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Considering a finite-length impulse response $h[n]$ of length $M $ (which amounts to considering $h[n] = 0,$ for $n \geq M$). The data model, with additive disturbance, is then written as:
$$y[n] = y_M[n] + \epsilon[n]$$
where
$$y_M[n]= \sum_{k=0 }^{ M-1} h[k]x[n-k].$$
We seek to estimate the impulse response $h[n]$, i... |
I am currently working on a project which requires evaluating slow changes over time in the magnitude of a signal's high frequency (over 10 kHz) components.
This signal was acquired in tests with a 25.6 kHz sampling rate and in "batches": every minute, one second of data was acquired. This was done in order to save sto... |
This question is perhaps related to the semantics or jargon of signal processing. I have checked plenty of advanced books/monographs on multivariable calculus and signal processing but could find an explicit answer.
Suppose we have a simple function $y$=$\sin(x)$. In short, if we have sampled a sine wave as a function ... |
I am trying to understand a MATLAB code of convolution animation.
Please check above link especially code in lines 15 and 16. I think author has mistakenly swapped comments of line 15 and 16. Please correct me if i am wrong
I am also placing the code here
close all
clear all
clc
% Initialization
t = -400:400; % Time r... |
I have the transfer function: $$H(z) = \frac{z^2 + 0.75z + 0.125}{z^2+0.5625}, |z| > 0.75 = \frac{(z-0.5) (z-0.25)}{(z - 0.75j) (z + 0.75 j)}$$
I attempted partial fraction expansion in order to use my lookup table for z-transformations. The issue is my poles are complex conjugate pairs. I have never had to deal with a... |
I have a touch signal on a plate recorded with 3 accelerometers with a sample rate of 150kHz over a duration of 5 seconds (so 750k samples). The goal is to localize the position of the touch in the end. But for that, I need to separate the reflections from the direct wave. And therefore need to do some signal analysis.... |
I have a simple $0-40 \texttt{Hz}$ IIR bandpass filter.
With pure sine inputs I see $60 \,\texttt{Hz}$ is completely gone in the output FFT as expected by looking at the filter frequency response.
However I fed it with non sine signal+noise (i.e real world recorded signal), and I see the FFT shows a peak at $60 \,\text... |
I'm implementing 2FSK and 4FSK modulation schemes for an experimental system. I'm using GNURadio, although that shouldn't affect the question.
I'm trying to figure out how the center frequency should be selected. Many 2FSK examples use a center frequency of 1700Hz, with a deviation of 500Hz, for a "space" frequency of ... |
I have an audio file that I encrypted and decrypted using the AES algorithm.
After the decryption is complete I output the audio file to a new file.
I wanted to calculate the root mean square between the original file and the newly decrypted file. It came out as 0. Why is that? Shouldn't the processing have introduced ... |
I have an In-phase signal collected by an FMCW radar. I am trying to reconstruct the analytical signal by applying the Hilbert Transform to the In-phase signal.
Are there certain conditions that need to be satisfied in order to correctly, reconstruct the analytical signal using Hilbert Transform ? If yes, could you lis... |
I'm studying for an exam and this is an old exam question that I don't understand:
Is the following system non-minimum phase?
$$G(s) = \frac{e^{-2s}}{s+2}$$
I can see that the real part of the pole is on the left half plane, but regarding the zeros I don't know what to do. If plotting $e^{-2s}$ it seem to never cross t... |
In this question the multiplication of two impulse functions is discussed
However, what if I have two shifted impulses say:
$z(t) = \delta(t-\tau)\cdot \delta(t-\beta)$
Now if I want to integrate $z(t)$ how would I go about it? Let's say the integral is:
$$\int_{-\infty}^{\infty}\delta(t-\tau)\cdot \delta(t-\beta) dt $... |
I have been reading a textbook on the "fundamentals" of signal processing but the author of the textbook has not given any explanation for the triangular graph located at the bottom of the figure.
I understand the general concept of aliasing, but I do not understand what exactly is being shown in the graph featuring t... |
https://www.youtube.com/watch?v=C_kwjJLepLg&ab_channel=NesoAcademy
Above youtube video mentions a tabular method for finding convolution in case of discrete time.
But i am bit confused? Is this tabular method only applicable to discrete time or is it also valid for continous time?
