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I am doubling the resolution of images by bilinear resampling (which amounts to averaging). I seem to understand that this should be combined to a sharpening filter for better quality of the reconstruction. Should the sharpening be applied before or after resampling ? How to design this filter (preferably a very simple...
This is my first time actually applying signal processing to a real problem. I'm trying to monitor some equipment for vibrations. The vibrations aren't constant but occur at some point in time - I've read that wavelets are a better choice for this rather than a simple threshold or performing an FFT; thus the choice to ...
I am working on reverse-engineering a few devices, I got some using ASK and FSK but I could not grasp this other one. I am attaching some photos from its captured signal took from URH (Universal Radio Hacker) and Inspectrum. Which type of modulation is this? and maybe some hints to how demodulate it. URH Inspectrum I...
My aim is to try out the 5G LDPC codes by using the aff3ct library. This library needs the parity check matrix loaded from a .alist or a .gc file to create the LDPC encoder. I've been looking how to generate a parity check matrix that is compliant with the 5G specs, can someone orientate me on this topic? Thanks a lot
As an exercise with IIR allpass filters, I am trying to compensate the phase of a lowpass Linkwitz-Riley filter using the Matlab integrated function iirgrpdelay. The code I am using is the following: clear; close all; clc; fs = 48000; NFFT_half = 4097; % Design Linkwitz-Riley 24 fcut = 300; [b,a] = butter(2,fcut/(fs/...
I have samples of wrapped $(-\pi,\pi)$ phase from a bandlimited signal $A(t)\cos(\pi\omega t + \phi(t)+\theta_0 )$ Frequency is constrained by very regular physics and I know a preliminary guess $\hat{\omega}$. I can also write the deterministic and interesting part of $\phi(t)$ as $\bar{\phi}$. So this could be writte...
I'm not sure what the correct signal processing tool for this task is. My file is in m4a format. I'm comfortable using Python (arbitrary library(ies)) or MATLAB, but don't need code, just advice on an approach. Possible ways to do this that I've thought about: high pass filter so that only the upper frequency of the v...
I'm doing a university project on Carrier Aggregation and I'm using a Matlab code to simulate the process. There's already a complete code about Carrier Aggregation in Matlab Library, but when I asked my supervisor about it he told me that I could not use a ready code (Either I write a new one or make an improvement on...
I would like to represent a second-order butterworth low-pass filter in a block diagram, how can I get started? As per the attached image
I did fft of a fish's trajectory, because it looks periodic and I tried to find the frequency. However, I can't understand what does the phase spectrum below represent. Does this lower left to upper right curve have any special meaning? Below is my Matlab code: L = length(X); Fs = 30; % Sampling frequenc...
Consider a filter of the form $$ _{posic}() = \alpha_1+\alpha_2e^{-sh}.$$ Find the parameters $\alpha_1, \alpha_2 \in \mathbb R$, and $h > 0$ such that $P_{\theta\phi}F_{posic}$ is an FIR (finite impulse response) system the static gain $F_{posic} = 1$, $h$ is a smallest possible delay guaranteeing all that in symbo...
Is there anyway that I can output a Time Sink's amplitude using a TCP Sink or, File Sink using GNU Radio?
I have a log likelihood that looks like the following. $$ \log(p(Z|\Theta)) = -\sum_{p = 1}^{N} \left[ L \log\left(\pi\left(A F(p, \Theta) + \sigma^2\right) \right) + \frac{\sum_{l = 1}^{L} Z_l(p) }{A F(p, \Theta) + \sigma^2} \right] $$ It comes from an exponential distribution. The observations are $Z_l(p)$, and $A F...
I wish to use the gradient descent algorithm to minimize the cost function $$J(\mathbf{w}) = (\mathbf{w} - \mathbf{w}_{o})^{T} \mathbf{A}(\mathbf{w} - \mathbf{w}_{o})$$ where $\mathbf{w} \in \mathbb{R}^{2}$, $\mathbf{w}_{o} = (-2, 2)^{T}$ and $\mathbf{A} = \textrm{diag}(20,1)$. In MATLAB, starting with an intialization...
