0.5 Sampling with automatic gain control  (Page 3/19)

Human hearing extends up to about 20 KHz. What is the minimum sampling rate needed to fully capture a musicalperformance? Compare this to the CD sampling rate of $44.1$ KHz. Some animal sounds, such as the singing of dolphins andthe chirping of bats, occur at frequencies up to about 50 KHZ. What does this imply about CD recordings of dolphin or bat sounds?

U.S. high-definition (digital) television (HDTV) is transmitted in the same frequency bands as conventional television (for instance,Channel 2 is at 54 MHz), and each channel has a bandwidth of about 6 MHz. What is the minimum sampling rate needed tofully capture the HDTV signal once it has been demodulated to baseband?

An analog signal has nonzero values in its magnitude spectrum at every frequencybetween $-B$ and $B$ . This signal is sampled with period $T$ where $1/T>B$ . TRUE or FALSE: the discrete-time signal can have components in its spectrumat frequencies between $B$ and $1/T$ .

The triangularly-shaped magnitude spectrum of a real message signal $w\left(t\right)$ is shown in [link] where $B=0.2$ MHz. The received signal

is modulated by an AM-with-suppressed-carrier with $f=1.45$ MHz, and attentuated. With $\frac{1}{2B}<T_1<\frac{1}{f}$ , select $T_1$ , $T_2$ , $T_3$ , and $\beta$ so the magnitude spectrum of $x\left[k\right]$ matches the magnitude spectrum of $T_1$ -spaced samples of $w\left(t\right)$ . Justify your answer by drawing the magnitude spectra of $x_1$ , $x_2$ , and $x_3$ between $-f$ and $f$ .

The signal $x\left(t\right)$ with magnitude spectrum shown in the top part of [link] is input to the transmission system in the lower part of the Figure.The lowpass filter with output $v_4\left(k{T}_s\right)$ has a cutoff frequency of 200 Hz, a passband gain of 1 and a stopband gain of zero.Specify all frequencies between zero and 2000 Hz at which the magnitudespectra of $|V_1\left(f\right)|$ , $|V_2\left(f\right)|$ , $|V_3\left(f\right)|$ , and $|V_4\left(f\right)|$ have nonzero values.