Questions tagged [conjugate]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
9 votes
1 answer
50k views

Conjugation in Fourier Transform

I have a very simple question. In Oppenheim book, it says that: If CT Fourier transform of $x(t)$ is $X(j\omega)$ then, CT Fourier transform of $x^*(t)$ is $X^*(-j\omega)$. What I can't ...
jason's user avatar
  • 205
9 votes
3 answers
32k views

How to make a signal conjugate symmetric?

Take the simple frequency-domain band-pass filtering operation below . . . ...
learnvst's user avatar
  • 1,513
4 votes
2 answers
8k views

Result of conjugate symmetry property of DFT

I know one of the properties of DFT for real-valued time series is conjugate symmetry. But what does it imply? In the textbook it says that for a DFT of the length M, this makes M/2-1 spectral ...
Shady's user avatar
  • 197
3 votes
1 answer
899 views

Fourier Transform gives unexpected results: signal reversal and conjugation

As far as I understand the math you can reverse a real valued signal by Fourier transformation, taking the complex conjugate of the result and inverse Fourier transformation, i.e. \begin{equation} \...
David Hoffman's user avatar
2 votes
2 answers
703 views

IFFT gives complex values in Matlab

I have frequency data from a VNA. I am trying to convert to time domain, and I can't figure out why I am getting complex valued time domain data. This is for ISAR measurements, and I can't get passed ...
Frank's user avatar
  • 33
1 vote
2 answers
3k views

How to interpret output of matched filter with complex input?

I have implemented a matched filter based on the Fourier Transform approach. In the real numbers domain that means that I use as the coefficients of my filter (B) the inverted time-samples of the ...
VMMF's user avatar
  • 1,110
1 vote
0 answers
24 views

please help me solve the question which proving X[N-k] is the complex conjugate of X[k] [closed]

Show for the DFT that if all x[n] are real, then X[N - k] is the complex conjugate of X[k] for k > 0. (i.e. if X[k] is a + bi, then X[N - k] is a - bi)
Reece's user avatar
  • 11
1 vote
0 answers
37 views

Could the conjugate derivatives of two independent random signals be uncorrelated?

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{\...
Loco Citato's user avatar
0 votes
1 answer
4k views

Meaning of Multiplying a complex number with its conjugate

While reading Estimation of Symbol Timing Offset, i came across an equation like multiplying a signal with its conjugate. $$ \hat{\delta} = \arg \max_{\delta} \sum_{i=\delta}^{N_g-1+\delta} \left|y^*(...
rajez79's user avatar
  • 357
0 votes
1 answer
62 views

Calculation confusing of conjugate in CT fourier transform

when calculate conjugate of $$X(f)=\int_{-\infty}^{+\infty} x(t)e^{-j2\pi ft}dt ,\tag{1}$$ I can get $$X^*(f)=\int_{-\infty}^{+\infty} x(t)^*e^{j2\pi ft}dt ,\tag{2}$$ so $$F[x^*(t)]=X^*(-f).\tag{3}$$ ...
Jeff's user avatar
  • 3
0 votes
1 answer
478 views

Intuition of odd and even complex conjugate symmetry definition of DFT/DTFT so that $X(e^{j w})=X_{e}\left(e^{j w }\right)+X_{o}\left(e^{j w}\right)$

I have been reading through my courses DSP slides and came across something which was not really taught in detail. You can look up here for reference, it is stated almost identical. Given the ...
OuttaSpaceTime's user avatar
0 votes
1 answer
259 views

Complex Conjugate Sinusoids in Forward DFT

I hope this isn't such a dumb question, but I'm finally getting to grips with the inner workings of the DFT. What I'm having trouble understanding is why the basis complex sinusoids in the "forward" ...
TSIguy's user avatar
  • 1