I am double integrating my acceleration to obtain the displacement. However, the displacement looks so strange. Basically this is the measured acceleration of a system under a impulse movement. and I am trying to obtain it's damping and stiffness properties from this experiment, and that why I would like to have the di...
I have a problem here - either I'm stupid or my hack rf is broken I am trying to send text via 2 hackrf like in this tutorialusing GMSK The simulation returns the text is correct, but when I run the rf hack it returns garbage to me, what could be the problem? TX RX Simulation I get it the text I am sending
I have a line sensor with a $n$ number of detector elements, pixels. This line sensor should be used to capture data while moving so that later from the captured data images can be generated. The sensor is moved vertically when the line is horizontally so that with both axes data is captured. Now to accurately generate...
This should be a simple problem, yet I can seem to figure out what am I doing wrong. I have a bunch of 1-D signals which I expect to look the same up to: shifting, maybe some scaling, and noise. I with to find the shift between adjacent signals. For example here is one pair: Each signal is expected to be of the same s...
I know it's a very basic question, but I've spent almost a full work day researching and still can't find a clear (or even just usable) answer. For the DFT of a real-valued signal the second half of the bins is just conjugates of the first half and can/should be ignored. But what about the complex-valued I/Q signal? I ...
For my homework I was given the signal by the illustration: I was asked to draw the illustration for $$x_1(t) = 3x(-1+0.5t) - \delta(-t+3)$$ I have figured out how to draw the $3x(-1+0.5t)$ part, but I'm not sure how to deal with the $\delta(-t+3)$ part. What does it mean to subtract a signal by a unit impulse?
I was going through some old exams and found this question: Find the inverse $Z$-transform of $z^{-1/2}$. I tried using the properties table, but I couldn't find a single useful property that would help me solve this question. I don't have the solution of the past exam, so I would really appreciate a solution.
Followup to this question, let the ramp be $r_0(t)$. We seek to plot $x(t) = r_0(t) + \delta(t + 1)$. Should it be as in left, right, or neither? Is there a convention? Note, in either case we could use either arrow size or label it to show its value; this question's about the tail's placement. Others validly pointed ...
Background I am having issues implementing an allpass filter to model wave dispersion in a stiff string. In order to simulate wave propagation in a string, I am using a digital waveguide. I implemented the matlab code referenced in this paper in c++, and my code produces the same coefficients. This leads me to believe ...
Suppose there are two independent signals, $s(t-\tau)$ and $n(t)$, and they are doubtly uncorrelated so that $\mathbb{E}${$s(t-\tau)\times n(t)$}=0. I wonder if the equation $\mathbb{E}${$\frac{\partial s^*(t-\tau)}{\partial \tau}\times n(t)$} still equal to zero, which are uncorrelated? I read the expression from a ra...
I am trying to make an algorithm that plots out the Discrete-Time Fourier Transform (DTFT) and the Discrete Fourier Transform (DFT) of the Gaussian filter. The impulsive response and its transfer function (TF) are respectively given by $$ g(t) = \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{t^2}{2\sigma^2}} $$ and $$ G(f) = \m...
I am reading about FM.Suppose the message signal $m(t) = \frac{1}{2}cos(t)$ and the frequency of the carrier signal is twice the frequency of the message signal and its amplitude is 1.The resulting modulated signal will be in this form $s(t) = cos((2+\frac{1}{2}cost)t)$.I tried plotting the modulated signal using the D...
(Related to: https://engineering.stackexchange.com/q/14619) Quick question: I am getting a strong initial value and strong undershoot in the step response. How can I suppress it with the feedback compensator? The context: I am modelling the close loop response of a pizeo-electric actuator, having an extremely small da...
We have implemented a way of approximating a data set with the following lines of code based on the dx/dt of wikipedia of leaky integrator. dy = -A * y_previous + C y_current = y_previous + dy*delta_t However, I am uncertain if we are allowed to call the following truly a leaky integrator. I was a bit confused how...
