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I've come across this equality that I don't know how to prove. I've tried using the delta function due to its relationship to the step function, but I can't reach any results.
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In Forney’s MLSE paper (link: https://ieeexplore.ieee.org/document/1054829), Forney mentioned that the matched filter output is still sufficient statistics even with ISI (second column on page 365).
I understand that a matched filter output is sufficient statistics when the channel has no ISI but only AWGN at the recei... |
I am tasked in an assignement to select an appropriate rate 1/2 convolution code for a QAM modulated transmitter with the following setup,
However, from my understanding of codes and modulation they can be viewed as individual blocks so it shouldn't matter which code I would select. So I should just select the best BE... |
A digital signal $x[n]$ is zero at odd sample numbers and one at even sample numbers.
What will be the value of this Signal at $n = \infty$?
Not exactly sure, but I thought that infinity (as a integer), has equal probability of being even/odd. That's why the signal should equal $1/2$ at infinity. But, my college mates ... |
I have a gray scale image of fibres in different orientations. My goal is to mark the area where the fibres have a specific angle and neglect the rest. In the future it should be an automated process with similar images but different width of the areas to mark. That's my input image with the marked area to extract:
At... |
Imagine someone had a signal of 32 samples. They cut it to two 16 sample pieces, converted to DCT frequencies, using DCT4.
What I get is these two arrays. My goal is to get a x2 higher freq resolution DCT, x2 less time resolution. Of course, I can convert these two pieces back to time domain, concatenate them to get 32... |
Coming from my previous question (link to this here). Given the following transmitter design,
with these parameters,
bit rate of 55 Mbps
maximum bandwidth of 17 MHz
code rate : 1/2
minimum SNR to design for 10dB
maximum SNR to design for 80dB
maximum data block length 256
decoding with Viterbi
How can I determine wh... |
I have an EEG recording of duration $2\text{s}$ with sampling rate $f_s=200 \,\text{Hz}$ and, as a mathematician, wish to familiarize myself with some of the standard terminology in signal processing. I've computed the DFT, it's magnitude squared, and the power spectral density using the periodogram.
First, the DFT, wh... |
Many modern digital communication systems repeat a preamble at the start of a frame/burst which is used by the receiver for timing and frequency synchronization. One example is 802.11a. Why are the preambles repeated versus using a non-repeating synchronization sequence? I can see how the repetition aids in a larger ca... |
The sound of the piano is something very complex. There are various elements to consider such as action, hammer, soundboard, sympathetic resonance, tuning age and even room reverb.
Some companies (such as Yamaha, Roland, Viscount and Modartt) have succeeded in realizing a realistic piano tone using physical modeling sy... |
I have a noisy signal around $15\text{s}$ long sampled a $32\,\text{Hz}$.
I am trying to estimate the peak frequency or period for a low frequency component with expected frequency in between $0.08\,\text{Hz}$ and $0.2\,\text{Hz}$.
Empirically I find easier to find such a peak in the time domain by measuring the lag at... |
I am into analyzing EEG signals with the help of this guide. So, I choose to inspect power in a frequency region before and after an event of interest (at t=o) and obtain the following plot:
How to make sense of the blue shade corresponding to negative values? Power can only be positive!
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The Wiener–Khinchin theorem states that the power spectral density of a wide-sense stationary stochastic process can be obtained through the Fourier transform of the autocorrelation of the signal i.e.
$$ S(\omega) = \int_{-\infty}^{\infty} R(\tau) e^{-j \omega \tau} d\tau $$
I would like to find out what happens when I... |
I read an article from T-Mobile link where they claimed a 3Gbps speedtest with the aggregation of 3 three bands in 5G.
How it is possible to make 3 Gbps with a 210 MHz bandwidth and using 256QAM in 5G?
210e6 x 8 = 1.680e9
|
The cross-correlation between two signals can be calculated using $\texttt{IFFT}\left(\texttt{FFT}(a) \cdot \overline{\texttt{FFT}(b)}\right)$ for two binary signals $a$ and $b$.
How could one speed up the calculation if you want only the first $n$ elements of the cross-correlation? In my case $n$ is much smaller than ... |
I am trying to write audio and image filtering together code in my project.
