How is a continuous spectrum for the DTFT possible?

1. How is DTFT continuous?
2. What is the possible range of frequency spectrum for DTFT?
3. Why should continuous Fourier transform be Aperiodic whereas DTFT is periodic?
4. In which frequency spectrum is continuous?

How is DTFT continuous?

The DTFT itself is a continuous function of frequency, but discrete samples of it can be readily calculated via the discrete Fourier transform (DFT) (see § Sampling the DTFT), which is by far the most common method of modern Fourier analysis. Both transforms are invertible.

What is the possible range of frequency spectrum for DTFT?

Ω=2πf is the angular frequency continuous-time Fourier Transform of x(t). Hence the range of |ω| should lie between 0 through π. Given that the spectrum of a discrete time signal repeats every 2π radians, we should see this spectrum replicated from 0 to π, 2π to 3π, 4π to 5π and so on.

Why should continuous Fourier transform be Aperiodic whereas DTFT is periodic?

The spectrum of any discrete signal has a period of 2*pi. Thus, the fourier coefficients occur periodically at interval of 2*pi. While , in case of continuous time signal the spectrum has no such definite period.

In which frequency spectrum is continuous?

A continuous spectrum consists of NOISE components. The spectrum of a sound may be determined by a SOUND ANALYSER or by FOURIER ANALYSIS and is distributed over the audible range (20 to 20,000 Hz). A partial spectrum is also known as a line spectrum, where discrete frequencies are present.