My own understanding is that this meth... |
I am considering an energy signal in MATLAB as I am going through the book Signals and Systems Laboratory with MATLAB by Alex Palamides.
My Matlab code is below:
clc;clear;close all
syms t T
x=heaviside(t)-heaviside(t-1);
d=int(abs(x)^2,t,-T,T);
Px=limit((1/(2*T))*d,T,inf)
Ex=limit(d,T,inf)
I have also attached of my ... |
Suppose we need to double the sampling rate of an audio signal.
Is adding a mean point between every two points a valid way of upsampling? If no, then why not?
For example, in images, pixels may be interpolated by averaging the extremes. Similarly, I imagine that in an audio signal, upsampling may be possible by averag... |
Here I have a diagram (at the bottom) and I am trying to create a difference equation for the filter.
I've been using practice examples to try figure this one out however I am unable to produce a complete difference equation.
For example:
x[n] ---| A |---+---| B |--- y[n]
z^-1 | z^-1
... |
I am trying to recreate the envelope function from matlab in python, but I have a problem with the initial values. I have a window of 1000 and the first 1000 values won't show up. Here is a snippet of my code with a picture from the result:
mean = np.mean(current_winners)
substract_current = [x - mean for x in current_... |
I am new to signal processing and I have likely a very easy question but I have found inconsistent answers everywhere.
When performing an FFT, does it matter what units the amplitude is in? Currently my input is in mV.
If I use mV for an FFT, then use it to get a spectrogram, what are the visual units (strength of sign... |
I am confused regarding the unit step signal. Is it considered to be periodic signal or non-periodic signal?
In MATLAB we use command heaviside to implement it but then that graph always shows a horizontal straight line after time is greater than equal to zero.
I am very confused. If it is periodic, what is its perio... |
The way of investigating the PAPR for OFDM system using MATLAB is known, but what I am looking for is: can we measure the PAPR effect in real systems?
For example, assuming we have a transmitter and a receiver. let's assume we have optical system, where the signal is transmitted through light source to the receiver dio... |
I am trying to replicate a spectrogram from MATLAB in Python. I've read other posts but they either don't use complex data or the data doesn't match between languages.
I've defined my FFT length (nff), sample rate (fs), overlap (nov) and window (hamming) to all be the same between MATLAB and Python.
Here is the spectro... |
I am trying verify the noise floor returned by Matlab sinad(). I am able to get the results matching by summing power spectrum density with $\frac{f_\text{s}}{N}$. But I am not able to match the results by following Parseval's theorem to root sum square the $X[k]$.
$$ S_1=\sum_{n=0}^{N-1} \big|w[n]\big| $$
$$ S_2=\sum_... |
For which values of step size $\alpha$ is LMS filter stable? I Wikipedia information on this question is incorrect.
For data sampled from zero-centered Gaussian in $d$-dimensions with identity covariance, we can show that LMS filter converges with probability 1 iff $\alpha<\alpha_c$ where
$d=1, \alpha_c\approx 2.421249... |
I’d like to know if it’s possible to calculate the RMS of a signal from its envelope which we can find from Hilbert transform?
|
I'm trying to do some example elementary denoising of the audio signal. Let's say input is speech with constant traffic background noise.
First I calculated block-based overlap-add Fourier transform (size 512) and continued in the frequency domain with the signal in[n].
Then I used minimum statistics method to estimat... |
I'm all new to wavelet analysis. I'm trying to get a working understanding of the continuous wavelet transform and its inverse.
By "working understanding", I really mean "getting some code to execute for 1D signals and have an intuitive understanding of what the result means".
I'm using the ssqueezepy library in python... |
I'm trying to make sense of different notations used in DSP. This is sometimes quite hard since notation brackets like in x[n] are used both to denote a single value or a sequence.
In mathematics, the generalized Iverson bracket notation is:
$$[P]=\begin{cases} 1 & \textrm{if P is true}\\ 0 & \textrm{otherwise} \end{ca... |
This is a follow up of my previous question Why is inverse CWT inexact / inaccurate?
Rephrasing its accepted answer in my own words:
The filterbank's transfer function gives information on what band of frequency is well represented using CWT. In my case, an important part of the spectrum lied in the not-so-well-recons... |
I've been trying to follow along with this example in the book "Understanding Delta Sigma Data Converters" and I am completely confused as to how the authors came about the appropriate values for the factors alpha, beta, and gamma.