Purpose: The main aim of this project is to combine audio with image filters; like for example passing low frequencies of an audio signal while decreasing the brightness of an image, and passing high frequencies while increasing the image brigh... |
I have a rather simple question, sorry in advance if it's too easy. I'm working on a waveform generation project on MATLAB. When I look at the examples, I see that the time variables are defined like this;
t = 0:1/fs:T-1/fs;
What is the point of -1/fs?
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I have two signals $x$ and $y$ (blue and red one)
the Pearson coefficient between them is 0.9659
The yellow signal is the ratio: x/y*mean(x)
The two signals are almost perfectly correlated. How can I have that sine curve?
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How can get the difference equation of a $\mathcal{Z}$-transform transfer function with time delay? How does a time delay influence the difference equation?
For example:
$$H(z) = \frac{8z^{94}}{z-0.9}$$ where $H(z)=\frac{Y(z)}{U(z)}$
I want to get the difference equation in terms of $y[k+1]$
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I'm making a basic symmetric decimating half band filter (M=2), with alternating 0 coefficients. The signal is oversampled by a factor of 2, at frequency $f$. I must be missing something simple, but it seems like the oversampling is redundant as the samples are never used in the output of the FIR filter.
I've tried to ... |
I'm hoping to put together a cheap modulation monitor for wideband FM radio using an rtl sdr usb, on the FCC website, it's listed that the modulation percentage for an FM station is the actual frequency deviation over the max allowable frequency deviation expressed as a percentage. I was hoping to avoid using the bess... |
I am working with PWM signals. These signals are generated by comparing a modulating (at frequency $f_m$), and a carrier (at frequency $f_c$), as shown in the following image:
In the resulting spectrum, there are baseband harmonics (at frequencies $n \cdot f_m$; $n \in \mathbb{N}$), carrier harmonics (at frequencies $... |
Given
$$x(n)=\left(\frac{1}{3}\right)^{n}u(n)-\frac{1}{5}\left(\frac{1}{3}\right)^{n-1}u(n-1)$$ the input to a LTI system, and output
$$y(n)=\left(\frac{1}{4}\right)^{n}u(n)$$
Find impulse and frequency responses.
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I'm working on an audio plugin which splits audio into frequency bands for individual processing. The filters must have zero latency, so no linear phase filters.
I would like to have perfect reconstruction in the magnitude spectrum, so that when you add together the lowpassed and highpassed signals, you get a perfectly... |
As I understand, by using multiple carriers, OFDM can mitigate the effects of multi-path delay as the symbol duration is larger than the delay.
In this case, why do we still need to add cyclic prefix in OFDM?
I have looked into several related threats but cannot find a clear answer.
|
Suppose we are studying a dynamic system believed to be well modeled via
$$
x'' + \frac bm x' + \frac cm x = \frac Fm$$
$x''$ - acceleration
$b$ - damping factor
$c$ - spring rate
$F$ - external force.
I remember studying - but can't find my notes - a formula for estimating $b/m$ and $c/m$ from eyeballing a step respon... |
I am an engineering student. I have some data stored in matlab. I need to build low pass filter to process my data. How can I write the transfer function? In my understanding transfer function is the output divided by input in laplace transform. But now I only have data, not function for input. My out put will also be ... |
I was reading a paper where they applied a hysteresis thresholding to help with segmentation of vessels in an image. It provided a formula to determine how to select a hard threshold (Th), which represents pixels with a high probability of being blood vessel pixels and a weak threshold (Tw), which keeps all the pixels ... |
What I need is to invert a signal (on spectrogram it would look like a vertical flip) of a WAV file. Actually, of a bandpass of a signal - from 500 to 800 Hz, for example.
This image will perfectly explain what I mean:
I am using C#, NWaves and R language (seewave library). But I can consider any language, tool, libra... |
Why does drawing bode plots on poles or zeros give different results?
