Date: Nov 17, 2012 11:02 PM
Author: Greg Heath
Subject: Re: question on fft example

"Nasser M. Abbasi" <nma@12000.org> wrote in message <k87rb1$edu$1@speranza.aioe.org>...
> On 11/17/2012 4:49 AM, Greg Heath wrote:
> > "Nasser M. Abbasi" <nma@12000.org> wrote in message <k829kk$hv6$1@speranza.aioe.org>...
> >> On 11/15/2012 2:33 AM, oversky wrote:
> >>> The mathwork fft example in the following link,
> >>> http://bit.ly/SO9TuV
> >>> why do we double abs(Y(1:NFFT/2+1) when plotting the amplitude?
> >>>
> >>> plot(f,2*abs(Y(1:NFFT/2+1)))
> >>>

> >>
> >> This was talked about before. can google it. Here is my take on it:
> >>
> >> "Why does it multiply by 2?"
> >>
> >> http://12000.org/my_notes/on_scaling_factor_for_ftt_in_matlab/index.htm

> >
>
> > To represent the same average power as the doublesided frequency representation.
> >
> > the DC and Nyquist components should NOT be doubled.
> >
> > plot((0:Fs/2), [abs(Y(1)), 2*abs(Y(2:NFFT/2)), abs(Y(NFFT/2+1)) ] )
> >
> > Hope this helps.
> >
> > Greg
> >

>
> hi Greg;
>
> Its been a while since I looked at this myself, so I am rusty now
> to remember all the details (that is why I write down everything
> before I forget it) but there were different views on these scaling
> factors. Here is the same question, asked in 2009 here FYI
>
> http://www.mathworks.com/matlabcentral/newsreader/view_thread/261034


Oh yeah.

1. In single-sided power and amplitude spectra, DC and Nyquist are never doubled
2. Other power spectrum components are doubled
3. Other amplitude spectrum components should be multiplied by sqrt(2)
because when they are squared they should represent the power spectrum.

Greg