# Questions tagged [dft]

The Discrete Fourier Transform (DFT) is a mapping between a finite set of discrete points in a (primal) domain (time, space) and the dual frequency domain. DFT requires an input sequence which is discrete, such as a sampling from an analogue audio signal.

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### Understanding the result of the fft algorithm

Understanding the result of the fft algorithm. I need help understanding the FFT calculation results. Recently, I have been interested in signal analysis, so I have created and understood fft ...
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### Calculating the DFT of the image after using a filter

Studying for my finals in Image Processing course. Trying to solve the following question: Let $h$ be a filter that replaces each pixel value with the average of it's 8 neighbors. Let $f$ be a ...
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### Fourier Transform of an 2D image and associated units

I have the following rather simple problem and unfortunately I am not getting forward. Imagine a simple 2D image with pixels and a unique value for each pixel of the image. For example, let the image ...
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### Why is frequency resolution dependent on the number of samples? (need for intuition)

I know the DFT, I agree with the formula and everything, but I don't get the intuition on the link between frequency resolution and number of samples. Like, why would I get a higher frequency ...
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### DFT algorithm output meanning [duplicate]

The result of calculating the amplitude of the audio through the DFT algorithm above is It came out as below. ...
1 vote
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### Why is the arithmetic mean the same as the DC component of its fourier transform?

When we define $$\overline{\left|x\right|} = \frac1T\int_0^T x(t) dt$$ as the arithmetic mean of a signal we can see that it is the same as its dc component in the fourier transform. Why is this the ...
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### Dirichlet sufficient conditions satisfiability checking

I have 4 signal functions like this: $1.\ e^{-2t}u(t)$ $2.\ e^{-2|t|}$ $3.\ (1-\frac{|t|}{2014})(u(t+2014)-u(t-2014))$ $4.\ u(t)$ I know the answer would be the third option since the other ones have ...
154 views

### Fourier transform of an aperiodic discrete-time signal

I have a signal of the form $x^{*}(-n+2)$. To derive the signal's Fourier transform I use The following properties of DFT: $x^{*}(n)=X^{*}(-\omega)$ and $x(n-k) = e^{-j\omega k}X(\omega)$ so the ...
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### Symmetries of analyticity / zero self-correlation

I seek to understand symmetry properties of analytic sequences, without referring to frequency domain: what criteria must a complex sequence $x[n]$ satisfy to be analytic? Framed alternatively, such a ...
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