For example I have a transfer function, I could write it for pole as $$\frac{1}{\left(1+\frac{s}{\omega_0}\right)} \tag 1$$ or write it for zeros as $$1+\frac{s}{\omega_0} \tag 2$$ Here are the plots for pole and zeros:
($\omega_0=3$ in this plot)
H... |
I am using PyWavelet to do continous wavelet transform of a 1D signal. The pywavelet continous wavelet transform function works with this line of code:
coef, freqs=pywt.cwt(signal, scales, waveletname)
As explained in the documentation https://pywavelets.readthedocs.io. However, from here, I do not understand what the... |
I am trying to use
$$
f(x, y) (-1)^{x + y} \Leftrightarrow F(u - M/2, v - N/2)
$$
to post-process the result of a Fourier-based filter operation, like so
engine.run<Dft::Direction::Backward>(size, input<0>(args), output_buffer.pixels().data());
auto sign_row = 1.0f;
for(uint32_t row = 0; row < size.height(); ++row)
{
... |
I am doing some analysis on a received OFDM signal using USRP N210 with GNURadio. Figure OFDM RX shows the OFDM receiver (please refer to GNURdaio workshop slides) . The transmitted OFDM signal is generated from another N210 USRP.
To do phase measurements, I used Complex to Mag Phase block after the OFDM serializer and... |
In GPS IMU nav systems Velocity and angular position are not explicitly measured states yet at each timestep it's necessary in order to integrate IMU information.
I'm curious how is this dealt with?
Is it computed via linear interpolation or is something else done? Sames goes for EKF based SLAM systems.
|
I have a problem to evaluate the PSD from auto-correlation.
As you know, PSD is the Fourier Transform of the auto-correlation.
But I observe the spur at PSD when I calculate the auto-correlation with down-sampled data.
Let me explain my code shown below.
import numpy as np
rntau = np.append(rntau, np.mean(phase[:R_siz... |
I am trying to cross correlate the short preamble of an OFDM transmission. This is the preamble I am using:
0.046 # I
0.046 # Q
-0.132 # I
0.002 # Q
-0.013 # ...
-0.079 # ...
0.143
-0.013
0.092
0
0.143
-0.013
-0.013
-0.079
-0.132
0.002
0.046
0.046
0.002
-0.132
-0.079
-0.013
-0.013
0.143
0
0.092
-0.013
0.143
-0.079
-0.0... |
I was using Scarlet 2i2 audio interface plugged into an Android phone. Monitor headphones on the interface sounded great! I recorded a WAV file of a kids' concert with the USB Audio Recorder Pro app, which is designed to get audio from AIs via USB.
I've done this before and everything worked great. This time something ... |
I have a real world system I am analyzing consisting of actual mechanical components that oscillate by rotating back and forth in a fixed axle (kind of like those finger fidget spinners but my system oscillates back and forth in its rotations within an angle bandwidth instead of endlessly rotating in the same direction... |
I am probably going about this completely wrong, but I'm trying to implement a filter bank in reaper's JSFX as follows: First, split the spectrum into half (via aritmetic and a fo-lpf), then split each half in half, and etc until I have 32 bands at the right half of a buffer. The problem is, listening to the intermedia... |
I have recorded the two words "Stop" and "Go" in the waveform. There is an orange waveform and any normal assumption would be the noise picked up by the receiver, but my professor asked "If the orange waveform is indeed noise, why is it not mixed up with the original signal and have stood out like a separate signal?"
... |
I am using MATLAB to simulate the DUC and DDC process of USRP N210. I have encountered some doubts. As I understand the DUC, the sampling rate of the incoming signal is set by the user (e.g. 12.5M). USRP first buffers the signal through a FIFO and then reads the signal to the interpolation filters (DUC) with the same ... |
In MATLAB, I have generated an FIR low pass and high pass filter of order 16. The code is as follows:
filter1 = fir1(16,400/16000,'low') %%pass band-400Hz, Sampling frequency-16000Hz
filter2 = fir1(16,800/16000,'high') %%pass band-600Hz, Sampling frequency-16000Hz
The sum of coefficients of low pass filter adds to 1 ... |
If I have a system with the output: $$y(t)=x(t)+0.7x(t-0.4)$$ For $x_2(t)=\cos(56t)$, how can we write $y_2(t)$ in the form $y_2(t)=A\cos(\omega t+B)$ and calculate the unknown values A, B and $\omega$?
