supported rectangular plate
i do random vibration input force $x(t)$ and measured displacement $y(t)$
In matlab, because that is noise free data, I obtain $h(t)$ from IFFT(FFT($y(t)$)/FFT($x(t)$)).
Transfer function in frequency domain is quite similar compared to... |
I'm trying to understand how I should create all these $z$ values.
Each $z$ values is equal to $z = e^{j\omega(i)T}$ were $j$ is the complex number (instead of $i$), $\omega(i)$ is the i:th wrequency in radians and $T$ is the sample time.
But when it comes it $z_1^{-1}, z_1^{-2}, z_1^{-3}, \dots , z_1^{-p}$. How should... |
I am reading a paper Recovery of Future Data via Convolution Nuclear Norm Minimization. Here, I know there is a definition for convolution matrix.
Given any vector $\boldsymbol{x}=(x_1,x_2,\ldots,x_n)^\top\in\mathbb{R}^{n}$ with a certain kernel size $\tau\in\mathbb{N}^+$ ($1<\tau<n$), then its convolution matrix is gi... |
I'm trying to solve the following problem:
Consider a linear time-invariant filter with linear phase:
$$H(e^{j\omega}) = a_0 + \sum_{i = 1}^{N} 2a_k\cos(k\omega)$$
Determine the coefficients of this filter such that it optimally
follows
$$H_d(e^{j\omega}) = \left\{\begin{align}
0.2 \quad &|\omega|<\omega_1\\
1 \quad &... |
Can a sinusoid with unknown frequency be constructed from other sinusoids with known frequencies? Are there any theorems for this problem?
|
A pop-quiz featured a system analysis of the following system:
$y[n]=\sum_{n=0} ^{-\infty} x[n]$
The professor argued that this system exhibits the following properties:
Linearity
Causality
Instability
Memory
Time-invariance
In general the system seems nonsensical, as it sums all samples from the beginning of time up... |
I'm trying to learn about why signals that cross in an STFT cause apparent artifacts in the magnitude. I've been looking at the example below, written in python, where a gaussian peak overlaps with a sinusoidal wave.
import numpy as np
from scipy import signal
import matplotlib.pyplot as plt
time = time = np.arange(0,... |
This is what I am trying to achieve:
See how the increasing number of harmonics are creating a good fit?
I am trying to find the components of a given wave (discrete samples), and then to make brief prediction about where the curve is going from the generated cosines. Is it ok to use the inverse DFT and use the return... |
I have a convolution kernel which I need to apply to an image. However, at each pixel in the image, I'm convolving using a rotated kernel, with respect to the center (think hands on a clock, with the convolution kernel being stuck at the end, moving up and down the hands length). Is there a frequency domain equivalent... |
I am not seeing a direct pair of DTFT transform of the unit step.
|
The task is to downsample (aggregate) a raster from 100m pixel size to 460m. The aggregation should be performed using a Gaussian filter. To better understand the task, I am following the paper ‘The effect of the point spread function on downscaling continua’.
Most of the paper is irrelevant to my task, all I care from... |
The original signal is at a) in the image below, and I'm confused as to what the exponent on the dependent variable does to the signal, so can anyone point me to where I go wrong and how do I actually answer b), which is $y(n) = x(n^2)$ ?
|
What steps are necessary to get the same impulse as before a FFT + IFFT.
At the moment I am trying out my code a bit and would like to do an FFT from an impulse response followed by an IFFT to generate the impulse response again.
Actually I would like to change the frequency range a bit and look at the impulse response... |
I'm pretty confused about SQNR/SNR conceptually. I understand that this is a function of the power of the signal to the power of the noise. Is it not the case that we would be able to derive a value of SQNR from a graph of the frequency response?
The image states the SQNR is 55 dB but I don't see any reason why that w... |
I am trying to find the reverberation time of a room using the Schroeder method (i.e., Reverse-time integration method). Therefore, impulse responses should be measured first.
There are many ways to obtain the impulse response (IR) of a room, such as maximum length sequence, exponential sine sweep method, etc. First, I... |
$\DeclareMathOperator{\sinc}{sinc}\DeclareMathOperator{\asinc}{asinc}$I'm trying to follow the proof of the Fourier Transform for an Impulse train given in Julius Smith's textbook. I come across the following:
\begin{align}
(2M+1)\asinc_{2M+1}(2\pi f) &= \frac{\sin [ \pi f(2M+ 1) ]}{\sin(\pi f)} \\
&= \sum_{k=-\infty}^... |
I trying to measure the frequency drift between two N210 USRPs using GNURadio Companion.
I used one USRP as a TX and the other one as an RX. The transmitted signal is a complex sinusoidal.
