A signal x[n] is analyzed using the time-dependent Fourier transform X_r[k], as defined in Eq. (10.36). Initially, the analysis is performed with an N = 128 DFT using an L = 128-point Hamming window w[n]. The time-domain sampling of adjacent blocks is R= 128; i.e., the windowed segments are offset by 128 samples in time. The frequency resolution obtained with this analysis is not sufficient, and it is desired to improve the resolution.

Several methods of modifying the analysis are suggested to accomplish this goal. Which of the following methods will improve the frequency resolution of the time-dependent Fourier transform X_r[k]?

METHOD 1: Increase N to 256 while maintaining L and R at the same values.

METHOD 2: Increase both N and L to 256, while maintaining R the same.

METHOD 3: Decrease R to 64 while maintaining the same N and L.

METHOD 4: Decrease L to 64 while maintaining the same N and R.

METHOD 5: Maintain N, R and L the same, but change w[n] to be a rectangular window.

X,[k] = X[rR. k] = X[r R. An). 0