# What's spectral “tilt”?

I am looking at article Speech-in-noise intelligibility improvement based on spectral shaping and dynamic range compression. In paragraph 2.2 the article mentions "tilt" of the spectral envelope. The tilt is computed using cepstrum, as follows:

$$\log T(\omega) = c_0 + 2c_1\cos(\omega)\tag{2}$$ where $$c(m) = \frac{1}{N/2 + 1}\sum_{k=0}^{N/2}\log E(\omega_k)\cos(m\omega_k)\tag{3}$$

$$E(\omega_k)$$ is the estimated spectral envelope (if needed see details in the paper).

What does the Tilt represent?

• Usually, the term spectral tilt is used to describe the overall slope of the power spectral density. In many cases for audio signals, for example, higher frequencies have less power than the low frequencies (1/f characteristic) leading to a spectral tilt. As I have not checked the article you mention, however, the definition therein may deviate from what I have described above. – applesoup Oct 6 '16 at 13:24