Sorry about the many posts

On Monday, March 13, 2017 at 11:51:37 PM UTC-4, Cedron wrote:
> [...snip...]
> >
> >if that's what you want.  what i was illustrating in the post that Dale
> >and someone else referred to is what happens when the N samples of x[n]
> that
> >are passed to you are understood as comprising one period of a periodic
> >function, how does the periodic continuous function look like.
> >
> [...snip...]
> >
> >it depends on what the definition of the original function is.  if the N
> >samples were sampled from a bandlimited continuous-time periodic
> function,
> >representing exactly one period of the discrete-time periodic function,
> >those N samples describe the bandlimited continuous-time function exactly
> and
> >at every single point within the frame or outside it, at integer sample
> >times or in between the sample times.
> >
> >if the N samples were yanked from a stream of samples where no such
> >assumption is made, *then* you have to consider windowing effects because
> yanking
> >out those N samples from the stream is, at least, applying the
> rectangular
> >window because you are using x[n]=0 to represent the samples outside of
> >the frame.
> >
> >r b-j
> 
> I'm sorry (keeping in the spirit of the title of this thread), my argument
> ignored the periodic constraint.

the periodic "constraint" is sorta inherent to the DFT itself.

r b-j

On Tuesday, March 14, 2017 at 12:58:44 AM UTC-4, Cedron wrote:
> 
> The whole transition between the continuous and discrete cases are of
> course of great importance in the study of DACs and ADC, and I recognize
> that although it really not an interest area for me.

no, the sinc() stuff isn't about the DACs or ADCs.  it's about interpolation.

> Once a signal is in
> digital form it does not matter if it from an analog source or produced
> computationally, the tools for processing it are in the discrete domain.

they're just numbers.

r b-j

>On Tuesday, March 14, 2017 at 12:58:44 AM UTC-4, Cedron wrote:
>> 
>> The whole transition between the continuous and discrete cases are of
>> course of great importance in the study of DACs and ADC, and I
recognize
>> that although it really not an interest area for me.
>
>no, the sinc() stuff isn't about the DACs or ADCs.  it's about
>interpolation.
>

I wasn't talking about the sinc.  What I am saying is the only time it is
necessary (need, not want) to consider the continuous case in relation to
the discrete case is during the conversion from one to the other.  The
discrete case can be fully understood on its own without any reliance (or
baggage) from the continuous case.


>> Once a signal is in
>> digital form it does not matter if it from an analog source or
produced
>> computationally, the tools for processing it are in the discrete
domain.
>
>they're just numbers.
>
>r b-j

I have put the math I posted in this thread into two new blog articles. 
For those who consider ASCII math too hard to follow the equations are
rendered in nice typeface with a lot more explanation than I provided
here.

The articles are titled "DFT Bin Value Formulas for Pure Complex Tones"
and "A Two Bin Exact Frequency Formula for a Pure Complex Tone in a DFT". 
You can find them here:

https://www.dsprelated.com/blogs.php

You will see my derivation of an exact frequency formula without any
interpolation function in sight.

Ced
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