Howtosignalprocessing
- What is the relationship between Fourier series coefficients of a periodic sequence and DFT?
- How is DFT related to FFT?
- What is its relation with DTFT and DFT?
- How do you calculate DFT coefficients?
What is the relationship between Fourier series coefficients of a periodic sequence and DFT?
Discrete Fourier Transform and Signal Spectrum
1. The Fourier series coefficients for a periodic digital signal can be used to develop the DFT. 2. The DFT transforms a time sequence to the complex DFT coefficients, while the inverse DFT transforms DFT coefficients back to the time sequence.
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 its relation with 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.
How do you calculate DFT coefficients?
The DFT formula for X k X_k Xk is simply that X k = x ⋅ v k , X_k = x \cdot v_k, Xk=x⋅vk, where x x x is the vector ( x 0 , x 1 , … , x N − 1 ) .
