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From: Clay on 29 Jul 2010 09:32
On Jul 29, 12:50 am, robert bristow-johnson
<r...(a)audioimagination.com> wrote:
> On Jul 28, 11:39 pm, Vladimir Vassilevsky <nos...(a)nowhere.com> wrote:
>
>
>
>
>
> > bharat pathak wrote:
> > > I was just trying to understand FFT and the presence of sine and
> > > cosine terms present as the basis functions.
>
> > Hm. What it should mean?
>
> > > I dont know whats wrong
> > > in asking questions and why cant experts make mistakes in understanding.
>
> > Oh, nothing wrong. You may even become a PhD.
>
> > > Long time back I had pointed an "understanding error" in Rick Lyons book.
> > > and he acknowledged the same. While discussion I had figured it out that
> > > his assumptions were wrong to begin with. Does that mean he does not
> > > know DSP?
>
> > "Stupid is as stupid does", as Forrest Gump used to say.
>
> > > Regards
> > > Bharat
>
> > VLV
>
> i think it's Simon Cowell spoofing Vlad V.  i didn't make it to the
> comp.dsp conference to meet "Vladimir" (who i am sure is Simon Cowell)
> first hand, so i leave it to those who did to verify my suspicion.
>
> r b-j- Hide quoted text -
>

Does Simon have a Russian accent?

From: Clay on 29 Jul 2010 10:41
On Jul 28, 9:58 am, "bharat pathak" <bharat(a)n_o_s_p_a_m.arithos.com>
wrote:
> Hello All,
>
>     Lets say,
>
>     N   = 32;
>     n   = 0 : N-1;
>     fin = 1500 hz;
>     Fs  = 48000 hz; % Fs/fin = 32/1
>
>     xn  = sin(2*pi*fin*n/Fs + theta)
>     xk  = fft(xn)
>
>     If Fs and fin are exact mutiple, if i have theta non-zero,
>     will it cause spectral leakage in FFT mag response, or it will
>     show up as an added offset in the phase plot?
>
> Regards
> Bharat

Try a little math.


For example let FFT(x) be a linear operator that operates on x

Then with x = sin(wt+theta)

Then apply trig to get to

FFT(sin(wt+theta)) = FFT( sin(wt)cos(theta)+cos(wt)sin(theta))

= cos(theta)*FFT(sin(wt) + sin(theta)*FFT(cos(wt))


This should allow you to clearly answer the issue about leakage where
leakage involves energy appearing at frequencies that weren't in the
original signal. This analysis shows no new frequencies due to phase
shifts.

Clay


From: HardySpicer on 29 Jul 2010 17:49
On Jul 30, 2:41 am, Clay <c...(a)claysturner.com> wrote:
> On Jul 28, 9:58 am, "bharat pathak" <bharat(a)n_o_s_p_a_m.arithos.com>
> wrote:
>
>
>
> > Hello All,
>
> >     Lets say,
>
> >     N   = 32;
> >     n   = 0 : N-1;
> >     fin = 1500 hz;
> >     Fs  = 48000 hz; % Fs/fin = 32/1
>
> >     xn  = sin(2*pi*fin*n/Fs + theta)
> >     xk  = fft(xn)
>
> >     If Fs and fin are exact mutiple, if i have theta non-zero,
> >     will it cause spectral leakage in FFT mag response, or it will
> >     show up as an added offset in the phase plot?
>
> > Regards
> > Bharat
>
> Try a little math.
>
> For example let FFT(x) be a linear operator that operates on x
>
> Then with x = sin(wt+theta)
>
> Then apply trig to get to
>
> FFT(sin(wt+theta)) = FFT( sin(wt)cos(theta)+cos(wt)sin(theta))
>
> = cos(theta)*FFT(sin(wt) + sin(theta)*FFT(cos(wt))
>
> This should allow you to clearly answer the issue about leakage where
> leakage involves energy appearing at frequencies that weren't in the
> original signal. This analysis shows no new frequencies due to phase
> shifts.
>
> Clay

Have you noticed that spectral leakage rhymes with anal seapage?
From: Jerry Avins on 29 Jul 2010 17:57
On 7/29/2010 5:49 PM, HardySpicer wrote:

> Have you noticed that spectral leakage rhymes with anal seapage?

I suppose it's worth knowing where your mind is.

Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
From: Clay on 30 Jul 2010 11:00
On Jul 29, 5:49 pm, HardySpicer <gyansor...(a)gmail.com> wrote:
> On Jul 30, 2:41 am, Clay <c...(a)claysturner.com> wrote:
>
>
>
>
>
> > On Jul 28, 9:58 am, "bharat pathak" <bharat(a)n_o_s_p_a_m.arithos.com>
> > wrote:
>
> > > Hello All,
>
> > >     Lets say,
>
> > >     N   = 32;
> > >     n   = 0 : N-1;
> > >     fin = 1500 hz;
> > >     Fs  = 48000 hz; % Fs/fin = 32/1
>
> > >     xn  = sin(2*pi*fin*n/Fs + theta)
> > >     xk  = fft(xn)
>
> > >     If Fs and fin are exact mutiple, if i have theta non-zero,
> > >     will it cause spectral leakage in FFT mag response, or it will
> > >     show up as an added offset in the phase plot?
>
> > > Regards
> > > Bharat
>
> > Try a little math.
>
> > For example let FFT(x) be a linear operator that operates on x
>
> > Then with x = sin(wt+theta)
>
> > Then apply trig to get to
>
> > FFT(sin(wt+theta)) = FFT( sin(wt)cos(theta)+cos(wt)sin(theta))
>
> > = cos(theta)*FFT(sin(wt) + sin(theta)*FFT(cos(wt))
>
> > This should allow you to clearly answer the issue about leakage where
> > leakage involves energy appearing at frequencies that weren't in the
> > original signal. This analysis shows no new frequencies due to phase
> > shifts.
>
> > Clay
>
> Have you noticed that spectral leakage rhymes with anal seapage?- Hide quoted text -
>
> - Show quoted text -

It may rhyme, but the spelling is different. Try "seepage"
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