It seems like the value of beta was found from dividing x2_max by x1_max and gamma was ... |
using python I have sampled a signal and made FFT to see the spectral picture of the time domain signal.
the plot bellow shows only 1st and 2nd nyquist zone.
I want to expend the spectral image and see the 3rd and 4th nyquist zones.
i have tried to double number of samples but it only expand the previos image two times... |
Suppose we have a system $S$.We give it the input $\delta(t)$ and get a response $S(\delta(t))$.If the system is linear and time invariant we can calculate every output $y(t)$ from any input $x(t)$ by finding the convolution of $x(t)$ and $S(\delta(t))$.But why does the system need to be time invariant?
|
Given a sequence
$$
x[n] = [0, 1, 2, 3, 4, 5, 6, 7]
$$
and its subsampling (by e.g. factor of 2)
$$
x_\text{sub}[n] = [0, 2, 4, 6]
$$
are $x_\text{sub}$ and $x$ related in spectrum? That is, given $X = \texttt{DFT}(x)$, is there an operation $\text{op}$ such that $x_\text{sub} = \text{op}(X)$? Can it also be described ... |
I was wondering how I would calculate the power of a noise, if I have a uniformly distributed white noise between $-\frac{q}{2}$ and $\frac{q}{2}$? My approach was to use the formula
$$\int\limits_{-\frac{q}{2}}^{\frac{q}{2}} x^2 \ \frac{1}{q} \ \mathrm{d}x = \frac{q^2}{12}$$
But I'm not sure if that is right. Or do I ... |
I am given a notch digital filter with the $z$-transform being:
$$W(z)=MF(z)F(z^{*})^{*}=M\frac{z-q}{z-p}\frac{z-q^{*}}{z-p^{*}}$$
where $M$ is the normalisation factor, $q=e^{-i2\pi\frac{f_0}{f_s}}$, $p=(1-\epsilon)q$ and $0< \epsilon \ll 1$. It is easy to see the zeros of this system are on the unit circle while the ... |
In order to get a better feel for phase response and how it applies across the field of dsp, I'm looking for example scenarios where a filter's phase response is a concern and where it is not.
Take for example the attached figure I've made. The graph compares an analog RC low-pass filter (S) with both its digital IIR c... |
I'm creating a RS(15,9) code and can't figure out how to determine when T>t (T>3) by using the syndrome components. I understand that to determine the error count you use the largest TxT matrix whose determinant is NOT equal to zero. However, by this logic, the only way to determine if T>3 would be to calculate the det... |
The following signal is an example of frequency shift keying. Let the
pulse rate be 100 bits/sec. If f1 = 1324 hz what should f2 be for the two tones
to be orthogonal?
I know that the formula to solve this is delta F = 1/2T, and I am given f1....what I am not understanding is what is T? Is it 1/pulse rate, which is 10... |
I am an undergraduate electronics engineering student taking a signal processing course this semester.
I have learned a lot of theoretical things in my lectures, such as how to shift or fold a signal, how to convolve 2 signals, how to take their Laplace or Z or Fourier transforms, but I want to build something useful i... |
I'm trying to perform a discrete convolution of two functions, $f(x) = 1$ and $g(x) = \exp(-x)$ of length nsize using FFTW. I have followed the procedure for zero-padding my data from here. My resulting values are qualitatively similar, but the magnitudes are way off from the expected result. I have attached the code I... |
Matlab command for inverse z transform iztransonly applicable for causal signals? or also valid for non causal signals?
Actually i want to find inverse z transform for the cases shown in attached snap and i am confused if iztrans command is applicable to all of them?
|
I am Ph.D in pure mathematics and interested in signal processing.
Theoretically, any illustration of the eigendecomposition of the discrete trigonometric transforms (DTTs) is worthwhile.
Q. What real applications can be followed by having the eigendecomposition of the discrete sine and cosine transforms? Any referenc... |
Does the Kramer-Kronig relations apply to this example $f(t) =\left(1-t^2\right)^4\cdot\theta(1-t^2)$?
with $\theta(t)$ is the Heaviside step function.
