## Chapter 7

## Q. 7.1

(a) Sketch the spectrum of voice for men and women. What does the difference imply about their time-domain waveforms?

(b) Estimate the averaging time, T , in Eq. (7.3) for voice signals.

P_{av} =\underset{T\rightarrow \infty }{\lim } \frac{1}{T}\int_{−T/2}^{+T/2}{x^2(t)dt} (7.3)

## Step-by-Step

## Verified Solution

(a) The human voice exhibits frequencies from 20 Hz to 20 kHz. Since women’s voice contain stronger highfrequency components, we expect the two spectra to differ as shown in Fig. 7.5(a). In the time domain, we observe faster changes in women’s voice [Fig. 7.5(b)].

(b) The averaging time must be long enough to include a sufficient number of cycles of the lowest frequencies. That is, the averaging must capture the slowest dynamics in the signal. We must therefore choose T to be at least about 10 cycles of 20 Hz, i.e., roughly 500 ms.