Questions tagged [inverse]

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Why not overlap save for inverse stft

Since STFT uses overlapped sections of the input signals and compute DFT, it resembles overlap-save method used for block convolution, instead the overlap-add method for block convolution uses non-...
Ras's user avatar
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1 answer
67 views

Inverse $\mathcal{Z}$-transform of a shifted Dirac delta function $\delta(z - z_{0})$

I'm looking for the inverse $\mathcal{Z}$-transform of a shifted Dirac delta function in the $z$ domain, i.e. $$ x[n] = \mathcal{Z}^{-1} \{ \delta(z - z_{0}) \} = \ldots $$ Does an analytic/closed-...
Bart Wolleswinkel's user avatar
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2 answers
180 views

Is it possible to predict the peak value of a time-domain signal from its frequency-domain spectrum?

As the question states, is it possible to predict the peak value of a time-domain signal given its frequency-domain spectrum? Since the time-domain signal is just the sum of the individual sinusoids ...
Darcy's user avatar
  • 296
1 vote
2 answers
420 views

Can someone explain the phase spectrum of a sinc function?

The Fourier transform of a sinc function will result in a rect function. Suppose I have a discrete time-domain sinc function with a frequency of $\omega_0 = 0.1$ Hz and amplitude of $A = 10^{-3}$: If ...
Darcy's user avatar
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-1 votes
1 answer
42 views

How to compute the ifft of a constant value?

I am clearly missing something obvious here because I am trying to do something that ought to be very simple: compute the ifft of a continuous signal. My understanding is that the ifft of a continuous ...
Darcy's user avatar
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1 vote
1 answer
174 views

Inverse Fourier Transform of $\omega ^2$ in $[-\omega _0,\omega _0]$

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 ...
Fern Mendiz's user avatar
0 votes
1 answer
92 views

Non-causality deepness of inverse system

Assume I have a FIR, stable and causal system. I want to know the deepness of non-causality on the inverse of my FIR system. It's obvious that the system is non-minimum-phase, since minimum-phase ...
mohammadsdtmnd's user avatar
0 votes
1 answer
32 views

Determining invertibility of weird system

Student here, As an academic exercise, is the system $$y[n] = x[n-1]x[2n]$$ Invertible? I thought it was since you could find an infinite multiplication series for y[n] that allows you to recover x. ...
dhdjkddkkshccuud's user avatar
1 vote
1 answer
72 views

How can one infer the input signal $x[n]$ from the output $y[n]$ of an LTI system with known Gain and Phase Response

I have the gain response of an amplifier and its phase response curves, in an appropriate frequency range. I also have a set of output (from the system) discrete data $y[n]$. How would one go about ...
Heath's user avatar
  • 131
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1 answer
171 views

Taking The Inverse FFT And Extrapolating For Future Predictions In R

This is what I am trying to achieve: See how the increasing number of harmonics are creating a good fit? I am trying to find the components of a given wave (discrete samples), and then to make brief ...
user2877551's user avatar
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1 answer
40 views

Acausal form of $Z^{-1}\left(\frac{1}{z-a}\right)$

We know that $Z^{-1}\left(\frac{z}{z-a}\right) = a^nu[n]$ if $|z| > |a|$. In addition, $Z^{-1}\left(\frac{1}{z-a}\right) = a^{n-1}u[n-1]$ if $|z| > |a|$. This is the delayed version of the first ...
sdkmlcngz's user avatar
5 votes
1 answer
190 views

Convolution theorem for inverse DTFT

in trying to understand the convolution theorem for DTFT, I'm faced with the following problem which I can't get my head around. First, let me state the convolution theorem for the DTFT as follows: \...
Tim Mak's user avatar
  • 225
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1 answer
92 views

How to find the inverse Fourier transform of $u(\omega) e^{-j \frac{\pi}{2}} + u(-\omega) e^{j \frac{\pi}{2}}$?

I have been trying to find the following inverse Fourier transform but without success: $$ H(\omega) = \begin{cases} e^{-j \frac{\pi}{2}} & \omega \gt 0 \\ e^{j \frac{\pi}{2}} & \omega \lt 0 \...
Constantinos Petrakis's user avatar
1 vote
2 answers
249 views

Reverse convolution

I was reading about linear systems and random processes and I came across this $$h_{k}*h_{-k}*rxx[k].$$ I know what convolution is and its formula. Does the minus sign affect both of the parameters in ...
makala's user avatar
  • 55
2 votes
1 answer
122 views

Is the system $y\left(t\right)=\int _{t^3-1}^{t^3}x\left(s\right)ds\:$ invertible? [duplicate]

