# Tag Info

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• 4,872
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### What does the exponential term in the Fourier transform mean?

It's a complex exponential that rotates forever on the complex plane unit circle: $$e^{-j\omega t} = \cos(\omega t) - j \sin(\omega t).$$ You can think of Fourier transform as calculating correlation ...
• 12.4k
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### Difference between CTFT and DTFT?

The difference is pretty quickly explained: the CTFT is for continuous-time signals, i.e., for functions $x(t)$ with a continuous variable $t\in\mathbb{R}$, whereas the DTFT is for discrete-time ...
• 80.2k

### Does the DTFT of $\frac{u[n-1]}{n}$ exist?

Note that the sequence $$x[n]=\frac{u[n-1]}{n}\tag{1}$$ is in $\ell^2(\mathbb Z)$ because $$\sum_{n\in\mathbb{Z}}|x[n]|^2=\sum_{n=1}^{\infty}\frac{1}{n^2}=\frac{\pi^2}{6}<\infty\tag{2}$$ but it ...
• 80.2k
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• 80.2k

### Difference between CTFT and DTFT?

I'll add a couple more facts, to sorta complete the definitions of things. As Matt represented the CTFT and DTFT, they are both shown as special cases of the Laplace Transform and Z Transform (...
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### why $-$ sign in DTFT pair for constant

It can also have a $+$ sign, there's no difference. Write down a part of the sum (around index $l=0$) and try to see that in both cases you're summing the same terms, just in a different order. More ...
• 80.2k
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### Is possible reach the DFT if I have the DTFT?

The DFT is a sampled version of the DTFT only for finite length signals. Otherwise, there is no point in comparing the DTFT with the DFT because you can only compute the DFT for finite length (or ...
• 80.2k

### What does the exponential term in the Fourier transform mean?

Whether it's the Fourier Transform or the Laplace Transform or the Z Transform, etc. the exponential is the eigenfunction of Linear and Time-invariant (LTI) operators. if an exponential function of "...

### What does the exponential term in the Fourier transform mean?

The Fourier Transform: $$f(t) = \frac{1}{2\pi}\int_{-\infty}^{\infty} F(t)e^{i\omega t} dt\\ F(\omega) = \int_{-\infty}^{\infty} f(t)e^{-i\omega t} dt$$ converts a function to an integral of ...
• 141
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### Why is this DFT of a real symmetric signal resulting in complex valued coefficients?

You defined the signal vector as x = [1 2 3 2 1]. Since the DFT is defined by $$X[k]=\sum_{n=0}^{N-1}x[n]e^{-j2\pi nk/N}$$ the command ...
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### Why DTFT coefficients are periodic and why continuous Fourier transform coefficients are not periodic?

The explanation by @Maximilian Matthé is a standard and formal approach for this question. But I think it is not intuitive and easy to understand the reason. In the following, I will try to explain ...
• 455

### FFT-like algorithm for fast DTFT computation?

According to Oppenheim and Schafer's "Discrete Time Signal Processing", the Goertzel algorithm will be more efficient than the FFT in computing an N point DFT if less than $2 Log_2 N$ DFT ...
• 37.1k
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• 80.2k

### Aliasing and DTFT of a real signal

We are analyzing a real signal with the DTFT. Since we are using a limited number of samples it's like we are transforming a finite signal. No. The DTFT takes an infinite discrete time signal as an ...
• 31.4k

### Why DFT is used for approximating CTFT when you can approximate CTFT-integral itself?

Assuming that future vistors won't take the time to read all the comments, I'd like to give a very simple and straightforward interpretation of the discrete Fourier transform (DFT) as an approximation ...
• 80.2k

### Difference between Fourier Transform and DFT? - Example

The difference is between $\mbox{sinc}$ and the periodic version obtained using the DFT. See this answer for a comparison. It strikes me that asinc = ratio of two sincs. The $\mbox{asinc}$ ...
• 22.3k