The issue that I am facing is how to get the modulated signal from the TX before the transmission through the antenna. In other wor... |
I am working through the book Geometric Deep Learning (https://arxiv.org/abs/2104.13478) and have hit the following descrition of Rectified Linear Unit (Chapter 5.1, page 70).
Perhaps the most popular example at the time of writing is the Rectified Linear Unit (ReLU): σ(x) = max(x, 0). This non-linearity effectively ... |
Apologies if this has been answered already.
I am very new to computer vision. I am kind of familiar with object detection and classification for many types of classes, which involves training data with all the different classes, then detecting the object and at the end classifying.
However, my current problem aims to ... |
The dechirp-on-receive procedure returns near-range at a higher IF frequency than the returns from the far-range. How do I invert this spectrum so that near-range returns appear at a lower IF frequency than far-range returns?
I have attached a plot where the y-axis refers to the azimuth-time and the x-axis refers to th... |
From the definition, we will use wavelet for expanding signals the same way
Fourier series use sinusoids:
$$f(t) = \sum a_{l}ψ_l(t)$$
The definition then defines that if $ψ_l(t)$ form an orthonormal basis for the function space
then
$$a_l = \, < f(t), ψ_l(t) >$$
How is this second equation derived?
Here is the link for... |
I have a piece of raw accelerometer data consisted of 10,000 samples to be processed offline. Since the movement or rotation of the object is moderately slow and smooth, I would think that I can apply a strong filter to filter out as much noise as I could, and if necessary, I can re-apply the same filter to the alread... |
Page 5 in link:
For the scaling function, it holds: $\int \phi(x)dx = 1 $ or,
equivalently: $\Phi(0) = 1$
How is this derived?
|
I have tried to read MATLAB documentation for the fourier command, but there isn't any information on whether this command is applicable to discrete time. For example, if I record any audio signal into MATLAB using the process and commands mentioned here.
Will this recorded object recObj be considered as a continuous-... |
If you are using a kalman filter with multiple sensing sensors there are two ways to fuse them.
One way is doing a single observation step where you include all the sensors in a single vector and a joint observation noise covariance matrix
Another way is to update the state sequentially, once for each sensor.
I don't u... |
I am a chemical engineer so I'm not very familiar with the methods of signal processing. Nevertheless I need to apply them now on my thesis work. Most recently a question occurred to me, that is probably answered easily with a certain insight on signal processing and FFT.
Here is my problem: I am researching residence ... |
I was following this interesting post by a new user Rubem Pacelli and got stuck at Proakis' referenced definition (see Section 4-1-4 starting on page 159 here). The math, all repeated further below, makes sense to me but my intuition doesn't and was hoping to better connect the two. It is likely a deeper detail I am mi... |
Not a veteran in Signal Processing, it would be extremely appreciated to help me understand the idea/heuristic behinde the idea in STFT that
$$\text{nfft} \ge \text{window length}$$
At least from a statistical perspective, I believe it's an overfit to the estimate of each coefficient of each frame of STFT given the fol... |
I have the following binary mask (If it helps you can assume that every it is always 1px wide).
I want to travel from one given point to another (from start to end in this case). You are given the coordinates (green circles) but they're not in any particular order.
A naive way to do is by taking the next closest coord... |
I have an audio clip containing speech and noise. I want to separate the noise signal from the speech signal.
I've looked at some deep-learning based models, but they only remove the noise, without giving me the noise signal. I've also tried Facebook's Demucs, which performs well on music source separation but fails to... |
As defined in the CCSDS (section 3.1.2), the impulse response of the Gaussian filter is given by
$$
h(t) = \frac{1}{\sigma T \sqrt{2\pi}}e^{-\frac{t^2}{2\sigma^2T^2}}
$$
where
$$
\sigma = \frac{\sqrt{\ln{2}}}{2 \pi B T}
$$
$B$ is defined as
one-sided 3-dB bandwidth of the filter with impulse response $h(t)$.
What is ... |
I'd like to know if there is some general Fourier transform or other signal processing algorithm, such as a discrete wavelet transform, that is rotation equivariant.
Rotational equivariance of a function means that $g:\mathbb R^{n\times n}\to \mathbb R^{n\times n}$ means that if $R$ is a rotation, then $g(RX) = Rg(X)$ ... |
I have several browser tabs open indicating this question is "similar to" but I still don't get it. Suppose I sample a simple cosine function having frequency 40 Hz, i.e., $x(t)=a\cos(2\pi\cdot 40 t)$, for three seconds at a sampling rate of $f_s=100$ Hz. Then
I have $N=300$ data points with sampling period $\Delta t=.... |
I have a set of vector valued signals $\boldsymbol{y}_{1:T}$ where each $\boldsymbol{y}_k \in \mathbb{R}^{v_k}$. Each signal is potentially of different dimensionality. I'd like to apply filtering and smoothing in the usual Kalman case but I'm unsure how to get around the problem of each $y$ having a different length. ... |
I stumbled upon Hilbert transform when researching single sideband modulation. Apparently when the demodulator frequency is bit off by $\Delta f$, the signal after demodulation and low-pass filtering is not $m(t)$ where $m(t)$ is the original signal, but rather:
$$m(t)\cos(2 \pi \,\Delta f \,t) + \hat{m}(t)\sin(2 \pi \... |
A maneuvering target is flying in 3d cartesian space, but a sensor (passive infrared or mic array, etc.) can only observe it in polar coordinate with 2d orientations
(azimuth, elevation). For simplicity, there is only one target and one stationary observer fixed in origin coordinates. The question is what's the best wa... |
My goal is to take any image and break it down to obtain its time-varying equations so it can be redrawn and store the picture as two equations. One for $x$ and one for $y$.