I have the following system: $$y\left(t\right)=\int _{t^3-1}^{t^3}x\left(s\right)ds\:$$ I was told to determine if it's invertible system, casual system, memoryless system and linear system. I was ...
sl99's user avatar
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2 answers
124 views

Sufficient conditions for invertibility of discrete LTI systems [duplicate]

Is $h[0] \neq 0$ a sufficient condition for the invertibility of a discrete, LTI, causal system? Can we get to similar results (i.e. get to some other sufficient condition(s)) for noncausal or ...
Dkpink's user avatar
  • 3
5 votes
1 answer
598 views

Deblurring 1D data using direct inverse filtering

In my assignment I have been given recorded temperature over a period of time (193 values) and the impulse response (5 values with n=0 corresponding to the middle value.) Data: data.csv ...
Mitul Agrawal's user avatar
3 votes
3 answers
1k views

Filter odd or even harmonics with notch or inverse notch filter

Hi i had the following question. I have a signal containing a 200Hz sine wave and it's odd and even harmonics (no other frequencys or disturbing signals are contained). What i'm looking for is a kind ...
Rabobsel's user avatar
3 votes
1 answer
2k views

Fourier Transform: $\omega$ vs $f$ as frequency variable

I try to understand how the Fourier transform changes when I try to compute $X(\omega)$ or $X(f)$. Can someone work me through the maths please for two examples, $x(t) = \exp(j\omega_0 t)$ and $x(t) = ...
makala's user avatar
  • 55
0 votes
2 answers
629 views

how to find the inverse response of a system

For the system described by the differential equation below find its inverse zero-state unit step response $$\dfrac{d^2y(t)}{dt^2}-2\dfrac{dy(t)}{dt}-8y(t)=\dfrac{d^2x(t)}{dt^2}-2\dfrac{dx(t)}{dt}-3x(...
Schach21's user avatar
  • 162
2 votes
1 answer
1k views

why use svd() to invert a matrix?

In MATLAB, i compared elapsed time to invert a Hermitian matrix using inverse(), svd(), and chol(). svd() took the longest. So is there any reason to prefer svd() to the other two methods?
j03y_'s user avatar
  • 111
0 votes
1 answer
981 views

Is Differentiation as a system, is an invertible system?

is the following system invertible? as I understand it, invertible means finding an inverse function which should return back the original input from an output of the given system. if so I ...
AboDa7aM's user avatar
1 vote
0 answers
78 views

Calculating DCT in reversed vector

I'm doing an exercise in which I need to show that the DCT of $\tilde{x} = (x_{N-1}, x_{N-2}, ..., x_1, x_0) $, with $\tilde x_m = x_{N-m-1}$, is equal to $ \tilde{X}_k = (-1)^{k}X_{k}$, but I have ...
Marcelo de Sousa's user avatar
1 vote
3 answers
150 views

Invertibility of an ideal differentiator

Is the system $y(t)= dx(t)/dt$ invertible or not? If yes, please determine the inverse system for it.
user50388's user avatar
3 votes
3 answers
492 views

Can I set a constraint on the first tap of an FIR filter such that its inverse is stable?

Let's say I have the following FIR filter $h[n]$, so the output $y[n]$ for an input $x[n]$ is $$ y[n] = \sum_{k=0}^{m-1}x[n-k]h[k] $$ The inverse of this filter is given by the IIR difference ...
Condensation's user avatar
1 vote
2 answers
2k views

inverse fourier transform of magnitude and phase

I stuck this question. Frequency response is written as magnitude and phase and I don't find inverse fourier given signal which as magnitude and phase.How can I solve it ? Can you explain the solution ...
Kerem Saruhan's user avatar
0 votes
0 answers
74 views

If you are given an inverse DFT, then how do you convert it back to the DFT without actually computing any DFT?

If you are given an inverse DFT, then how do you convert it back to the DFT without actually computing any DFT?
Electronics Engineer's user avatar
1 vote
1 answer
119 views

Build an inverse model for a train of gaussian pulses

I have a stationary signal from a train of Gaussian pulses. My sampling window is too wide (cannot be reduced). In the example 1 ms. So it is not possible to clearly distinguish one pulse from another....
Crandel's user avatar
  • 111
1 vote
1 answer
563 views

inverse discrete FFT in python, multiple times?

