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Need help with DTFT problem

Hint: it comes from the Fourier transform of $x[n]$. Once you calculate that, it will be obvious why $Y(\omega)$ only has support in those regions.
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1 vote
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Fourier transform why can I convert one of the axes into an imaginary number?

Fourier transform are able to approximate a wite range of complex function $f(t) = x(t) + j\cdot y(t)$ that satisfies the Dirichlet conditions, with negligible small mean square error. Well, in ...
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2 votes

Periodicity of a discrete time complex exponential signal?

You have a sequence of complex numbers $$x[n]=e^{j\pi an},\quad a\in\mathbb{R},\quad n\in\mathbb{Z}\tag{1}$$ $x[n]$ is periodic with period $N$ if $x[n]=x[n+N]$ is satisfied for all $n$. For the given ...
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1 vote

Periodicity of a discrete time complex exponential signal?

A signal $x[n]$ is periodic with period $P$ if $$ x[n] = x[n+P]$$ for all $n$. That means that some "sinusoidal" signals which are periodic when $n$ is real-valued and continuous are not ...
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0 votes

How to compute convolution using the Discrete Hartley Transform

You forgot to roll the array after flipping. What you want is x0, x(n-1), x(n-1)... x2, x1 but you are using ...
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0 votes

Odd artifacts after sinc interpolation

I agree that some amount of ringing is normal in sinc() interpolation. However, the function you are using does the calculation as if all samples outside the input ...
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8 votes
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Odd artifacts after sinc interpolation

So, this is what I'd consider -- contrary to your title -- to be perfectly normal and expected artifacts from sinc interpolation. Keep in mind that the sinc function rings forever. This means that if ...
  • 9,136
3 votes
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Different PI controller implementations and their respective discrete transfer functions

On the 2nd approach, your transfer function looks fine but translating it into C code appears wrong. To re-write your z-domain as a discrete finite difference equation where $y$ is the output and $a=...
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1 vote

Why use sinc function to downsample an image in fourier domain?

Downsampling operation, with an integer factor M, involves two steps: first a lowpass filtering is applied to bandlimit the input so as to avoid any possible aliasing, then a compressor (decimator) ...
  • 27.1k
1 vote

Why use sinc function to downsample an image in fourier domain?

Zeroing higher frequencies of the image in the Fourier domain (multiplying it with an ideal box filter) is equivalent to filtering the image in the time domain with a sinc function of infinite extent. ...
  • 900
1 vote
Accepted

Sampling Precision, Jitter, and PID

Treating quantization noise as random noise is pretty well treated in the DSP literature. Quantization in control systems usually exhibits as random noise, with $\sigma^2 = \frac 1 {12} q^2$, where $q$...
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