# Interpolate DFT Coefficient of a Frequency That Is Not in the DFT Bin

I'm using the Jacobsen interpolation to get a more precise frequency of my signal. To get the corresponding DFT coefficient I'm doing:

$$X_{f} = \sum_{n=0}^{N}{x_{n} e^{-2\pi ifn}}$$

Where $x_{n}$ is the samples of my signal and $f$ is the frequency found by the interpolation (that is not one of those in the DFT bins). This is a quite heavy computation for large signals.

Is there a method to interpolate the coefficient corresponding to that frequency without having to compute the sum?

• Have look at Goertzel based solution. – jojek Sep 7 '16 at 12:48
• But the Goertzel solution also requires looping throw the samples, I was looking more for an interpolation method using the closest DFT bins. – user2906781 Sep 7 '16 at 13:17
• This answer might be helpful. – Matt L. Sep 7 '16 at 14:49