My 1st attempt:
I have written $y_2(t)$ as $y_2(t)$ = $x_2(t) + 0.7 x_2(t-0.4) = \cos(56t) + 0.7\cos(56t-22.4)$ and k... |
I am using the following code to generate an allen variance plot from some accelerometer data
https://github.com/nmayorov/allan-variance/blob/master/allan_variance.py
It seems a sound implementation looking at Allan variance definitions I can find online
How do I interpret this graph?
|
I received this as a practice problem (part b only).
I was able to figure out that $E[Z^2(t)]$ = $R_X(0)+R_Y(0)-2R_\text{XY}(0)$ but did not see how to continue.
Checking the answers, I saw this line of reasoning:
Both steps do not make sense to me; it seems as if a few steps that should have been in between were lef... |
I am solving an L1 regularized least squares of the form like:
$$ \arg \min_{\boldsymbol{x}} \frac{1}{2} {\left\| A \boldsymbol{x} - \boldsymbol{y} \right\|}_{2}^{2} + \lambda {\left\| \boldsymbol{x} \right\|}_{1} $$
I saw that for the L2 norm case there are several methods to obtain the magnitude of $\lambda$ as seen ... |
From what I know about root locus is that if all roots are located on the Left Half of the S-plane the system is stable. That's why I expected the unit step response of a system to be stable.
Transfer function:
$$ G(s) = \frac{1+s}{s(s+1)^{2}} $$
After I plotted the locus and step response in Matlab, I got stuck.
Ma... |
I have a complex bandpass signal. I need to upconvert it from 230.4 Msps to 245.75 Msps, i.e. by a factor of 16/15. What would be the best way to do it?
|
I'm a DSP newbie trying to get into the field. Despite being able to use some of the MATLAB tools, I'm still not completely solid on some intuition of the frequency domain.
I've implemented a biquad Chebyshev type 2 filter in direct form II using design() and fdesign(), and cascaded an all pass filter before it to make... |
I have been trying to solve the following problem. I have a DSP algorithm where these variables occur:
$$x(k) = \cos[\theta(k)],\quad y(k) = \sin[\theta(k)]$$
I have recorded both of them and I would like to determine their frequency using offline processing.
The first way I was able to come up with until this moment ... |
I want to find the median frequency from the FFT result. All I have is binned data I got from FFT (An array).
I'm doing this calculation in C, so I don't have access to the statistic tools from MATLAB or Python. I can't figure out the calculation to the median algorithm. How can I find the bin containing the (estimate)... |
Moving average system……………………….
How to solve this one?
|
Up until now, I have dealt with finding Fourier Coefficients for functions: $f(t) > 0$
Which made it convenient calculating the Fourier Analysis Integral. However, I am now presented with functions: $f(t) < 0$
My question is, would I need 3 different bounds when performing integration for this particular function? ... |
I have an object moving with sinusoidal motion. I estimate the position of the object using lidar and camera separately. Then I want to fuse these two estimation data in the optimal way. For example I apply Kalman filtering to lidar data and I get estimated position and variance. This same process can be applied to cam... |
accf=fft([zeros(1000,3);acc;zeros(1000,3)]);
cutoff1=0;
X1=[0,0,0;
zeros(round((size(accf,1)-1)/2*cutoff1/50),3); %% 50 ??
ones(ceil((size(accf,1)-1)/2)-round((size(accf,1)-1)/2*cutoff1/50),3);
ones(floor((size(accf,1)-1)/2)-round((size(accf,1)-1)/2*cutoff1/50),3);
... |
I considered a time sequence of sine wave t = [0,0.707,1,0.707,0,-0.707,-1,-0.707]
I took spectrum = fft(t) and got the spectrum. I then gave spectrum_shifted = fftshift(spectrum) to the spectrum and obtained a zero frequency point at the center of the spectrum.
Now, I want to get back to the time domain and reach t, ... |
I'm new to signal processing, and I believe to understand what additive noise is. However, while reading several ECG denoising papers, I've noticed that some combine multiple noise sources from the MIT BIH Noise Stress Test database. For example, in here and here.
I'm also considering that applying a single noise sourc... |
My text book, Communication systems by Simon Haykin says
Block codes in which the message bits are transmitted in unaltered form are called systematic codes.
I am not getting what it means. A diagram is given below the statement in which parity bits are left of the message bits.