To my knowledge, white Gaussian noise (WGN) is defined as a process with a correlation function: $$ R[k]=\sigma^2 \delta[k] $$ and whose symbols are distributed according to $N(0,\sigma^2)$. Naturally, when simulating such noise, the mean won't be zero for a specific realization but it would be close. However, if I try...
I wrote some golang code which implements 3Blue1Brown's Hilbert's Curve: Is infinite math useful? ... give the code an image and it returns back its audio equivalent ( inverse Fourier Transform ) ... also wrote the same algo in reverse ... give it audio and it returns the image representation ( Fourier Transform ) Th...
In short: what kind of mathematical function was applied to this sine WAVE? I am trying to implement my own distortion plugins. Amongst other things I have read several chapters of Will Pirkle's book ("Designing audio effect plugins in C++"). In the few examples there are in this book and that I could find on the inter...
I am learning about the MMSE detector and how to implement it. I looked at some example codes on the Internet but many of them directly use the perfect channel when calculating the MMSE estimated channel. For examples this one: https://uk.mathworks.com/matlabcentral/fileexchange/46856-channel-estimation-using-ls-and-mm...
How a fish sonar is built and signals from sensors processed ? There are $50 fish wireless sonars on the market. I would to buy one but need to know how it works, what is a number of sensors and if sensors rotate, at what frequency and what is a load of data to be processed real-time. No such data come with fish sonar ...
I've seen a lot of people use image set classification recently. However, I haven't been able to find anywhere explaining the specifics of why image set classification is preferred. Are there only advantages to image set classification over normal image classification? Are there instances you might prefer the conventio...
Given a physical system (e.g., loudspeaker and microphone) with DA and AD converters. Playing a single pulse from the loudspeaker, I will most likely receive the pulse at the microphone with a fractional delay. If the system and sound propagation were ideal, this fractional delay would extend infinitely to the past (se...
I am interested in troubleshooting why I get a very different answer when doing fourier transforms of my data in Mathematica vs Python. The version in Mathematica is well behaved, yet all versions of fourier transforms in Python (scipy/numpy) do not seem to work. Is there any obvious reason why this is the case? I have...
I am trying to detect meteors in a video, and so far, what I did. Preprocessing: changing to grayscale and morphological operations like dilation and erosion. background subtraction method adding images to see a pattern or event in the video. What i got is, But now how i say that meteor is detected? Due to higher sa...
Request to Experts: I am a DSP novice. I would like to experiment with some methods for low pass filtering in the time domain. To that purpose, I would like to generate a tone in audacity and export it as a raw file (without headers), then process it using simple C/Java file handling programs (without using audio proce...
For a personal project I am trying to make a software to synthesize plucked and hammered string instruments. This is a whole research topic and there are already some models and algorithms such as the Karplus. I have thought a parallel way of solving the problem but I am trying to see whats wrong with it compared to ex...
Since I've last posted on dsp@stackexchange, I have been working on my algorithms and recently came across a useful radix-2 implementation which delivers performance as good or better than that of numpy's fft, as long as it is used with a fixed input(which is always the case for my work. I adapted it and unrolled it an...
I have some understanding problems with OFDM. I think I have understood most of the theoretical concept. At the moment, I am trying to write some Python code to simulate the transmitter part. This is just to see what the signal looks like in the time and frequency domain. As an example, I want to build a transmitter wi...
Good time. I would like to compute EVM for a Rayleigh channel including additive Gaussian white noise. The accepted EVM for BPSK issued by IEEE is -5dB. Since the variance of white noise depends on the SNR, I am wondering the accepted EVM has been issued for which value of white noise. Could you please help me to resol...
I have successfully implemented the Sony PlayStation 1 reverb effect, until I realized that it strictly works at a sample of 44.1 kHz. A quick web search shown that (as far as I understand), an IIR reverb effect will only work at the sample rate it's been designed for. I was planning to use that reverb effect for a gam...
