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### Is there a standard for FFT windows for very low frequencies?

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```I've been looking in all of my books, and cannot determine if there is
a standard for how many samples/what duration to take a Fourier
transform of, in order to represent a low frequency signal well.  I
understand that in a pulse, or square wave, there are infinite
frequencies that can be generated, including 1Hz or lower, but I'm
under the impression currently, that a 1/4 second window would be
needed to determine that there is a 1Hz component with a relatively
generous magnitude.

What I'd like to know, is if what I'm asking is acutally an issue?  A
signal in the frequency domain...well, a discrete signal processed
through a Fourier Transform, has a continuous frequency
spectrum...which would suggest to me that there is no issue with lower
frequency components in any window...or is there?

Please give me any feedback or experiences with this, I appreciate your
time.

```
 0
Reply henrybg (38) 4/22/2005 8:27:56 PM

```"Benry" <henrybg@gmail.com> wrote in message
> I've been looking in all of my books, and cannot determine if there is
> a standard for how many samples/what duration to take a Fourier
> transform of, in order to represent a low frequency signal well.  I
> understand that in a pulse, or square wave, there are infinite
> frequencies that can be generated, including 1Hz or lower, but I'm
> under the impression currently, that a 1/4 second window would be
> needed to determine that there is a 1Hz component with a relatively
> generous magnitude.
>
> What I'd like to know, is if what I'm asking is acutally an issue?  A
> signal in the frequency domain...well, a discrete signal processed
> through a Fourier Transform, has a continuous frequency
> spectrum...which would suggest to me that there is no issue with lower
> frequency components in any window...or is there?

Most people usually apply the DFT (or FFT) to a discrete time signal in
which case you don't have a continuous frequency spectrum. A general rule of
thumb is you need to capture about 1 sec of data to see signals that are 1
Hz apart. This is a little different from just wanting to view a signal at
1Hz or lower. If you don't care about signals getting 'lumped' together or
if you know you only have 1 signal in the entire set of freqs from 0 - 100
Hz, then (in this case) you could get away with capturing only 10ms worth of
data before performing the DFT.

Cheers

>
> Please give me any feedback or experiences with this, I appreciate your
> time.
>

```
 0

```Benry wrote:
> I've been looking in all of my books, and cannot determine if there is
> a standard for how many samples/what duration to take a Fourier
> transform of, in order to represent a low frequency signal well.  I
> understand that in a pulse, or square wave, there are infinite
> frequencies that can be generated, including 1Hz or lower, but I'm
> under the impression currently, that a 1/4 second window would be
> needed to determine that there is a 1Hz component with a relatively
> generous magnitude.
>
> What I'd like to know, is if what I'm asking is acutally an issue?  A
> signal in the frequency domain...well, a discrete signal processed
> through a Fourier Transform, has a continuous frequency
> spectrum...which would suggest to me that there is no issue with lower
> frequency components in any window...or is there?
>
> Please give me any feedback or experiences with this, I appreciate your
> time.

Although the actual process is a bit more involved, the procedure is this:

Decide what the highest frequency of interest is.

Filter the signal to remove higher frequencies.

Sample the signal at a rate higher than the highest frequency remaining.

Collect twice as many samples as you want bins.

Modify their amplitudes with a window, i.e., Hamming.

Perform a discrete Fourier transform.

You now have one number per bin.

Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
```
 0
Reply jya (12870) 4/23/2005 2:48:41 AM

```perfect answer has been given by Mr Jerry.Follow that.

>Benry wrote:
>> I've been looking in all of my books, and cannot determine if there is
>> a standard for how many samples/what duration to take a Fourier
>> transform of, in order to represent a low frequency signal well.  I
>> understand that in a pulse, or square wave, there are infinite
>> frequencies that can be generated, including 1Hz or lower, but I'm
>> under the impression currently, that a 1/4 second window would be
>> needed to determine that there is a 1Hz component with a relatively
>> generous magnitude.
>>
>> What I'd like to know, is if what I'm asking is acutally an issue?  A
>> signal in the frequency domain...well, a discrete signal processed
>> through a Fourier Transform, has a continuous frequency
>> spectrum...which would suggest to me that there is no issue with lower
>> frequency components in any window...or is there?
>>
>> Please give me any feedback or experiences with this, I appreciat
your
>> time.
>
>Although the actual process is a bit more involved, the procedure i
this:
>
>Decide what the highest frequency of interest is.
>
>Filter the signal to remove higher frequencies.
>
>Sample the signal at a rate higher than the highest frequency remaining.
>
>Collect twice as many samples as you want bins.
>
>Modify their amplitudes with a window, i.e., Hamming.
>
>Perform a discrete Fourier transform.
>
>You now have one number per bin.
>
>Jerry
>--
>Engineering is the art of making what you want from things you can get.
>�����������������������������������������������������������������������
>

This message was sent using the Comp.DSP web interface o
www.DSPRelated.com
```
 0

```Sometimes the fingers lag behind the mind.

I wrote:

> Sample the signal at a rate higher than the highest frequency remaining.

True, but only by nitpicking; it's not what I meant. Sample the signal
at a rate higher than _twice_ the highest frequency remaining.

Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
```
 0
Reply jya (12870) 4/23/2005 2:08:55 PM

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