I made a detailed related question here with full explanations, where I got no answers, but the main doubt could be solved just by knowing if the KK-relation conditions... |
Suppose there's a vector of $d$ of positive numbers $x(1),\ldots,x(d)$ which I need to obtain from a vector of $d$ derived quantities $m(t_1),\ldots,m(t_d)$ where $\{t_i\}$ is some conveniently chosen vector of real numbers and
$$m(t)=\sum_{i=1}^d x(i)^t$$
Is there a practical way to obtain $x$ from $m$? For instance, ... |
I’m trying to simulate a TLL loop using Gardner TED. I set symbol rate is 1000 and 8 samples for 1 symbol. First I use Root-raised-cosine filter to shape the symbols, then I use interp1 in matlab to resample the signal to add sampling delay. And then I feed the signal to the match filter, then I downsample the signal t... |
Suppose I have a list of amplitude (straight line signal):
x = [1,1,1,0,1,1,1,1]
By intuition, zero value in list x makes the noise of straight signal.
If we modified some value, such as 2, we get more noise level.
y = [1,1,1,0,1,2,1,1]
Hence by my intuition, SNR of list x is greater than SNR of list y.
So how do I ... |
I want to find the transfer function h(t) of the below positive feedback system. I came out till this.
How can i get the inverse laplace of this function? say β = 1 and γ = 1
|
For a course that i'm taking im asked a question about the ambiguity function of a FMCW radar. However i have not found a good source for reading about this so don't quite understand it.
I get given the following cuts:
I understand it in the following way: If there are 2 targets, i cannot distinguish between them if t... |
I am having issues with my implementation of a FIR high pass filter. The low pass filter has an acceptable level of attenuation in the stopband, but the high pass filter has poor attenuation in the stopband. I have not seen any mention of this occurring in the sources that I read and I am unsure why this is occurring.
... |
I am currently trying to understand librosa.feature.melspectrogram in a mathematical sense.
In my understanding, spectrogram is based on the STFT which is for a given discrete time sequence $x[n]$ of length $L$, the value corresponding to a frame of $x[n]$ at time index $m$ and frequency index $k$ is
$$
X_m[k] = \sum_{... |
From what I know noise-canceling headphones generate sound waves that are 180° out of phase with the ambient noise. I understand that they are not effective at canceling out sudden and unpredictable sounds, such as a car horn or a dog barking, because there isn't enough time for them to process the sound and generate t... |
I have to apply a downsampling filter on a realtime data stream (signal) and I want to do it in python. The data is sampled at 16 kHz and loaded in a loop in chunks of 1 second. I have to downsample the data with the following:
Forward-backward filter for downsampling to preserve phase (zero-phase filter).
Downsample ... |
The discrete cosine transform(DCT) is a popular choice for spectral analysis in audio, video, image compression algorithms. This is primarily due its efficient "spectral compaction" property in comparison with Fast Fourier Transform(FFT). Is there a way to measure approximate "spectral compaction-gain" (if its appropri... |
I am solving a problem to find the zeros and poles. Subsequently, it is requires to determine the impulse response. Below is the system function:
$H(z)=\tfrac{z}{20z^2-4z+1}$
I am able to compute the poles by quadratic factor:
$z=\tfrac{-b \pm \sqrt{b^2-4ac}}{2a}$
$$=\tfrac{-(-4) \pm \sqrt{4^2-4(20)(1)}}{2(20)}$$
$$=\t... |
I have short segments of a biological signal interpolated at 10 Hz (anywhre from about 8.5 sec to 10 sec length). I want to use a cwt to then convert this segment to frequency over the short time frame. I believe need to window the time function and remove the average to make the average value zero, and then pad with z... |
Maybe a example of coupling effect in frequency modulated continuous (FMCW) radar will be helpful to better demonstrate my problem.