Are the following forms valid?
1)\begi... |
I’m trying to gain a deeper understanding of what the cross-spectral density of two signals represents. I know how to compute it, and I know it represents a covariance of sorts, as it appears in the formula for coherence. It’s the nature of the “similarity” that I’m unclear about.
As an example, I'm sampling from two ... |
With sampling modeled as a multiplication with a dirac comb, we can recover the original signal perfectly with a low pass filter given that the sample-rate criterion is satisfied.
What about a more practical case where the signal is sampled with a pulse train, and not an impulse train? E.g. rectangular pulse train with... |
I have the sample set of ideal and real secondary current during CT saturation, need to apply the DFT analysis to samples and estimate the fundamental phasor (magnitude and phase angle) of samples:
I am far from digital signal processing but I suppose the main idea is to perform computation at each sample $m$ on the b... |
I want to track the movement of a person in a 2D plane using a 9-axis IMU. The size of the plane in which the movement is not bigger than 6 by 6 meter.
The IMU is mounted on the head of the person and there is unfortunately no possibility to add other sensors or change the sensor location.
The IMU provides acceleration... |
I'm having a lot of fun writing signal processing code in Python / numpy, and I'm resisting the urge to pre-optimize the code. But my biquad implementation is slower than I want. Here's the inner loop -- it uses afor loop: is there a way to vectorize it? Alternatively, could I use a scipy filter, and if so, how do I... |
I've just been working through the questions in Discrete-Time Signal Processing (Oppenheim and Schafer) and I came across this (Q33):
Consider an LTI system defined by the difference equation $$y[n] = -2x[n]+4x[n-1]-2x[n-2]$$
...
(b) Determine the frequency response of this system. Express your answer in the form $$H(... |
I have some problems with the error estimation of a frequency response measurement. The measured transfer function $H$ has to be fitted to a model $$H=A+i\omega B,$$ where $A$ and $B$ are the unknowns and $\omega=2\pi f$ ($\omega$=angular frequency).
In the model, $A$ represents a stiffness and $B$ represents a damper.... |
I have a question regarding the capabilities of the discrete Kalman filter for estimation of the unmeasurable state variables of a dynamic system.
In the time being I have been using a discrete Luenberger observer for estimation of the unmeasurable state variables of a dynamic system. The observer provides pretty good ... |
I'm new to DSP and I'm interested primarily in the implementation of audio filters. I've been reading about FIR filters as they seemed like a good place to start but now I'm stuck. I've written some code that implements a basic FIR filter and to test it I've tried out a low-pass filter. As far as I can tell it works bu... |
So I took this digital LPF from some website:
And tried implement it first in MatLab to see how it goes, here's the code used:
x=[0 0 0 0 0 0 0 0 0 0 0];
y=[0 0 0 0 0 0 0 0 0 0 0];
t = linspace(0,1,100);
%a = sin(2*pi*0.1*t)
%plot(t,a)
yy = zeros(1, 100);
for c= 1:100
x(1) = sin(2*pi*1000*t(c));
y(1) = ((1.*x(1)+2... |
I am trying to compute the PSD of a signal in MATLAB using Welch's periodogram method as shown in the code snippet below.
sine = dsp.SineWave('Amplitude',1,'Frequency',10e6,'SampleRate',fs,'SamplesPerFrame',1000000);
y = sine();
nsc = 500000; % 5000 50000
nov = floor(nsc/2);
nff = max(256,2^nextpow2(nsc));
[pxx, f] =... |
I'm trying to implement a digital filter that has the frequency response shape equal to the image below:
Where i will use equation (11) to implement it with a sampling frequency of 48kHz.
The filter coefficients can be found in the same document:
Where each w' follows the formula above.
So i put everything into mat... |
Let's say I would like to use the discrete version of the Kalman filter in a role of a state observer of a linear dynamic system. The observed continuous time domain dynamic system can be described with following state space model:
$$
\begin{eqnarray}
\dot{\mathbf{x}} &=& {\mathbf{A}}\cdot{\mathbf{x}} + {\mathbf{B}}\cd... |
I'm coding the amplitude spectrum plot of a square wave signal with the following relation@
|(=3,5,7,...)|/|(=1)|∝^
where I've already calculated the constant by taking the signal FFT and fitting the peaks. However, I'm having trouble figuring out what the amplitude is to plot in this case - any insight would be appr... |
I am new to signal processing, but I have background in mathematics. I am trying to use Bluetooth Low Energy (BLE) on three mobile devices, where one device is being tracked and the other two act as antennas. I would like to compute the angle of arrival to compute the position of the device.
