Howtosignalprocessing
- What are the the disadvantage of DTFT?
- What is the condition for the existence of DTFT?
- What is inverse DFT?
- What is the difference between discrete-time Fourier transform and discrete Fourier transform?
What are the the disadvantage of DTFT?
Two computational disadvantages of the DTFT are: the direct DTFT is a function of a continuously varying frequency and the inverse DTFT requires integration. The Fourier series coefficients constitute a periodic sequence of the same period as the signal; thus both are periodic.
What is the condition for the existence of DTFT?
So existence means simply that the sum that defines a DTFT does not blow up. This is easy to prove for absolutely summable sequences. If you take the magnitude of the DTFT at any point omega, this is equal to the sum for n that goes from minus infinity to plus infinity of x[n] times e to the- j omega n in magnitude.
What is inverse DFT?
An inverse DFT is a Fourier series, using the DTFT samples as coefficients of complex sinusoids at the corresponding DTFT frequencies. It has the same sample-values as the original input sequence. The DFT is therefore said to be a frequency domain representation of the original input sequence.
What is the difference between discrete-time Fourier transform and discrete Fourier transform?
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.
