The Discrete Fourier Transform (DFT) is given by
$X_k = \sum_{n=0}^{N-1} x_n e^{2\pi i k n/N}$
for $k=0,1,\ldots N$. I store the variables $X_k$ and would like to add $m$ zeros to the variables $x_n$. After concatenating $m$ zeros I would like to find the values of the new $X_k$. That is, I would like to compute the values
$Y_k = \sum_{n=0}^{N-1+m} y_n e^{2\pi i k n/(N-1+m)}$
for $k=0,1,\ldots N+m$ where $y_n = (x_0,\ldots,x_{N-1},0,\ldots,0)^T$. Currently, I'm using the inverse DFT to get to the x_k coefficients, concatenating $m$ zeros to them and then using the DFT to find the $Y_k$.
Is there a better way?
Thanks.