Questions tagged [symmetry]

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Symmetric half-band FIR re-timing

I'm trying to get my head around an FPGA implementation of a half-band FIR filter. I'm trying to draw the block diagram to help with that. I've started with a 10th order example as so: Due to the ...
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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 ...
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4 answers
259 views

Linear Phase Filters and FFT

The FFT decomposes a signal into cosine and sine functions, respectively, even and odd components of the signal. Hence, I would expect even symmetric filters to have zero imaginary parts. Suppose a ...
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3 answers
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Do symmetric discrete signals have zero phase?

I generated a Hanning window having an even symmetry: where for even-sampled case we either take "left" and "right" to include or exclude the center sample. I was surprised to ...
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137 views

Finding the Energy & Power of a Composition of Odd and Even Signal

Given two CT signals $x_1(t)$ (even signal) and $x_2(t)$ (odd signal). If $x_1(t)+x_2(t)$ is an even signal then what is the energy and power of $x_2(t)$. My Attempt $\int \limits _{-\infty}^{+\infty}$...
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Finding causal impulse response given the imaginary part of the frequency response

I understand that I would need to calculate inverse Discrete Time Fourier Transform (iDTFT) to find $h(n)$. Since $h(n)$ is real, iDTFT of the imaginary part of $H(e^{j\omega})$ gives the odd part of ...
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DFT symmetry vs DFT duality in Richard Lyons' "Understanding DSP"

I am reading Richard lyons, understanding dsp, chap 3. Article 3.2 is about property of dft symmetry but any where in this chapter, i am unable to find discussion about dft duality property I want ...
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Real time signal processing use cases for eigenvalues of symmetric matrices

I realize that this might be somewhat of an unusual and specific question. I know that the eigenvalues of symmetric matrices are used in a number of ways in scientific computing, such as for finding ...
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2 answers
356 views

Significance of steps involved in flipping process of an image?

The above image on the right was obtained by following steps Multiplying the image on the left by $(-1) ^ {(x+y)}$ Computing the DFT Taking the complex conjugate of the transform Computing the ...
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Fourier transform in Matlab and hermitian symmetry

According to the conjugate symmetry property of Fourier transform, shouldn't the following command not return 1 (=true): ...
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2 answers
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Why is the fft magnitude spectra of sine not symmetric?

I thought that the magnitude spectra of real signals was symmetric. When I take the absolute value of the fft of a sine wave the result is not symmetric. There seems to be a peak at the first ...
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DFT of 2d real signal and Hermitian symmetry

Knowing that DFT of n-values real signal in 1d consists of n/2+1 different values where the second half of the spectrum is complex conjugate of the first one (Hermitian symmetry). However in the ...
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Fourier Transforms, symmetry, real/imaginary

I was hoping to clarify if the following was correct: A real function (neither even nor odd) in time exhibits conjugate symmetry in frequency, so the real part of the frequency response is even, and ...
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4 votes
2 answers
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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 ...
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Exploiting coefficients symmetry of a FIR interpolation filter in a polyphase implementation

I'm trying to figure out whether there is a way to exploit a symmetry of a FIR interpolation filter in a polyphase implementation. I know for a fact that we can exploit the symmetry in a normal FIR ...
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639 views

Evaluate image symmetry

I am trying to evaluate the symmetry of an image with Matlab. My approach is far is based on: convert image to BW get 2D gaussian from the BW pixel cloud get center and axis rotate to get horizontal ...
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2 answers
6k views

Even and odd signal energy property

In Signals and Systems by A. V. Oppenheim, A. S. Willsky, S. Hamid Nawab, 2nd Edition, and Signals and Systems, Simon Haykins, Barry Van Veen, 2nd Edition there is a problem related to energy of real-...
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What do we achieve by using PAM symbols symmetrical with respect to 0?

I can't seem to find the answer to this one anywhere online. We want them symmetrical with respect to 0 and also at even distance between each other. Why is this important?
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Are there analogues to orthogonal transformations in non-orientable surfaces?

