Why window the signal before computing LPC coefficients? What is the whys of windowing? I know windowing can prevent spectrum leakage,but LPC is none of business of FFT, so it has no spectrum leakage. Any comments would be appreciated!
Windowing problem before LPC
Started by ●March 16, 2010
Reply by ●March 16, 20102010-03-16
On Mar 16, 6:57=A0pm, "hyeewang" <hyeewang@n_o_s_p_a_m.yahoo.com.cn> wrote:> Why window the signal before computing LPC coefficients? =A0 > > What is the whys of windowing? =A0I know windowing can prevent spectrum > leakage,but LPC is none of business of FFT, so it has no spectrum leakage=.> > Any comments would be appreciated!LPC (like many other methods of modeling and analysis) is used to describe processes that vary over time.The coefficients are calculated from data sets short enough that the coefficients don't change too greatly in the data set. The process of selecting a finite contiguous set of samples from a longer set is windowing. The choice made to weight some samples differently from others is also part of windowing. Weighting all samples the same has consequences in the analysis of the data set. Different weightings of samples have different consequences. Dale B. Dalrymple
Reply by ●March 17, 20102010-03-17
hyeewang wrote:> Why window the signal before computing LPC coefficients? > > What is the whys of windowing? I know windowing can prevent spectrum > leakage,but LPC is none of business of FFT, so it has no spectrum leakage.Because if you don't window the signal prior to the LPC, then the LPC will try to model the signal as if it abruptly starts from zero and goes to zero at the end. The overall accuracy of the LPC is going to be much worse in this case.> Any comments would be appreciated!How much is the "would be appreciation" ? Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com
Reply by ●March 17, 20102010-03-17
On Mar 16, 11:08=A0pm, Vladimir Vassilevsky <nos...@nowhere.com> wrote:> hyeewang wrote: > > Why window the signal before computing LPC coefficients? =A0 > > > What is the whys of windowing? =A0I know windowing can prevent spectrum > > leakage,but LPC is none of business of FFT,oh?> > so it has no spectrum leakage.are you sure about that, Hyee?> > Because if you don't window the signal prior to the LPC, then the LPC > will try to model the signal as if it abruptly starts from zero and goes > to zero at the end.specifically, LPC is computed from the autocorrelation of the (normally windowed) data. even though it can be computed using different (time-domain vs. frequency-domain) methods, the autocorrelation is the inverse DFT of the magnitude-square of the spectrum. the magnitude-squared spectrum will tend to have frequency components that the spectrum has and tend not to have frequency components that the spectrum doesn't have. now windowing in the time domain is equivalent to convolving (against the DFT of the window) in the frequency domain. not windowing is really windowing with the rectangular window; so the issue is, essentially, your choice of window. windowing with the rectangular window will have the narrowest bestest main lobe (that's generally good) but also has the biggest worstest side-lobes (that's generally bad). convolving with a function with big side lobes creates frequency components (of significant amplitude) that may not have existed in the pre-windowed spectrum of the data. so you probably want to trade away some narrowness of the main lobe to gain more suppression of spurious frequency components lest your LPC alg will think there are some resonances in the data that actually aren't there.> The overall accuracy of the LPC is going to be much > worse in this case.yes, what Vlad said. r b-j
Reply by ●March 17, 20102010-03-17
>On Mar 16, 11:08=A0pm, Vladimir Vassilevsky <nos...@nowhere.com> wrote: >> hyeewang wrote: >> > Why window the signal before computing LPC coefficients? =A0 >> >> > What is the whys of windowing? =A0I know windowing can preventspectrum>> > leakage,but LPC is none of business of FFT, > >oh? > >> > so it has no spectrum leakage. > >are you sure about that, Hyee? > >> >> Because if you don't window the signal prior to the LPC, then the LPC >> will try to model the signal as if it abruptly starts from zero andgoes>> to zero at the end. > >specifically, LPC is computed from the autocorrelation of the >(normally windowed) data. even though it can be computed using >different (time-domain vs. frequency-domain) methods, the >autocorrelation is the inverse DFT of the magnitude-square of the >spectrum. the magnitude-squared spectrum will tend to have frequency >components that the spectrum has and tend not to have frequency >components that the spectrum doesn't have. > >now windowing in the time domain is equivalent to convolving (against >the DFT of the window) in the frequency domain. not windowing is >really windowing with the rectangular window; so the issue is, >essentially, your choice of window. windowing with the rectangular >window will have the narrowest bestest main lobe (that's generally >good) but also has the biggest worstest side-lobes (that's generally >bad). convolving with a function with big side lobes creates >frequency components (of significant amplitude) that may not have >existed in the pre-windowed spectrum of the data. so you probably >want to trade away some narrowness of the main lobe to gain more >suppression of spurious frequency components lest your LPC alg will >think there are some resonances in the data that actually aren't >there. > >> The overall accuracy of the LPC is going to be much >> worse in this case. > >yes, what Vlad said. > >r b-j > >Thank you all. Especially grateful to robert. You are always tell the essence.
