We leared in the class that a FM signal can be written in the form: SFM (t) = Jk (B) are the Bessel Functions of order k. This shows that the frequency spectrum consists of an infinite number of side bands. Referring to the Bessel Function Table (see Cheat Sheet), draw the spectrum with the sidebands for B = 6. Ignore amplitudes less than 0.10. 8 JK (B) cos(wc + kwm) t.

A sequence of alternating 1s and 0s is transmitted as a square wave. What is the fundamentalfrequency and how many harmonics can be used if the available BW is 100 MHz and a data rate of 56Mbps is desired? Express the signal as a mathematical function of time (s(t)) and sketch the resultingsignal in both the time and frequency domains. Is this a “good enough” representation of the squarewave? Why or why not?

SIGNALS AND INFORMNATIONS

Answer all question.

The equation for finding the period, when frequency is kniwn is . .

Measurements taken of a square-wave signal using a frequency-selective voltmeter (called a spectrum analyzer) show its spectrum to contain adjacent components (spectral lines) at 98 kHz  and 126 kHz of amplitudes 63 mV and 49 mV, respectively. What would direct measurement of the fundamental show its frequency and amplitude to be? What is the rms value of the fundamental? What are peak-to-peak amplitude and period of the originating square wave?

An FM signal has a maximum frequency deviation of 1500h and a modulating frequency of 500h, its total power is 6500w, applied to a resistive load of 1ohm, the carrier frequency is 400Mhz. Determine the sensitivity of the modulator, and the magnitude spectrum

The plot in the figure below shows the magnitude frequency content of a signal. Determine the approximate frequency, in Hertz, of the largest sinusoid present in the signal given that the sampling frequency (fs) is 458 Hz. DFT (Magnitude Spectrum) of a Signal Magnitude See 140 120 100 80 60 40 20 G Answer: 916 The correct answer is: 134.7059 G G Frequency Bins 10 12 14 16 for more info on this problem.

Q 2 : An audio signal given by 15 sin( 000 pi t)+20 sin(8000 pi t) amplitude modulated DSB-FC) a sinusoidal carrier wave 60 sin(100,000 ) a. Derive an expression for the modulated signal. b. Find the modulation index. c. Find the spectrum of the modulated signal. d. Sketch the spectrum of the modulated signal e. Which type of demodulation method you propose to reconstruct the audio at receiver. Why? Q 2 : A modulating signal is used to modulate a carrier signal(AM modulation). Let P T . P c ,P SB . P USB , P LSB and u are the total power, carrier power, side band power, upper side band power, lower side band power and modulation index respectively, Prove the following: a. P c =P T ( 2 2+m^ 2 ) b. P SB =P T ( m^ 2 2+m^ 2 ) c. P USB =P LSB = 1 2 ( m^ 2 2+m^ 2 )P T

For an FM signal, the maximum frequency of the modulating signal is 100 kHz and the frequency deviation is 10 kHz. Find out the bandwidth of the FM modulated waveform.