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ICM 2008 Tutorial Sheet (2)

1.1) An AM carrier, with a carrier frequency of  f c = 5kHz, is modulated by, t t m 1cos   , where f 1 = 500 Hz. Assume the carrier amplitude is Ac=1.

(a) Write the expression for the AM signal in the time domain.(b) Evaluate and sketch the double-sided spectrum of this AM signal

1.2) An AM carrier, with a carrier frequency of  f c = 5kHz, is modulated by,

t t t m11

  2coscos   , where f 1 = 500 Hz. Assume the carrier amplitude is Ac=10.

(a) Write the expression for the AM signal in a time domain.(b) Evaluate and sketch the double-sided spectrum of this AM signal

1.3) The filtered output of the mixer is found to be,

  40 cos400 + 4 cos360 + 4cos440 assuming that the input was a baseband AM signal, g in(t )=[1+m(t )], determine,

(a) the local oscillator frequency,(b) the message signal, m(t ).

1.4) A “square-law detector” is a nonlinear device whose transfer characteristic is defined by, 

t vat vat v   212112

   

where a1 and a2 are constants, v1(t ) is the input, and v2(t ) is the output. The input consists of anAM wave,

  t  f  t m At v cc     2cos11  

(a) Evaluate the output v2(t ).(b) What conditions must be satisfied in order to recover the message m(t ) from v2(t )?

1.5) The AM signal,

  t  f  t m At  s cc     2cos1  is applied to the system shown below and the message is strictly bandlimited, ( f > B. Show that m(t ) can be obtained from this system.

2.1) A series of square pulses is defined as follows:

  ∑ Π ( 2   )=∞

=−∞ 

Sketch the double-sided amplitude line spectra of S(f), to the 3rd harmonic frequency, given that

the Fourier transform of a square pulse Π is T  Sa(πTf  ).

3.1) An audio signal occupies the frequency range 30Hz

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3.2) A DSB-SC signal, with a carrier frequency of  f c = 5kHz, is modulated by,

t t t m11

  2coscos        , where f 1 = 500 Hz. Assume the carrier amplitude is Ac=10.

(a) Write the expression for the DSB-SC signal in the time domain.(b) Evaluate and sketch the double-sided spectrum of this DSB-SC signal

3.3) A DSB-SC modulated signal is demodulated using a coherent detector.

(a) 

Evaluate the effect of a frequency error  f  in the local oscillator frequency of the detector,measured with respect to the carrier frequency of the DSB-SC modulated signal.

4.1) A PAM signal is generated using a sequence of triangular pulses, where the pulse amplitudes are

 proportional to the signal samples. The message signal w(t)  is limited to a bandwidth of  B Hz

( f