Problem 6: In a binary phase shift keying (BPSK) communications system, one of two equally probable bits, 0 or 1, is transmitted every T seconds. If the kth bit is je {0,1}, the waveform ;(t) = cos(27 fot + j) is trans- mitted over the interval [(k- 1)T, KT]. Let X(t) denote the random process in which two symbols are transmitted in the interval (0, 27], and let fo = 2/T. Sketch the sample space and corresponding sample functions of the process X (t).

V(t) = Vp sin(ωt +/- ɑ)Vp = 12mVω = 2πf --> ω = 2π * 2kHz --> ω = 12566Ɑ = 3π / 4 * (180/π) --> 135  --> Ɑ = 135° degreesV(t) = 12sin(12566t + 135)mV   is the answer correct?

2. Consider a unit-energy root-raised-cosine (RRC) pulse which spans over 8 symbol durations. We take 10 samples per symbol (sps) from this RRC pulse. Write an RRC filter function that employs pulse-shaping using the RRC pulse described above. (If there is a single symbol and s=[1 0], the energy of the corresponding length-81 samples vector should be equal to 1.) The parameters of the RRC pulse are roll-off factor, span, and samples per symbol. You should write your pulse-shaping function according to the prototype given below txFilt = myRRCFilter(s, rf, span, sps) where txFilt is the pulse-shaped signal (transmitted signal), s denotes the transmitted symbols, rf is the roll-off factor, span is the span of the filter, and sps is the samples per symbol.

3.

7.26. The sampling theorem, as we have derived it, states that a signal x(t) must be sam- pled at a rate greater than its bandwidth (or equivalently, a rate greater than twice its highest frequency). This implies that if x(t) has a spectrum as indicated in Figure P7.26(a) then x(t) must be sampled at a rate greater than 2w2. However, since the signal has most of its energy concentrated in a narrow band, it would seem reason- able to expect that a sampling rate lower than twice the highest frequency could be used. A signal whose energy is concentrated in a frequency band is often referred to as a bandpass signal. There are a variety of techniques for sampling such signals, generally referred to as bandpass-sampling techniques. x(t) X(jw) 1 -02-01 (a) +00 p(t) 8(t-nT) Xp (t) W1 W2 W H(jw) x(t) p(t) H(jw) 1 T дід. Wa (b) Wa w Figure P7.26 Chap. 7 Problems 565 To examine the possibility of sampling a bandpass signal as a rate less than the total bandwidth, consider the system shown in…

Construct a truth table in standard binary form for a function of four variables,F(W,X,Y,Z) = ABC,where ABC is the signed 3-bit sum of the signed 2-bit numbers WX and YZ.

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