Howtosignalprocessing
- How is DFT related to FFT?
- What is the relation between DFT and IDFT?
- What is the relationship between sampling frequency and FFT?
- How does the length of a signal affect the DFT?
How is DFT related to FFT?
The discrete Fourier transform, or DFT, is the primary tool of digital signal processing. The foundation of the product is the fast Fourier transform (FFT), a method for computing the DFT with reduced execution time.
What is the relation 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).
What is the relationship between sampling frequency and FFT?
The frequency resolution is equal to the sampling frequency divided by FFT size. For example, an FFT of size 256 of a signal sampled at 8000Hz will have a frequency resolution of 31.25Hz. If the signal is a sine wave of 110 Hz, the ideal FFT would show a sharp peak at 110Hz.
How does the length of a signal affect the DFT?
The length N of the DFT is the number of frequency points that will result in the DFT output. Zero padding will result in more frequency samples, however this does not increase frequency resolution, it just interpolates samples in the DTFT.