I need to remove trend from my time-series which looks like the following images. However, I want to estimate the trend before removing it. Hence directly removing it won't do it. The simple polynomial models didn't work, because — I think — the signal is long and the trend is changing. Also, filtering the signal with ...
My question is about the difference between single scale and multi scale in scale space theory. But I think I have to write what I understand about scale space theory and what I guess is the difference between single scale and multi scale: Kernel is an operator which we put on detected data and save its result as samp...
Does anyone know which chips Phonak uses in their products to run the DSP algorithms? Thanks.
Does someone have full code for this example : https://ch.mathworks.com/help/rf/ug/designing-broadband-matching-networks-part-2-amplifier.html I get Error: File: hw.m Line: 10 Column: 36 The expression to the left of the equals sign is not a valid target for an assignment. And also when I try to load example like th...
I am trying to model the phase noise $\phi(t)$ of laser used in self-heterodyne method using python code. The noise is time-dependent. The noise follows the condition that $$\langle(\phi(t)-\phi(t-\tau))^2\rangle = \exp(-\tau/\tau c),$$ where < > represents the mean value. I know this noise model can be generated usi...
I am trying to implement the fast fir-filter in a C++ application. I have implemented the same code in matlab as a way to double-check my implementation and have ran into a problem. When running matlab's fft() and ifft() I get vastly different results when compared to FFTW_FORWARDS and BACKWARDS. I have tried running F...
I seek to calculate, mathematically, the Discrete Fourier Transform, $$ \texttt{DFT}\{x\}[k] = \sum_{n=0}^{N - 1} x[n] e^{-j2\pi k n / N} $$ of any arbitrary real-valued sine: any frequency, duration, phase shift, and number of samples. The expression should reflect practical use, in that it's how we'd sample a sine in...
I have the response signal of a piezoeletric transducer. I'm trying to acquire the phase velocity of the echoes I'm receiving. The resonancy frequency of the transducer is 5 MHz. I'm using an oscilloscope (Tektronix MSO 3054) to aquire the signal. I can calculate the time propagation in the time domain, but I'm having...
I am trying to write a small synth code that goes something like this, I have an abstract symbolic sound representation, sine/square/saw waves. To generate final sound and make it sound good I thought of the following steps; At first oversample the abstract symbolic representation apply noise shaped dither apply anti-...
Looking at the basic characteristics of a Chebyshev Filter, I was wondering if there were any analogous type filters in Computer Vision? The way that it can minimize the error between the idealized and the actual filter characteristic sounds a lot like edge detection to me. Is there an analog between these to? If not, ...
I am measuring a room's acoustic impulse response by playing a log sine-sweep through a speaker from 20hz to 24 khz, and then recording it using a microphone. The sweep is 10 seconds long, followed by 4 seconds of silence. There is some fading at the end of the sweep. In order to compute the room's impulse response, I ...
Currently I am reading Principal Component Analysis-Based Low-Light Image Enhancement Using Reflection Model. That article proposes a way for obtaining the illumination coefficient of the original image (). This is a quotation from it, after extracting illumination coefficient: Suppose: is the enhanced image. is th...
How correctly choose a channel model: Rician and Rayleigh channel model? The Rician channel assumes dominant line of sight (LoS) paths from the transmitter to the receiver and other scattering paths. Rayleigh channel consists of scattering channels from the transmitter to the receiver, i.e., there is no dominant LOS p...
I am given a set of $N = 649$ color PNG images, each of size $W \times H \times 3 = 586 \times 689 \times 3$. The corresponding pixels in each image represent the same object. Many of the pixels in each image are black $(0,0,0)$ which corresponds to "no data" for that image. Below are the top portions of four of those ...
I have a 20Hz PWM signal (0 - 5V) with a duty cycle of 30%. What would be the minimum/recommended sample rate to count all rising edges in this signal? I'm unsure because Nyquist does not really work with all the harmonics in the spectrum.
