Zero Padding Examples

Let's look at the effect of zero padding on the Fourier transform of the popular (causal) Hamming window:

$$w(n) = 0.54 - 0.46\, \cos \left( \frac{2 \pi n}{M} \right), \quad n=0,1,2,\ldots M-1$$

where $M=21$ in our examples.

We will look at shifts of the

• critically sampled window transform $W(\omega_k-\omega_0)$ , and
• $2\times$ oversampled window transform $W(\omega_{k^\prime}-\omega_0)$

where $\omega_0=2\pi\cdot 3/M = 2\pi/7 \approx 0.9$ rad/samp is the normalized radian frequency of the test sinusoid to which the window is applied.