As I understand, MATLAB's Discrete Fourier Transform breaks down images into their Fourier coefficients, so for a circle it would be easier to jus... |
Suppose I have a signal $x(t)$ with baseband bandwidth $W$ Hz and power $P$, and consists of $K$ samples, and I draw the two-sided power spectral density (PSD) of this [baseband] signal in MATLAB as
xFFT = fftshift(fft(x));
psd = (1/(fs*K))*abs(xFFT).^2; %fs is the sampling frequency
freqAxis = -fs/2+fs/K:fs/K:fs/2;
pl... |
I'm reading the original paper on PSOLA (Pitch-Synchronous Overlap-Add), and am struggling with equation (2), in which the authors analysed the effect of a simple pitch-and-time-scale modification on a stationary noise process $n(m)$, which is super-positioned on a periodic signal $d(m)$ with period $P$.
Here, the anal... |
I have an acceleration signal sample and I need to get velocity and movement spectrum (amplitudes and phases) from it. I try to solve this problem in two ways:
First method
Get FFT of acceleration signal.
To get velocity amplitudes I divide each acceleration amplitude by $2\pi f$ and subtract $\pi/2$ from each accel... |
Suppose I have a gaussian impulse like in the picture below, given by
$$Ae^{t^2/\sigma^2}e^{j\omega_0 t}$$
I can do an FFT, add a quadratic phase to it and go back to the time domain. This will result in a chirp as we see in the orange line.
I've always had the intuition that Fourier Transform gives you the amplitude ... |
From this page: https://community.sw.siemens.com/s/article/window-correction-factors there is a list of correction factors for popular windows. Is there a correction factor for Tukey window, depending on factor for the Tukey-window? Have not found this as yet.
|
I haven't touched my signal processing courses for a long time and I forget how to work with these kinds of signals.
I have a signal that comes from a sensor that has 3 time periods.
The time vector of my signal is described by something like this:
\begin{bmatrix}
\begin{align}
&t\\
&t+T_0\\
&t + T_0 + T_1\\
&t + T_0 +... |
Suppose we have 2 different levels of a quantized signal.
Let's say that the range is $[-1,1]$. The number of bits necessary to encode these levels is$\log_2(2) = 1$. However if the value of the analog signal $x(n)$ is exactly equal to $0$, then can we choose freely to encode it as $0$ or $1$?
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With regard to delta-sigma modulation, I understand that SQNR is the ratio of the signal power within our frequency bandwidth to the noise power within our bandwidth (in-band quantization noise). What I don't understand is how this is functionally different from SNDR (signal-to-noise distortion ratio). Is there even a ... |
Setup
I'm estimating the phase velocity in a wooden table by using an actuator and 3 sensors. The actuator sends out a chirp and on the table there are 3 accelerometers with distance $d$ between them. I am using chirp compression to make it "easier" to work with. Then I look at the chirp compression from sensor 1 and s... |
I have been trying to understand certain aspects of FIR filter design which have frankly annoyed me for some time such as exactly why the critical frequency $\omega_c$ in a low-pass FIR filter is mapped to the $-6\;\text{dB}$ point for a non-ideal low-pass FIR filter and also why the critical frequency is mapped to poi... |
I am a statistician by training, and I am very new to signal processing, but I would appreciate some help and patience!
Suppose I have a digitized signal measured at a given frequency, range, resolution (in bits), and step size ($\text{range}/ 2^\text{resolution}$).
I want to compute a summary of the signal (the summar... |
I am working with a PDM digital microphone and I've sampled the data using a FPGA.
For the beginning I am working in python to do all the algorithm, then I will implement it in FPGA.
I am using two LPF filters using firwin and remez functions for testing by now, and as far I understand the audio baseband pass without a... |
I am looking for a python code to double integrate signals in the time domain using Fast Fourier Transformation (FFT).
The idea is to apply FFT to the signal data in the time domain. Then dividing the transformed data by FFT scaling factor (time-integration property of FFT) in the frequency domain. After that, applying... |
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