I was wondering what really happens when taking the inverse discrete FFT on some set of numbers, for 3 times? Because looking at it, it looks like we're getting an output that is identically with the ...
C. Cristi's user avatar
  • 111
0 votes
1 answer
512 views

Frequency domain Inversion of a signal

I have been trying to calculate the inverse of a sweep (by inverse I mean something that when convolved with my original signal will yield a unit impulse) and although I managed to find a time-domain ...
ZaellixA's user avatar
  • 1,178
0 votes
1 answer
237 views

Inverse Fourier Transform Dirac impulse with scaled argument

Currently, I am dealing with the sampling problems and I don't understand how to calculate inverse Fourier transform of a scaling impulse function $\textrm{IFT}\{\delta(\Omega T)\} = ?$, $T$ is ...
PhilN's user avatar
  • 3
-1 votes
2 answers
717 views

How to get the inverse of Filter based on channel

Given a signal $X$, and a channel $h$, and the received signal $Y = Filter(h,1,X);$ What's the inverse of filter, it means if I know $h$, how can I get back $X$ ?
New_student's user avatar
0 votes
0 answers
28 views

Inversion problem for big dataset

Suppose my goal is to solve for $x$ in $Ax = b$ using CG method and $A$ is Toeplitz. The problem is that $b$ is extremely large in size and I can't just read in the whole vector $b$ and then solve for ...
Ong Beng Seong's user avatar
0 votes
1 answer
491 views

Inverse system of a box function

I learned about the inverse system. Suppose I have an impulse response $h(t)$ which is a box function. ($A = 1, T = 2$) If I take the Fourier transform and referring the transform pairs, $$H(j\omega)...
David Badger's user avatar
0 votes
2 answers
476 views

My impulse response does not tend to zero

I am doing an IFFT of frequency response data achieved with Simulation tools. When I plot my impulse response it looks wrong as the response does not tend to zero as it should. Instead there seems ...
Eske August Jayaswal's user avatar
1 vote
2 answers
4k views

Z transform - Inverse System function - Why number of poles and zeros myst be equal?

I know that if a system is causal then the system function H(z) must have : a) a ROC that spans from the exterior of the most distant pole and b) the number of zeros must not be greater than the ...
manpad's user avatar
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0 votes
1 answer
237 views

How can I find the value of Inverse DFT

I have dt signal $x[n]={[6.29, 8.11,-7.46,8.26,2.64,-8.04,-4.43,0.93,-9.29]}$ And I need to give the function value of: 1) sum of $x[n] = \sum\limits_{k=0}^{N-1} X[k] \, e^{-j 3 \pi k/5}$ from k=0 ...
Nada Hamad's user avatar
2 votes
1 answer
2k views

Is the inverse of a causal system also causal?

If I have a causal system H(z) and I find the inverse of this system: $$ G(z) = \frac{1}{H(z)} $$ Is G(z) also causal?
MrCasuality's user avatar
1 vote
1 answer
270 views

Problems with IFFT not being symmetrical

I have two signals, a measurement and a reference which I have performed an FFT on. They have both been windowed with a Hanning window, and now I would like to deconvolve these to get the impulse ...
Sam Proctor's user avatar
0 votes
2 answers
1k views

Is $y[n]=x[n] * x[n^2]$ invertible?

Is the following system invertible or not? $$y[n]=x[n] * x[n^2]$$ where $*$ stands for the aperiodic convolution operator. I have not been able to find a mathematically sufficient argument for it...
user avatar
0 votes
2 answers
1k views

Inverse system of a system with integral

I am trying to find the inverse system of the following (I tried finding the mathematical inverse function but since it is not the same I am not so sure) . Can someone help me find it? $$ y(t)=\int_{...
user avatar
2 votes
0 answers
105 views

Normalized LMS with a posteriori Error and Woodburry's Matrix Inversion

I was going through this paper and the author mentioned that we can prove the following using the Matrix Inversion Lemma (AKA Woodburry's Matrix Inversion Identity): Using matrix inversion lemma we ...
Copernicus's user avatar
0 votes
1 answer
572 views

Programming the IDWT for image processing

I want to program the 2D inverse discrete wavelet transform (only 1 level) in the case of image processing. In the matlab website there's this diagram: now, I want to program the IDWT with haar ...
S.E.K.'s user avatar
  • 165
1 vote
2 answers
5k views

Discrete time inverse fourier transform of cosine squared

$$ X(\omega) = \cos^2(\omega)$$ I tried this problem, and I ended up getting $0$, which doesn't make any sense. I integrated: $$ x(n) = \frac{1}{2\pi}\int_{0}^{2\pi} \cos^2(\omega)e^{j{\pi}n} d\...
One Normal Night's user avatar
3 votes
1 answer
3k views

Is this system invertible or not?

Prove that the following system is invertible. $$y(t) = \mathcal{T}\{x(t)\} = \int_{-\infty}^{3t} x(\tau) \,\mathrm d \tau$$ Answer: yes, the system is invertible. I need some hint here, not the full ...
fpsshubham's user avatar