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Accepted

• 5,020

### Link between DFS, DFT, DTFT

Yes your understanding is basically correct. The 1st paragraph (2 lines) expresses the fundamental relation between the DFS and the DFT of a finite-length sequence $x[n]$ while the 2nd paragraph tries ...
• 28.3k

### 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 ...
• 90.3k
Accepted

### 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 ...
• 90.3k

### 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 (...

• 90.3k
Accepted

• 127

### 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 ...
• 465

### 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 ...
• 51.9k

### Discrete-time Fourier Transform of the unit step sequence $u[n]$

I'll provide two relatively simple proofs that do not require any knowledge of distribution theory. For a proof that computes the DTFT by a limit process using results from distribution theory, see ...
• 90.3k

The DTFT relationships $$x_{even}[n]=\frac12\left(x[n]+x^*[-n]\right)\Longleftrightarrow\textrm{Re}\left\{X(e^{j\omega})\right\}$$ and $$x_{odd}[n]=\frac12\left(x[n]-x^*[-n]\right)\... • 90.3k 4 votes ### Aliasing and DTFT of a real signal We are analyzing a real signal with the DTFT. Since we are using a limited number of samples it's like we are transforming a finite signal. No. The DTFT takes an infinite discrete time signal as an ... • 45.3k 4 votes Accepted ### Getting the DTFT from the DFT samples Myth: DTFT is Sinc-interpolated DFT. Problem with the above statement: Sinc is not 2\pi-Periodic function, but all DTFTs are. Correct Answer: Theoretical, Continuous-\omega 2\pi-Periodic DTFT ... • 2,611 4 votes Accepted ### Z-transform of the Unit Step and DTFT Assuming that the \mathcal{Z}-transform X(z) of a sequence x[n] exists, there are three cases we need to distinguish when considering the relation between X(z) and the corresponding DTFT X_F(... • 90.3k 3 votes Accepted ### Magnitude and phase of -\delta[n]? If the magnitude is 1 and the phase were 0, you would get$$H(e^{j\omega})=1$$which corresponds to h[n]=\delta[n]. So this is obviously wrong. The fact that the phase of a negative real-... • 90.3k 3 votes Accepted ### Frequency Response with Delta Function? The long road computes the modulus of the DTFT. This works in general, but can be tedious. When the formula possesses some symmetry, like here (the two coefficients are the same), you can more ... • 31.9k 3 votes ### Frequency Response with Delta Function? Hint: Expand e^{j \omega} using Euler's formula. This will enable you to express H(\omega) = R(\omega) + j I(\omega) where R and I are the real and imaginary parts and then the magnitude of ... • 4,134 3 votes Accepted ### Why DTFT coefficients are periodic and why continuous Fourier transform coefficients are not periodic? The result of a DTFT is periodic, because any discrete-time signal has a continuous spectrum. This can be e.g. explained by the following: Let x(t) be a time-continuous signal. Now, making it ... • 6,218 3 votes Accepted ### The DTFT of \{1,1\} is 1+e^{-j\omega} but what is the DTFT of \{1,-1\}? You should consider the DTFT pair:$$\delta[n] \xrightarrow{\text{DTFT}} 1$$and the time-shifting property of the Fourier transform$$x[n-n_0] \xrightarrow{\text{DTFT}} X(e^{j\omega})e^{-j\...
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 $\mbox{asinc}$ ...