Correct way of zero padding in time domain

Question

I am very new to signal processing and want to learn the correct way of zero padding for 'n' even and odd input signals.

For example,

$N=6\;\&\;M=32$

$x(n)=[a, b, c, d, e, f]\;\;\;n=0,1,\dots,N-1$

$x_{zeros}(m)=[a, b, c, d, e, f, zeros(M-N)]\;\;\;m=0,1,\dots,M-1$

-or-

$x_{zeros}(m)=[left\;zeros\dots a, b, c, d, e, f,\dots right\;zeros]\;\;\;m=0,1,\dots,M-1$

-or-

$x_{zeros}(m)=[a, b, c,\dots zeros\;in\;the\;middle\dots d, e, f]\;\;\;m=0,1,\dots,M-1$

What to consider when the input is $\mathrm{Real}$ or $\mathrm{Complex}$ of even and odd lengths?

Answer 1

Zero padding changes the bin size of the DFT resulting a finer frequency resolution. It is done by appending zeros to the end of the signal because we are only artificially increasing the length to decrease the bin size, $\frac{2\pi k}{N}$. An $N$ point DFT is just evaluating the DTFT on certain frequencies. If you were to append some zeros to the front of the signal then you are doing a time shift, and a shift in time domain is modulation in the frequency domain: $x[n-k]=X(\omega)e^{-j\omega k}$.