To do this, I have found th... |
I have a signal which has human speech, background voice and noise as it can be seen in below figure.
I have calculated its power spectral density (PSD) using many different methods which can be seen in below figure.
As far as I guess, peak regions which are spotted in red rectangle on the PSD belong to harmonics of th... |
I'm trying to classify a stimulus-response relationship and would like to fit a filter that best explains the response. I don't really work in DSP so there may be some vocabulary I'm missing, but searching for filter fitting methods is only redirecting me back towards filter design. The best solution I can come up with... |
Excuse my silly question, but I think the energy increases as the sampling rate increases. In the time domain, the number of samples increases so the energy increases; In the frequency domain, doubling the sampling rate also increases the amplitude of the spectrum, thus doubling the energy. But the sampling rate doesn'... |
I am currently attempting a project of plasma analysis. One of the aspects of this project is to determine the stability of the plasma, when a plasma is unstable it loses its shape partially or starts bending.
Some examples here.
I have attempted to use OpenCV contours and matchShapes modules. The contours were able to... |
Fourier transform can be used to analyze the frequency domain of a specific period of signal. However, I saw many of these transforms in textbooks are based on entire signal sequences, not processing them on a serial manner. For example, we have a sequence $x[n]$ and we can transform this sequence to $X[k]$. But many s... |
I have been working on a Scilab simulation of the discrete Kalman filter which is used as a state observer of the
linear dynamic system. The Scilab script for the discrete Kalman filter is as follows
function [is_alpha_estimate, is_beta_estimate, psir_alpha_estimate, psir_beta_estimate] = MachineModel(vs_alpha, vs_beta... |
I am very new to the area and I have a question. I came across this example, I'd appreciate it if anyone could clarify this for me. In the paper it says:
For example, we assume a multiple access scenario with 4 activated users $\mathcal{X} = \{1,2,3,4\}$. The equivalent transmission powers of 4 users are assumed as $P... |
I'm trying to understand the Fourier series coefficients of the sum of two discrete-time periodic signals.
Consider two discrete-time periodic signals $x[n]$ and $y[n]$. $x[n]$ has period $N$, its Fourier series coefficients $a_k$. $y[n]$ has period $M$, its Fourier series coefficients $b_k$.
According to this problem ... |
Objective:
Estimate the mechanical tension of a cable using the velocity of the waves travelling along it.
Experimental setup:
I have a cable in tension equipped with accelerometers. I measure a strong cross-correlation between the sensors which corresponds to waves propagating along the cable.
Tension measurement:
I h... |
I have a signal constituted by known OFDM symbols, and my goal is precisely estimate the Sampling Time Offset (STO). However, while the STO in the context of a single-carrier modulation is pretty clear in my head, its effects on an OFDM symbol and how to estimate it remain a mistery to me.
From what I've been able to r... |
I am trying to understand the full mathematics behind FMCW. Using linear-frequency chirp $x(t)$ that has center frequency $f_c$, bandwidth $\Delta f$, duration $T_r$, and amplitude $A$, the transmitted chirp is
$$x_T(t)=A\cos\left(2\pi f_c t+\pi\frac{\Delta f}{T_r}t^2+\phi_0\right)$$
The received signal reflected from ... |
I have a 2D signal, and I want to compute a new signal by calculating a weighted mean of each sample's neighbours. However, I also have a 2D bitmask, the same size as the original signal, which indicates that samples in certain positions should be ignored in any average they appear in, including not being counted in th... |
I'm a mathematician seeking to improve my conceptual understanding of what the coherence between two signals, $x$ and $y$, represents. I know it's analogous to a linear regression coefficient, in that it's calculated by computing the magnitude-squared of the cross-spectral density, $P_{xy}$ and dividing the result by t... |
I am trying to model the response of an amplifier. As per the main answer on this question, if one wishes to do so, they have to look at the Fourier decomposition of the input signal $x(t), \, \tilde{x}(f)$ in relation to the Fourier decomposition of the output $y(t), \, \tilde{y}(f)$. The amplifier response $H(f)$ con... |
I am very new to the concept of Fourier transforms and DFTs so please explain in as simple terms as possible.
