Similarity in absolute value of nearby DFT coefficients

1. How do you calculate DFT coefficients?
2. What are the DFT coefficients?
3. What happens if we apply DFT twice to a signal?
4. What is symmetry property of DFT?

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 ) .

What are the DFT coefficients?

DFT coefficients, Xk, give amplitudes and phases of complex sinusoids at integer frequencies k, from 0 to N−1, that sum to the original signal x[n], comprised of N points.

What happens if we apply DFT twice to a signal?

Applying the DFT twice results in a scaled, time reversed version of the original series. The transform of a constant function is a DC value only.

What is symmetry property of DFT?

DFT conjugate symmetry says that there is redundancy in the spectral content of a real-valued signal. But what exactly is the minimal set of frequencies that we must compute to fully represent the signal? We can think of this by working through each. N − 1 and seeing which other components can be inferred once we have ...