I am trying to model an OFDM signal based on original QPSK stream and compare their baseband spectrums. I've used this article as a reference for plotting spectrum and this as a MATLAB OFDM reference Here are my signal presets carsN = 8; % number of OFDM subcarriers N=carsN*1024; % length of bits/symbols stream m = 2; ...
Considering a bandpass communication system, where $y(t)=x(t)*h(t)+n(t)$ ($x(t)$ is the transmitted bandpass symbol, $h(t)$ is the channel impulse response, $n(t)$ is the AWGN, and "$*$" means convolution). I can write its baseband equivalent model as $v(t)=u(t)*h_l(t)+n_l(t)$, where $v(t),u(t),h_l(t),n_l(t)$ are the c...
$F^\ast(x(t))=F(x^\ast(-t))$ I'm trying to use this identity in Matlab. I expect this should translate to: conj(fft(x)) == fft(conj(flip(x))) It doesn't work out. I run: x = rand(1, 4) + 1i*rand(1, 4); f1 = conj(fft(x)); f2 = fft(conj(flip(x))); And here are the results: x 0.9649 + 0.4854i 0.1576 + 0.8003i ...
From the first sentence of section 4 in the paper "A harmonic analysis view on neuroscience imaging", Since all images have compact support in the space domain $\mathbb{R}^d$ ($d = 2$ or $d = 3$), their conversion from analogue to digital form occurring during acquisition requires truncating the image in the frequency...
There are many methods of computing estimations of the bispectrum, and in particular regarding methods to give unbiased estimations of this quantity. I was wondering whether if, given a complex-valued signal $x_t$, one can obtain an unbiased estimate of the bispectrum $B(\xi_1,\xi_2)$ for any given $\xi_1$ and $\xi_2$ ...
Suppose that we have a signal with a length of 4096 and want to down sample it by a factor of 2 and obtain a signal with a length of 2048. Suppose that the the maximum frequency content of the signal is low enough that we do not have any concern about aliasing. Obviously, the direct way is to keep every sample with an ...
What is the wrap-around effect?
I was given the following problem at my university: We are given an audio file which we have to download. Following that we have to create a MATLAB code that can create a discrete-time graph of the signal in the time domain. Following that we have to create another graph this time displaying its Fourier transform. The ...
I have an exercise that gives me the following transfer function $$ \frac{0.5}{s+0.5} $$ and an assumed step change in the target of 20 I am asked to calculate the maximum input for the assumed step change. I know the answer is 500 but can't figure out how to get there. I have seen this which gives me the following but...
To start learning to use asoundlib.h, I am writing a simple program that plays a tone. I am filling an array of shorts, samples of length buffersize. with samples of a sine wave. When I pass samples to snd_pcm_writei() with its length, buffersize, the samples in samples are played for half of the time and noise is play...
For the following I use the terms “time domain signal” and “frequency domain signal” as a Fourier Transform pair. The question is for generalized cases of continuous-time signals that once sampled in the time domain will then be discrete-time signals. I will also use the phrase “sampling in the frequency domain” which ...
First I am very new in this field,and i am doing a college project and i stuck at determining phase of msk signal which is transmitted from a radio stations called NWC Australia 19.8Khz , so let me give you some background, i am building a software like UltraMSK like or spectrum Lab like which is basically do two thing...
Assuming the convolution in the time domain produces a signal which spectrum is the product of individual spectrums, when the two convoluted signals are sinusoids with different frequencies, the DFT coefficients should be null. I'm trying to verify this property, but my spectrum (last column) is not null. Assuming the...
I'm workding on nand flash DSP (Digital Signal Processing) now, and encounter obstacle, which is: how to generate and update Log-Likelihood Ratio (LLR) LUT for Triple- and Quad Level Cell (TLC and QLC) NAND flash memory? any suggestion or reference will be very useful! I've tried in MLC case, but it performance is poor...