Let us consider a FMCW radar system. We have a complex transmitted signal $\textbf{x}(t)$ with bandwidth $B=50 \, \textbf{MHz}$, and duration time $T=7.3 \, \mu s$ of a chirp and $N=1024$ ... |
How we can use MATLAB for z domain especially in scenarios where we have two different expressions of Z transform(one has negative powers of z and other has positive powers of z)
I have added a link and snapshot of that and relevant MATLAB code where i get different poles and zeros when i switch from z^-1 form to z for... |
I have data $d$ recorded from an antenna of sensors. These data are composed of a Gaussian noise $n$ and a signal $s$ which I try to estimate. This signal propagates on the antenna with frequency dependent attenuation and velocity. Below is an illustration of such simulated data. We can observe that the signal comes fr... |
Per the Space Exploration SE question Are launch windows to Mars avoided if they result in landings during dust storm season? the synodic period of the relationship between the motion of Earth and Mars in their orbits with the approximation that they are circular and periodic is given by the following:
Launches to Mar... |
I just want to understand, why is the result of my wavelet(?) transform so bad.
For $0\le i< k$, where I set $k$ to $10$, I split the signal in blocks of length $s_i:=2^{i+2}$, overlapping by $s/2$. I then take the absolute value of the dot product of the block with $[e^{i4\pi(k+0.5)/s_i}]_{0\le k<s_i}$ and store it ... |
In literature, $V_\max = \lambda\cdot \operatorname{PRF} / 2$; should it be $V_\max = \lambda \cdot \operatorname{PRF} / 4$, which would be consistent with FMCW $V_\max = \lambda / (4 \cdot T_c)$?
This is because $\operatorname{PRF} = 2 f_d = 2 \cdot (2 V_\max / \lambda)$.
|
In Continuous Wavelet Transform (CWT) To achieve energy normalization and to ensure that all wavelets have the same energy regardless of their scales, each wavelet is divided by the square root of the the scale S.
|
Here's response of FIR design:
which shows SPL 0dB and here's a wave file exported from ( DRC ) FIR design software: FIR48kHz.wav.
Audio software (internally uses FFTW routines) where this filter is then used/measured reports +2 dB peak gain for full range 0-24kHz filter and +4dB for reduced range 0-20kHz filter (soft... |
I am simulating a first order delta sigma modulator (DSM) used as an ADC. The input to my DSM is a full scale sine wave.
The power spectral density I expect from the DSM output is as follows :
The sinusoid peak as well as some noise that is shaped to the higher frequencies.
In order to avoid any spectral leakage, I def... |
I want to simulate the process of obtaining the impulse response of a room.
What I did:
Generate a room impulse response sequence by using the python module: rir-generator
Generate a sine sweep signal with this formula
$$
f(t) = A\sin\left(\frac{2 \pi f_{1}T}{\ln\left( \frac{f_{2}}{f_{1}} \right)}\left(e^{\frac{t}{T} ... |
I acquired some noise signal (5GHz samplerate, 520 samples) data from a device and recognized that it is not gaussian distributed. There seems to be some slow sinusoidal signal underlying. I tried to visualize it by applying a moving average filter to my waveforms. Here are some examples:
It also shows when the nois... |
I've been looking for info on this topic for a while and I came across several algorithms that may be suitable for this purpose.
Specifically I'm interested in getting a frequency representation like this in real time
from where I can extract multiple pitches (chords), if any. But the frequency must have an exponentia... |
i got little problem. I'm trying to detect HFOs in single channel EEG (the recording is multichannel, but there is not enough channels to use ICA) for my diploma thesis experiment and i want to first preprocess the intracranial EEG signal (rats with electrodes placed in CA2 thalamus) by filtering movement artifacts.
I ... |
I need to filter some array of data before differentiating it, I do this so I don't drown the signal in noise.
It's also important that no delay is applied to the signal, that's why I decided to use a forward-backward filter like scipy's sosfiltfilt and implemented the following:
order = 4
freq = 0.00025
sos = sc.sign... |
I am trying to implement the DFT circular frequency shift property in MATLAB and my code is below. I have also attached a snapshot from the Proakis book where this property is highlighted but I am confused why I am not getting same equal value of LHS(Left Hand side) and RHS(Right hand side)
clc;clear;close all
x=[1:8... |
I am currently struggling on the book "System Identification: Theory for the User" by Lenart Ljung (freely available here) about the definition of the spectrum (around page 33). As I have seen elsewhere, it is defined as the Fourier transform of a fancy autocorrelation function. This gave rise to many questions and I w... |
What is a numerically stable way to obtain the inverse transfer function from a measured response?
