Howtosignalprocessing
- What is relation between DTFT and DFT?
- What is the difference between DFT and IDFT?
- How do you convert DTFT to DFT?
- Why do we use DTFT in DSP?
What is relation between DTFT and DFT?
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 difference between DFT and IDFT?
The DFT allows one to convert a set of digital time samples to its frequency domain representation. In contrast, the IDFT can be used to invert the DFT samples, allowing one to reconstruct the signal samples x(k) directly from its frequency domain form, X(m).
How do you convert DTFT to DFT?
The continuous variable found in the DTFT (ω) is replaced with a finite number of frequencies located at 2πk/NTs. Here Ts is the sampling rate. In other words, if we take the DTFT signal and sample it in the frequency domain at omega=2π/N, then we get the DFT of x(n).
Why do we use DTFT in DSP?
The Discrete-Time Fourier Transform (DTFT) is the cornerstone of all DSP, because it tells us that from a discrete set of samples of a continuous function, we can create a periodic summation of that function's Fourier transform.