I am computing the discrete convolution of a signal $x[n] = a^nu[n]$ with a delayed unit step, say $h[n] = u[n-5]$. If I place both directly into the discrete convolution formula I end up with: $\frac{1 - a^{(n-4)}}{1 - a}u[n-5]$, which I think is correct. However, if I make $u[n-5] = u[n] - \delta[4] - \delta[3] \cdot...
[cross-post on MathExchange] I am trying to implement a 2nd-order EKF and am having some issues with the propagation equation for covariance. From the literature (see end of post for references), if $X$ has covariance $P$ and the propagation function $f$ has jacobian $J$ and hessians $H^1$, $H^2$, ... the propagation /...
This question also discusses what I am asking but the answer states that Parseval's theorem is for periodic functions as per wikipedia's notation here. However, Parseval's relationship also holds for continuous-time aperiodic signals as follows: $$\int_{-\infty}^{\infty}|x(t)|^2 dt = \frac{1}{2\pi}\int_{-\infty}^{\inft...
I was given Matlab code to process a signal file. I do not have any details as to the ADC specs or the code's author. The variable, cxSamps (complex double), contains the signal's IQ data read from the entire file. I see this line of code: cxSamps = cxSamps / mean( abs(cxSamps ) ); The comment says that this boosting...
Say we have a 12-bit ADC measuring a signal with a voltage range of 0-10V, but the signal is corrupted by uniformly distributed 3-bit white noise. What's the correct way to get the variance of the noise? I would have thought that you calculate the maximum voltage of the noise signal by doing $$\frac{2^{\text{noise bits...
I have audio of VHS with speech and music, and with noise of frequency that's higher and lower than most of human speech, with apparently least but still significant energy in-between, that cannot be filtered with band-rejection. The best audible SNR improvement I got was by eliminating (FFT-zeroing) below 320 Hz and a...
Let's say I am trying to validate a model. I have a signal from measurement and a signal from the simulation of the model. Simulation was done with the same initial and boundary conditions as measurement. Now I want to compare two signals (e.g. temperatures of one modeled component). I want to have a number (or more th...
This is perhaps a bit of a weird idea but suppose I want the latent variables of a Kalman filter to be small (like as if the states were being regularized). This is kind of like putting an extra prior on each latent variable at each time step t as a normal centered around 0. I'm pretty sure this could be done with a pa...
Please find attached snap of proakis dsp book. It shows rectangular window has minimum value of stop band attenunation and transition width and as we go on towards Hamming and Blackman window,stop band attenunation and transition width both parameters keep on increasing While according to my understanding ideal filter...
The definition for the time of arrival is: $TOA=\frac{d}{c}+t_e$ where $c$ the wave speed, $d$ the range between the transmitter and the receiver and $t_e$ the transmission time of the signal to the transmitter. My question: I don't understand why there is the term $t_e$ for me the TOA is just $\frac{d}{c}$
The terms digital and electronic are often used interchangeably but I know that it's not correct because something can be digital but not electronic. Something can be digital in the sense that it's discrete both in time and magnitude. A picture of a ruler appearing each second is discrete in time because this timing is...
let's consider I have an antenna array with N-elements, and its sensors are not placed in a uniform linear array fashion (may be randomly placed, a coprime array, or a nested array, for example). What would the spark of the corresponding dictionary array manifold be? We know that Vandermonde matrices can be considered ...
Above is a block diagram of a discrete-time system $T\{x[n]\} = y[n]$. Here, $h[n]$ is the impulse response of an arbitrary LTI system. Firstly, is this overall system LTI? I don't think so because the downsampling operator is not time-invariant but I am not sure. Secondly, what would be the purpose of such a system?...
I have read many of the posts here on the stack regarding sample rate conversion but have yet to find one that does not rely either upon asynchronous or synchronous clocks. It occurs to me that the simplest and best approach to sample rate conversion is to first convert the digital signal back to the analog domain usin...
I have an accelerometer sensor with gyro and need to figure out the vertical displacement from the acceleration data. The device that contains the accelerometer will move up and down in fairly consistent cycles (kind of like oscillating motion but not really). The force that is being applied to the device will stay mos...
