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I am a student with very little background on signal processing and am studying the Linear Predictive Coding algorithm. I came across the term spectrally flat in this article, https://ccrma.stanford.edu/~hskim08/lpc/ and am not sure what it means. I know that spectral is talking about frequency.

There are two possible signals for the source: an impulse train or random white noise. These signals model pitched sounds and plosive/fricatives respectively. The common characteristic for both impulse train and white noise is that they are spectrally flat; all spectral information is modeled in the filter.

So my question is:

1) what does spectrally flat mean ?

2) why does an impulse train have a flat spectral ?

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1) what does spectrally flat mean ?

Spectrally flat means that the signal has energy at most / all frequencies, and this energy is roughly the same level across the frequency range.

2) why does an impulse train have a flat spectral ?

As you're probably aware, the Fourier transform of an impulse train is also an impulse train. That means that the claim by the link that the impulse train is spectrally flat is not correct.

The reason an impulse train is used in modeling speech is because it gives a tonal quality for non-fricative sounds (mostly vowel sounds). That tonal quality is hard to generate by filtering if the source being filtered is white noise.

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  • $\begingroup$ Ty ! So i guess what they meant is that the 'envelope' of the impulse train is spectrally flat. One last question: Intuitively, what the LPC does is try to model the spectra of speech sounds ? $\endgroup$ – Kong Oct 5 '18 at 14:14
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    $\begingroup$ @kong Yes, that was an initial application. The idea was to allow speech to be analyzed and synthesized. The GSM mobile telephone standard used it to compress speech. See this slide deck for example. $\endgroup$ – Peter K. Oct 5 '18 at 14:19

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