I am working on extremely large, symmetric matrices of counts, and attempting to identify patterns/shapes within them. Wavelets are a popular tool in image processing, and have some nice statistical ...
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1 answer
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Optimization‏ FIR filter

I have a doubt about this : Iterative methods for optimization‏ in FIR filter (on the one hand traditional like window,frequency sampling ,WLS,Remez Exchange...,on the other hand evolutionary methods ...
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1 answer
273 views

symmetrical wav audio in time domain and Phase spectrum significance

I have plotted many wav files in MALTAB and tried to understand their time domain plot , Magnitude spectrum and Phase spectrum. But I don't get why time domain plots of speech wav files are ...
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1 answer
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On the symmetry of a $2$-dimensional discrete-time signal

Can we distribute the minus sign as follows? $$-h[n_1,n_2] = h[-n_1,-n_2]$$
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2 votes
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discrete fourier transform circular symmetry

I was reading digital signal processing. In topic Discrete Fourier Transform, circular symmetry it is said that circular advance is obtained by shifting x(n) in clockwise direction. i.e. to obtain x(n+...
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1 vote
0 answers
880 views

Symmetry and mirror of inverse FFT

I am trying to do an inverse FFT to get the real signal from a derived formula which describes the Fourier transformed signal. I am doing this with FFT. I am fairly new to the theory of FFTs, so my ...
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3 answers
1k views

Effect of zero padding an odd symmetric FIR filter in the time domain

I have a symmetric lowpass FIR filter with 1149 time domain taps (all real coefficients). For implementation purposes, it would be easier if the filter had 1200 taps. Since it has an odd number ...
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1 vote
2 answers
521 views

Non-symmetrical DFT of real valued signal

I have a homework assignment to take the $64$ DFT of $\cos((5\pi/32)n)$ and $\cos((5\pi/64)n)$. However, for the second case I obtained DFT spectrum such that I have that famous symmetry in real part ...
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Why do linear phase filters have symmetric impulse responses?

It was given as a fact that linear phase filters have symmetric impulse responses, but I don't see why that has to be true. Can somebody please explain or prove this?
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2 votes
2 answers
214 views

Conditions for symmetric and unimodal windows in both time and frequency domains

After a lecture on harmonic analysis and time/frequency methods, I reconsidered the Gaussian kernel, defined in continuous time. It is unimodal and symmetric, and its continuous Fourier transform is ...
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9 votes
2 answers
3k views

Fourier transform artifacts

My starting point in what follows is a radially symmetric random field. Taking the Fourier transform of this (and plotting it in logarithm to highlight the patterns), I obtain the following image in ...
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0 answers
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Filtering with filters without even or odd symmetry in the fourier domain

I am doing a project where I have to use the fourier domain for convolution. I have been reading Digital Image processing by Rafael Gonzalez but I unsure about one thing, and I could not find anything ...
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1 answer
107 views

Odd sampling for symmetric functions?

I have just started my first proper course in DSP, and am a little confused about a statement in my textbook. The book states: "Notice that when the Nyqust-frequency is defined as $\pi/\Delta t$, we ...
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6 votes
2 answers
419 views

Can you quarter the processing time for real, symmetric FFTs?

The DFT of a real signal is Hermite-symmetric, so you can roughly halve the computation time/memory by not bothering to calculate half the values of the spectrum (and complex conjugating the existing ...
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769 views

How to express linear convolution using positive frequencies from channel and symbol DFT vectors?

Sorry for the long question, but I'm struggling to implement something related to this question. Your help would be appreciated. Background Notation: In the sequel, the uppercase letters represent ...
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3 answers
262 views

How can a linear operator on DFT vector produce the same vector using only half of the DFT vector?

Suppose there is a DFT vector $\mathbf{X}$ with length N, which presents complex conjugate symmetry around its middle point, i.e., $X(1) = X(N-1)^*$, $X(2) = X(N - 2)^*$ and so forth. $X(0)$ and $X(N/...
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8 votes
3 answers
29k views

How to make a signal conjugate symmetric?

Take the simple frequency-domain band-pass filtering operation below . . . ...
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