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

1. Does the DTFT exist?
2. What does the DTFT do?
3. How do you find DTFT from DFT?
4. What is DTFT and its properties?

Does the DTFT exist?

In the case of finite-length sequences such as the impulse response of an FIR filter, the sum defining the DTFT has a finite number of terms. Thus, the DTFT of an FIR filter as in (7.1) always exists because X(ej ˆω) is always finite.

What does the DTFT do?

In mathematics, the discrete-time Fourier transform (DTFT) is a form of Fourier analysis that is applicable to a sequence of values. The DTFT is often used to analyze samples of a continuous function.

How do you find DTFT from DFT?

Correct Answer: Theoretical, Continuous-ω 2π-Periodic DTFT can be obtained by continuous Lagrangian-interpolation of the DFT Samples. So that the values at ω=2πk/N will be the DFT Samples X[k] for k=0,1,...,N−1 and the Interpolation-function's zero-crossings are at 2πk/N.

What is DTFT and its properties?

The discrete time Fourier transform is a mathematical tool which is used to convert a discrete time sequence into the frequency domain. Therefore, the Fourier transform of a discrete time signal or sequence is called the discrete time Fourier transform (DTFT).