If we excite a LTI system with the Dirac delta $\delta(t)$, the system outputs the impulse response $h(t)$. For a LTI system, it doesn't matter when we excite the system with the Dirac delta, we will always get the same impulse response. However, that is not the case for a linear time-varying (LTV) system. If, say, we ...
Let the complex exponential Fourier series coefficients of two periodic signals $x_1(t)$ and $x_2(t)$ be $C_{1n}$ and $C_{2n}$, respectively, with $T_0$ being the fundamental time period of both the signals. Let the signal $x(t)$ be equal to $x_1(t) * x_2(t)$, where $*$ denotes the periodic convolution operation, and i...
More specifically, I'm curious how we can represent sound waves in a way that would both distinguish between individual voices and also recognize, e.g. that recordings of different people saying the same word contain the same word. That is, if I say "tree", for instance, it would sound different than if you said it, b...
I am trying to make a phase diagram for three variables . a=[0.01 0.5 1 1.5 2]; b=[0.1 1 2 5 10]; and their mean squared error value in variable 3 (having 5 rows and 5 columns) mse = 0.0000 0.0284 0.0311 0.0177 0.0112 0.0113 0.0381 0.0449 0.0339 0.0236 0.0517 0.0800 0.0768 0.0701 0....
In OFDM system, the cyclic prefix is added into the head of time-domain signal to enable the circular convolution with the channel, and then perform one-tap frequency-domain equalization at the receiver. However, what's about if we added the cyclic prefix into the end of the time-domain signal, is there a way to consid...
Respected all, I am trying to plot the power spectra of a ST (Stratosphere Troposphere) Radar to estimate the doppler shift. I am able to obtain a 3D plot between range, FFT point and Power density using the 'mesh' function, but want to obtain a plot similar to the 2nd plot attached below. Which command or process sho...
This question stems from the discussion we had on a previous question of mine. The point of contention is whether the downsampling operator is time invariant or not. Which gives us a new condition to check whether such systems are LTI independent of the input is bandlimited or not. Essentially, if there's a criteria ot...
Subtract the output of a linear time-invariant system whose shock response is $h \left[ n \right] = \left( \frac{1}{4} \right)^{n} \left( u \left[ n \right] - u \left[ n - 2 \right] \right)$, for input $x \left[ n \right] = u \left[ n \right] - u \left[ n - 3 \right]$, where $u \left[ n \right]$ is the step function.
I have below given digital signal (sampled with period $T = 1\,\mathrm{ms}$) for which I need to evaluate its decrese. Namely I am interested in regions where the signal decreases faster than $-1000\,\mathrm{V}\cdot s^{-1}$. My first idea how to do that was to evaluate the first derivative of the signal and compare it...
I have my DSP final soon and I have been reviewing some past exams. Here is a question from one of these exams: Let x[n] be a real valued finite duration signal in n $\in [0,N]$. Another signal $x_1[n]$ is defined as: $$x_1[n] = \begin{cases} x[n], & \text{if } n=0 \; or \; n=N ,\\ ...
I was studying the phase variation of a signal using sliding window FFT generated using below python code. The phase variation produced for my signal starts from somewhere in middle of the signal cycle (indicated by black circles) however the phase angle for a simple smooth up and down signal starts with the cycle itse...
Please find attached snapshot. I am confused regarding power spectrum in MATLAB as according to google definition in attached snapshot"the distribution of the energy of a waveform among its different frequency components." But how can we interpret the spectrum displayed in MATLAB where we have values in negative db and...
I am having some trouble working through verifying linearity and shift invariance when the transformation is under a summation. The given transformation is as follows: $$ y(m,n)=\sum_{i=-1}^{i=1}\sum_{j=-1}^{j=1}x(m+i,n+j) $$ I understand the basics of verifying linearity ($T[a_1f_1(x,y)+a_2f_2(x,y)]=a_1T[f_1(x,y)]+a_2...