# FFT with sub-Hz resolution?

Started by January 7, 2009
```Newbie question:

I am learning FFT and wandering how to achieve sub-Hz resolution. If
the sampling rate is Fs, and you take N points out of the samples to
do FFT, then the maximum resolution is 1Hz. Or can you take more
points than sampled in a second to achieve sub-Hz resolution?

Maybe the zoom FFT can achieve sub-Hz resolution?

Can somebody enlighten me on this? Thanks!
```
```
> can you take more
> points than sampled in a second

Yes

-jim
```
```On Jan 7, 11:56&#2013266080;am, me4dtrade <me4dtr...@gmail.com> wrote:
> Newbie question:
>
> I am learning FFT and wandering how to achieve sub-Hz resolution. If
> the sampling rate is Fs, and you take N points out of the samples to
> do FFT, then the maximum resolution is 1Hz. Or can you take more
> points than sampled in a second to achieve sub-Hz resolution?
>
> Maybe the zoom FFT can achieve sub-Hz resolution?
>
> Can somebody enlighten me on this? Thanks!

If you need to detect a 1/2 hz sinewave, then the FFT needs 2 seconds
worth of data to see a complete 1/2 hz sinewave.

Likewise if you need to resolve a 1,000,000Hz and 1,000,000.5 Hz
sinewaves, you need 2 seconds worth of data before the FFT can see the
difference between the two signals.
```
```me4dtrade wrote:
> Newbie question:
>
> I am learning FFT and wandering how to achieve sub-Hz resolution. If
> the sampling rate is Fs, and you take N points out of the samples to
> do FFT, then the maximum resolution is 1Hz. Or can you take more
> points than sampled in a second to achieve sub-Hz resolution?
>
> Maybe the zoom FFT can achieve sub-Hz resolution?
>
> Can somebody enlighten me on this? Thanks!

Where do you get 1Hz???

The frequency resolution is the reciprocal of the time span of the samples.
For Sub-Hz resolution this means it must be greater than 1 second.

So, if the sample rate is fs, then the sample interval is 1/fs.
And the number of samples "N" must be such that N/fs > 1 second.

Thus N > 1 second * fs hz a dimensionless number.

Fred

```
```Fred Marshall wrote:
>> Newbie question:
>>
>> I am learning FFT and wandering how to achieve sub-Hz resolution. If
>> the sampling rate is Fs, and you take N points out of the samples to
>> do FFT, then the maximum resolution is 1Hz. Or can you take more
>> points than sampled in a second to achieve sub-Hz resolution?
>>
>> Maybe the zoom FFT can achieve sub-Hz resolution?
>>
>> Can somebody enlighten me on this? Thanks!
>
> Where do you get 1Hz???
>
> The frequency resolution is the reciprocal of the time span of the
> samples. For Sub-Hz resolution this means it must be greater than 1
> second.
> So, if the sample rate is fs, then the sample interval is 1/fs.
> And the number of samples "N" must be such that N/fs > 1 second.
>
> Thus N > 1 second * fs hz a dimensionless number.
>
> Fred

And, I might have added, that selecting N is a function of how "sub" you
want to go.

Fred

```