Contents
What is basis function in DFT?
The sine and cosine waves used in the DFT are commonly called the DFT basis functions. In other words, the output of the DFT is a set of numbers that represent amplitudes. The basis functions are a set of sine and cosine waves with unity amplitude. The parameter, k, sets the frequency of each sinusoid.
What are the main differences in the DTFT and the DFT?
What is the difference between DFT and DTFT?
| DTFT | DFT |
|---|---|
| DTFT is periodic | DFT has no periodicity. |
| The DTFT is calculated over an infinite summation; this indicates that it is a continuous signal. | The DFT is calculated over a finite sequence of values. This indicates that the result is non-continuous. |
Is the DFT a continuous representation of the original sequence?
The DFT is therefore said to be a frequency domain representation of the original input sequence. If the 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.
How is the DFT related to the Fourier series?
The DFT can be compared with the Fourier series, by which a periodic function is expanded as a linear combination of infinite function (for all ) used as the basis functions of the function space:
How are DFT coefficients represented in the time domain?
As the basis vectors are periodic, their DFT coefficients are also periodic: Summary A periodic signal can be equivalently represented in the time domain by a set of samples over an interval of , separated by the sampling period , or
How is the formulation of the DFT possible?
Formulation of the DFT Most time signals in practice are continuous and non-periodic, and their analytical expressions are unavailable. The spectrum of such a non-periodic and continuous signal can only be obtained numerically by a digital computer. To do so, the signal needs to be modified in two steps: