# Frequency Resolution of Chirp Z Trans. vs DFT

Started by May 1, 2012
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If someone is well versed in the Chirp Z transform, could you help me out a
little.

Im a little confused about the freq. resolution one can attain using the
CZT on a contour on the unit circle.

I understand that the CZT gives one the flexability to evaluate frequeny
samples at arbitrary points on the unit circle (or other splinelike
contours), but that doesnt say much about the frequency resolution one can
attain.

Is the CZT limited in frequency resolution by the number of time samples
recorded like the DFT is? Or is it possible to gain resolution by using
such a transform?
```
```On May 1, 9:34&#2013266080;am, "westocl" <cweston_@n_o_s_p_a_m.hotmail.com> wrote:
> If someone is well versed in the Chirp Z transform, could you help me out a
> little.
>
> Im a little confused about the freq. resolution one can attain using the
> CZT on a contour on the unit circle.
>
> I understand that the CZT gives one the flexability to evaluate frequeny
> samples at arbitrary points on the unit circle (or other splinelike
> contours), but that doesnt say much about the frequency resolution one can
> attain.
>
> Is the CZT limited in frequency resolution by the number of time samples
> recorded like the DFT is? Or is it possible to gain resolution by using
> such a transform?

The CZT gives you the flexibility to evaluate the Z transform other
than uniformly around the unit circle. But it doesn't affect the
underlying resolution of what you are evaluating.

The CZT can be used to evaluate only a small part of the DFT around a
frequency band of interest - but this is essentially the same thing as
mixing a signal to baseband, low pass filtering + decimating and then
doing a DFT. That's just one example - the CZT is more flexible than
just that. But you can see from this example it wouldn't improve the
frequency resolution.

Cheers,
Dave

```