I have a system that shows a low-pass behavior. I would like to increase the bandwidth by some form of pre-emphasis. I have measured the response of the system to the shortest square pulse excitation I can do. This looks ... |
Let T1 and T2 be two separate systems and T be the cascaded system:
Prove if the statement "T1 is LTl and T2 is not LTl, then T cannot be LTl" is correct
I would truly appreciate it if you could provide us with some hint. My intuition told me the statement is false, but I could not get any counter example
|
We performed some vibration tests on a shaker, with two accelerometers on our setup.
One was on the shaker table, to measure the input signal. And the other one was on a flexible part of our test setup, this is considered the output signal. The input was zero mean band limited white noise acceleration, between 100 and ... |
Title says it all.
Are there processors with FPUs that deal with denorms arithmetically correctly (don't assume they're zero nor flush them to zero) and don't cause an exception? I would be interested in knowing who the black sheep and the white sheep are. Like the Intel Xeon or AMD Opteron, are denorms for them just a... |
I'm missing a step to understand the factorization of the FIR filter transfer function:
$$H(z)=\sum\limits _{k=0}^{M}b_{k}z^{-k} \tag{1}$$
From DSP First:
The $z$-transform of a finite-length signal, such as $H(z)$ for an FIR filter, is a function of the complex variable $z$, and it is also an $M^{th}$-degree polynomi... |
Given
$$ Y(t) = A X(t) \cos(\omega t + \phi) $$
with $X(t)$ is zero-mean WSS (wide-sense stationary) process, $\phi$ ~ Unif$(0,2\pi)$. Suppose $X(t)$ and $\phi$ are independent random variables. I want to compute the mean and autocorrelation functions of $Y(t)$.
My attempt is (using independence of $X(t)$ and $\phi$, a... |
We are receiving 3 phase current readings from Induction motor using CT sensors. I am not aware of what processing is being done on the spot. My job is to do Motor Current Signature Analysis on it using python. But the currents have weird spikes everywhere.
Sampling frequency is 6500, Fundamental Frequency = 50Hz
Plot ... |
Suppose I have several groups of signal measurements, each containing multiple replicates, and I know that within each group the signal "shape" is approximately the same but with variance/error that depends on the signal. E.g. for each group I would have a set of vectors of the same length, which are strongly correlate... |
I am studying signal processing and currently doing signals & systems. While going through convolution and especially the impulse response , there are problems where LTI systems wherein the input is an unit impulse at $ t=0$ ,but the output pulses are generated at $t\ge 0 $ as well as $t\lt 0 $ as well. Consider the fo... |
There are lots of options in textbooks, youtube and website blogs.
There seems to be three options:
Calculate phase difference between samples to infer frequency error or offset.
Calculate phase difference between symbols to infer frequency error or offset.
Use a band edge filter (derivative of the pulse shaping filte... |
I'm wondering if there is a standard definition for global gain and frame gain in audio and speech processing. I found these terms together with an imprecise definition in a text about bandwidth extension in speech coding. However, I'm not able to find this definition in any other publication, lecture notes, or textboo... |
I am getting a shocking result from my matched filtering simulations and math. It would seem unlikely, but I'm seeing a 3dB gain in SNR if I process real samples instead of complex. Where is the flaw in this reasoning?
A matched filter is a convolution of the received noisy signal with a conjugated reversed copy of t... |
Let's consider baseband complex signal like this:
red: real part of signal
blue: magnitude^2
green: mean value of magnitude^2
as you can see, there are a lot of peaks but only one has value greater than 10. From definition PAR=Ppeak/Pmean... question is what would be Ppeak in this case? Max(pepeak) could be taken, but... |
I have encountered a text (a specification) in which $$\text{FFT}\left(f\left(x\right)\right) = f\left(\text{FFT}\left(x\right)\right)$$ is clearly presumed (for the functions they are applying).
Thus, I believe a composite function and the property sought is commutativity (of the composite function).
What I would like... |
Supposing there is a 16-bit data bus between the CPU and the memory, I want to save 16-bit data 1000 0000 0000 0001 to memory with a given address. The data bus consists of 16 wires(I don't know the terminology for "wire") connecting between the D0~D15 pins of the CPU and the same name pins of the memory.
