Dtft vs dft

DTFT is an infinite continuous sequence where the time signal (x(n)) is a discrete signal. DFT is a finite non-continuous discrete sequence. DFT, too, is calculated using a discrete-time signal.

1. What is difference between DFT and DTFT?
2. What is the relationship between DTFT and DFT?
3. What is difference between DFT and FFT?
4. Is DTFT same as Z transform?

What is difference between DFT and DTFT?

original sequence spans all the non-zero values of a function, its DTFT is continuous (and periodic), and the DFT provides discrete samples of one cycle. If the original sequence is one cycle of a periodic Page 2 function, the DFT provides all the non-zero values of one DTFT cycle.

What is the relationship between DTFT and DFT?

The DFT differs from the discrete-time Fourier transform (DTFT) in that its input and output sequences are both finite; it is therefore said to be the Fourier analysis of finite-domain (or periodic) discrete-time functions.

What is difference between DFT and FFT?

Discrete Fourier Transform (DFT) is the discrete version of the Fourier Transform (FT) that transforms a signal (or discrete sequence) from the time domain representation to its representation in the frequency domain. Whereas, Fast Fourier Transform (FFT) is any efficient algorithm for calculating the DFT.

Is DTFT same as Z transform?

Also, if r = 1, then the discrete time Fourier transform (DTFT) is same as the Z-transform. In other words, the DTFT is nothing but the Z-transform evaluated along the unit circle centred at the origin of the z-plane.