2X Oversampled Hamming Window Transform

Let's now zero-pad by a factor of 2 in the time domain, before we perform our DFT:

• Zero-padding factor $L \;\mathrel{\stackrel{\mathrm{\Delta}}{=}}\;\frac{N}{M} = 2$
• N = DFT size = $2 M$
• DFT frequency samples at $\omega_{k^\prime} = {k^\prime}\frac{2\pi}{N} = {k^\prime}\frac{2\pi}{2M}$

Causal zero-padding by a factor of two ($L=2$ ):

• DFT bin width $= \frac{1}{L}\frac{2\pi}{M} = \frac{2\pi}{2M}$ ($2\times$ oversampled)
• $8$ samples per main lobe (Hamming window)