Bluestein's algorithm to evaluate the DFT from $f_o$ to $f_o + k\Delta_F$
The convolution in Bluestein's algorithm is a linear convolution, not circular. Since the approach is to use standard FFT's for the convolution operation, the underlying waveforms being convolved must be zero padded out to $M \ge 2N-1$ to compute the linear convolution accurately.