In this problem, we explore some of the filtering issues involved in the commercial vers...

In this problem, we explore some of the filtering issues involved in the commercial version of a typical system that is used in most modern cassette tape decks to reduce noise. The primary source of noise is the high-frequency hiss in the tape playback process, which, in some part, is due to the friction between the tape and the playback head. Let us assume that the noise hiss that is added to the signal upon playback has the spectrum of Figure P6.56(a) when measured in decibels, with 0 dB equal to the signal level at 100 Hz. The spectrum S(jω) of the signal has the shape shown in Figure P6.56(b).

The system that we analyze has a filter which conditions the signal s(t) before it is recorded. Upon playback, the hiss n(t) is added to the signal. The system is represented schematically in Figure P6.56(c).

Suppose we would like our overall system to have a signal-to-noise ratio of 40 dB over the frequency range

(a) Determine the transfer characteristic of the filter

(b) If we were to listen to the signal p(t), assuming that the playback process does nothing more than add hiss to the signal, how do you think it would sound?

(c) What should the Bode plot and transfer characteristic of the filter be in order for the signal 1(t) to sound similar to s(t)?