>> On Sun, 07 Oct 2012 18:14:16 -0400, robert bristow-johnson
>> <r...@audioimagination.com>  wrote:

>>> On 10/7/12 12:46 PM, Eric Jacobsen wrote:
>>>> On Sun, 7 Oct 2012 12:52:17 +0000 (UTC), mblume
>>>> <foo...@invalid.invalid>   wrote:

>>>>> So it is not just a number (200 = sum(f(tsamples)), but 200 ***Hz***.
>>>>> Knowing that a sine wave has a frequency of 200 Hz allows to reconstruct
>>>>> every value of it.

>>>>> Another trick is that the FFT is based on the assumptions that
>>>>> (a) the N samples repeat over and over again continuously (x[i] = x[i+N])

>>>> That's an often-repeated misconception.

>>> what's the misconception?  that the FFT considers that x[n+N] = x[n] or
>>> that it's a trick?

>> It is a misconception that the derivation or understanding of the
>> DFT/FFT "assumes" or requires that the input vector repeats
>> continuously, i.e.,  (x[i] = x[i+N])

>     I believe only living creatures can make assumptions
> and the DFT is not alive. (Square root algorithms don't
> make judgments, logarithm operations don't have opinions,
> and FFT algorithms don't make assumptions.)

>>> On Sun, 07 Oct 2012 18:14:16 -0400, robert bristow-johnson
>>> <r...@audioimagination.com> wrote:

>>>> On 10/7/12 12:46 PM, Eric Jacobsen wrote:
>>>>> On Sun, 7 Oct 2012 12:52:17 +0000 (UTC), mblume
>>>>> <foo...@invalid.invalid> wrote:

>>>>>> So it is not just a number (200 = sum(f(tsamples)), but 200 ***Hz***.
>>>>>> Knowing that a sine wave has a frequency of 200 Hz allows to
>>>>>> reconstruct
>>>>>> every value of it.

>>>>>> Another trick is that the FFT is based on the assumptions that
>>>>>> (a) the N samples repeat over and over again continuously (x[i] =
>>>>>> x[i+N])

>>>>> That's an often-repeated misconception.

>>>> what's the misconception? that the FFT considers that x[n+N] = x[n] or
>>>> that it's a trick?

>>> It is a misconception that the derivation or understanding of the
>>> DFT/FFT "assumes" or requires that the input vector repeats
>>> continuously, i.e., (x[i] = x[i+N])

>> I believe only living creatures can make assumptions
>> and the DFT is not alive. (Square root algorithms don't
>> make judgments, logarithm operations don't have opinions,
>> and FFT algorithms don't make assumptions.)

> ya know, perhaps Daniel Dennett is correct and we are *all* just
> automatons that merely *think* we have consciousness and self-awareness
> (and can make assumptions or have opinions).

> doesn't change the fact that the DFT periodically extends the finite
> data set passed to it. the misconception is the denial of the fact. the
> periodic extension is hidden in the trivial case that no operation
> causes shifting, but is exposed for all to see when some operation
> causing shifting (like multiplication by something non-constant) is
> applied.

>>On Tue, 09 Oct 2012 15:36:10 GMT, eric.jacob...@ieee.org (Eric
>>Jacobsen) wrote:

>>>On Tue, 9 Oct 2012 02:25:03 +0000 (UTC), glen herrmannsfeldt
>>><g...@ugcs.caltech.edu> wrote:

>>>>Eric Jacobsen <eric.jacob...@ieee.org> wrote:

>>>>(snip)

>>>>> It is a misconception that the derivation or understanding of the
>>>>> DFT/FFT "assumes" or requires that the input vector repeats
>>>>> continuously, i.e.,  (x[i] = x[i+N])

>>>>OK, not assumes, but it is based on the solutions to a
>>>>differential equation with periodic boundary conditions.

>>>>> I know you may disagree and I'm inclined to ignore any attempt to drag
>>>>> this into yet another discussion on the topic.   Your views are well
>>>>> known.

>>>>-- glen

>>>You've mentioned that before, but I'm not directly familiar with that
>>>treatment. There are some common approaches that assume periodicity in
>>>order to simplify the analysis and I think these are what lead people
>>>to believe that it is a property or requirement when using a DFT/FFT.

>>>It is not necessary to make that assumption, and one can do so without
>>>a loss of generality:

>>>http://www.dsprelated.com/showarticle/175.php

>>HI Eric,
>>   One misconception that some people have is that
>>the spectral characterisic we call "spectral leakage"
>>is caused by, is due to, is a shortcoming of the
>>DFT.  I believe the cause of leakage is the
>>act of sampling an analog signal, ...and it seems
>>to me that the DFT merely quantifies, illustrates,
>>reveals spectral leakage.

>I think the "leakage", i.e., the sidelobe energy, is a result of
>having a finite non-zero data set, specifically a "window" around the
>data.   The transform of the window is the template for the "leakage"
>that gets convolved with the transform of the input.

>This works out for continuous or sampled signals, so the connection to
>sampling isn't clear to me.