I am messing around with Fourier transforms in processing. I wanted to determine the average wavelength of an input - trigonometric or otherwise.
void generateHeightsCos()
{
heights = new float[xResolution][y... |
In 4G LTE/5G NR, the modulation schemes 8-PSK (which is an intermediate scheme between QPSK and 16 QAM) ,32-QAM (which is in between 16 and 64 QAM) are omitted. If the channel is bad , or the distance increases between user and base station, from 16 QAM, the user/Base station fall back to QPSK. I feel an intermediate m... |
I have a wide sense stationary stochastic process ${{X_t;t\in \Re}}$ with mean 0 and autocorrelation function $R_x(\tau)=1-\frac{1}{4}|\tau|$ for $|\tau|=0,1,2,3;$ and zero anywhere else. I'm supposed to calculate the linear minimal mean square estimator (LMMSE) of $Z=\frac{1}{2}(X_t+X_{t-1})$ based on $(X_{t-2},X_{t-3... |
There are few notes online stating that an all-pass filter is a maximum phase filter (e.g., Link). The core of the claim is that an all-pass filter is a maximum phase filter since its zeros are outside the unit circle, which is the definition of a maximum phase filter.
However, according to the MIT lecture note, a maxi... |
I have been solving following problem. I have two open loop state estimators used for estimation of the unmeasurable states of a given linear dynamic system. The first estimator provides estimate $\hat{\psi}_{r_{{\alpha\beta}_i}}$ which is accurate at low frequencies and inaccurate at high frequencies. The second estim... |
Solving for ill-posed linear models, I saw that Maximal entropy is also parsimonious and in that regards similar to L1-sparsity promoting regularization. How is it different and are they interchangeable ? is it the entropy maximization always convex?
In the L1 case I use PBDM to minimize the combined terms looking for ... |
I'm trying to understand how American FM multiplexing works. As I understand it, your average FM signal can be made out of:
The mono "sum" channel from 30 Hz to 15 kHz, made out of left + right
The stereo pilot tone at 19 kHz, indicating the FM station is in stereo
The stereo difference channel, made out of left - rig... |
I have just started trying to self-study an intro course on signal processing. I have just been introduced to the periodogram and have a hard time understanding why completely different signals can sometimes have the same periodogram. Take for example the two signals in the below image:
It is stated that these two sig... |
If I perform a FFT of a real signal which is limited on time (for example the atmospheric pressure in time from 0s to 5000s), is it possible that the fact that is limited on time can affect the FFT results? I read this thread and I don't know a priori how many cycles can fit inside it. Is it possible that spectral leak... |
I was able to demonstrate that for a signal $x(t)$ real, we can write the truncated Fourier series as:
$x_N (t) = A_0 +\sum\limits_{k=1}^{N}A_k\cos(kω_0t + \varphi_k)$, but now I've been given the signal shown below:
And now I have to find the values of $A_0, A_1, A_2, A_3, A_4, A_5, A_6, A_7, \varphi_1, \varphi_2, \v... |
This paper gives a spectrum analyzer using the multirate filter bank technique. The basic idea of the paper is that STFT can be interpretated as a uniform DFT filter bank. But the baseband filter of DFT filter bank has strong sidelobes. So it tries to design a prototype filter with better passband and stopband response... |
I studied Kalman filters some time ago, and recently came to realize I do not understand some parts on them. Specifically related to the difference between
using a static Kalman-gain, found by solving the Riccati Equations
Using a recursively updated/dynmamic Kalman-gain, by applying this scheme
I have some questions... |
What is the energy ratio of signal at frequency domain?
What is its mathematical formula at frequency domain and what can stand for?
I found it in this paper
https://www.researchgate.net/publication/332075345_MVMD-MOMEDA-TEO_model_and_its_application_in_feature_extraction_for_rolling_bearings
and also I found this Matl... |
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