I wonder if ... |
I am trying to display a growing sinusoid in MATLAB and i know that imaginary part corresponds to oscillations but i am confused how can i incorporate real part in exp argument? I have also attached my current code and current out put and desired output
clc;clear;close all
% Generate a sine wave using exponential funct... |
Let N be an even integer, and $x[n]$ be a finite length signal over the interval $n\in [0,N-1]$; let $X[k]$ be the N-pt DFT of $x[n]$.
Analytically find the DFT of each sequence below in terms of $X[k]$. (The DFT size is N unless specified otherwise):
a) $x_1[n] = x[N-1-n]$
b) $x_2[n] = (-1)^n\cdot x[n]$
For part a) I ... |
I'm trying to match a signal with a rectangular pulse shape using a rrc filter. Which alpha (0.25, 0.5 or 0.75) is best for doing this and why? My gut says 0.25 but I really don't understand.
Edit: The output signal looks as follows and was passed through a rectangular filter for pulse shaping: The signal gets transmit... |
I am not from electrical eng. or physics background, so a layman explanation would be appreciated. I work with sensor data (accelerometer) from wearable device, collected for few hours.
I take few samples from it, and prepared a fixed sized samples of 100-time steps. This is the acceleration (actually 1 dim) magnitude ... |
im trying to denoise a signal to which i added AWGN. Here is what ive done so far:
import numpy as np
import matplotlib.pyplot as plt
from scipy import signal
"""Creating a cosine and adding AWGN to it. Then denoising it.
"""
# Create cosing and cosine with noise
f_0 = 50
f_max = 2*f_0
t = np.linspace(0, 2*1/f_0, 256)... |
I've been learning about signals for a while now, and I'm just starting to learn about Continuous time Fourier transforms. In this particular case, we were asked to get the inverse Fourier Transform of
$$F(\omega)=\begin{cases}\omega^2\,&\ -\omega_0\leq \omega \leq \omega_0\\0,&\textrm{otherwise}\end{cases}$$
and I jus... |
Cascaded integrator-comb (CIC) filters are used in decimators, and decimators with a gain that is a power of 2 are popular (at least at my workplace) because the gain can be normalized with a right shift of the output data.
My understanding of decimators comes from Discrete Time Signal Processing by Alan Oppenheim, whe... |
Here is my attempt to perform an FFT on a random signal with 2 tones in which I applied zero padding AFTER windowing.
(I did not apply zero padding before windowing because that would suggest that the zeros are part of the original signal which is not correct.)
The signal amplitude is around 3.5 but the FFT amplitudes ... |
Most of us have come across the impulse response of an ideal (continuous-time, unity gain) low pass filter with cut-off frequency $\omega_0$:
$$h_{LP}(t)=\frac{\sin(\omega_0t)}{\pi t}\tag{1}$$
The question is what happens if we replace the sine in the numerator of $(1)$ by a cosine? What type of filter is it? What is i... |
I am investigating the time-domain response of electromagnetic waves. The input signals are a chirp with linear frequency sweep 2.5 Hz->4.5 Hz -> 2.5 Hz and another signal which is abruptly turned off at 10 seconds.
Let's call this $x(t)$.
I then find the Fourier Transform of these signals.
I have the experimental v... |
I am trying to find a mathematical model to understand the correlated phase noise.
Here, I see the reference phase noise is almost the same after up-conversion and then down-conversion. How does correlated noise get canceled as though the mixer has not added any noise at all?
I am looking for a signal processing angle ... |
Let's say the N-Point DFT of $x[n]$ is $X(k)$.
Now from this question, I know how to compute the 2N-Point DFT of the same $x[n]$ in terms of $X(k)$
However, this idea doesn't translate well if I have to compute the 2N-Point DFT of $x_1[n]$, for example, where:
$$x_1[n] = \begin{cases}
x[n], & \text{... |
I have a waveform that's modulated by a trapezoidal function. I fitted the envelope to the expected function to show if the amplitude is modulated correctly.
I also plotted the difference of the fit and the envelope
This is an example of a fairly "healthy" waveform. Sometimes my amplifier likes to compress and decomp... |
I have signal which a sinous wave with frequency 1MHZ and DC signal at 0.9V.
The signal is sampled every T the total length is 5e-6 sec so for T=3.301028538570082e-09 i have 220 samples.
sampling frequency is Fs=302935884.4722904Hz
The original sinous plot is shown bellow.
As you can see Sinous amplitude is 0.1V
But... |
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