N ATIONAL U NIVERSITY of S INGAPORE
DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING
Course: EE2009  SIGNALS
EXPERIMENT S2 FREQUENCY MODULATION LABORATORY MANUAL
_
IMPORTANT!
READ THIS MANUAL CAREFULLY AND PREPARE FOR THE EXPERIMENT BEFORE YOU
Must the Nyquist rule be always obeyed?
The Nyquist rule is a simple one and is formulated for signal which is low pass in nature. Consider a signal with spectrum as shown below.
0 20 k
f
The signal occupies a band from  20 to 20 kHz, and has an
What is a D/A Converter?
A D/A or digital to analog converter is a device that converts a bit stream that represents a digital signal into an analog signal. Very simply, its function is the reverse to that for an A/D converter.
What is an A/D Converter?
An A/D or analog to digital converter is a device that converts an analog signal into a bit stream that represents a digital signal. A common example is the A/D used in digitizing speech signal in, say, a GSM handphone. In s
What is the meaning of carrier in AM and FM?
The word "carrier" is used loosely in general to mean the use of a high frequency waveform or oscillator to shift the spectrum of a message signal to a higher value. This shifting of the spectrum is someti
Will the answer to the spectrum be different be if we simply FT an impulse train rather than using FS?
F[ + ( t ) + ( t  3) + ( t  6 ) + ] = + 1 + e  j 3 + e  j 6 + It can be shown (not so easy) that the r.h.s. actually converges to an impul
Is time expansion the same as dividing t and time shift the same as subtracting t?
There is no need and is in fact harmful to remember this type of things. The best or surest way is to look at or sketch the waveform. It is best that ones run away fro
Is it true that by simply replacing s with j , we will get Fourier transform from Laplace transform?
A simple answer is sometimes yes and sometimes no. The Laplace transform of xa ( t ) is X a ( s ) = xa ( t ) e  st dt
0
Since the integration is
When we derived the FT from the FS, the spectrum becomes a function of f. But it was a function of k and f0. Is there a contradiction there?
Run the demonstration program. Does the spectral density at the bottom depend on T0 as T0 or f 0 0 ? It te
Is there any mistake to the pole zero diagram in the Chapter on Digital Systems? Yes. There are some misprints on the size and shape of the unit circle and other symbols. The correct diagram is given in the next page.
Digital System  Poles and Zero
Why is it that we just need to have 3 sinusoids to represent a periodic digital signal with period 3?
Consider an analog periodic signal xa ( t ) with a period of, say, 4 seconds. To represent this analog signal using Fourier series, we need an infin
N ATIONAL U NIVERSITY of S INGAPORE
DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING
Course: EE2009  SIGNALS
EXPERIMENT S1 SIGNALS AND SPECTRA LABORATORY MANUAL
_
IMPORTANT!
READ THIS MANUAL CAREFULLY AND PREPARE FOR THE EXPERIMENT BEFORE YOU
Hints to Problem Set 5
1 (a) Sketch the power spectrum. You can do it component by component.
(b) Assume the triangles to be impulses recall what you see on the spectrum analyzer in laboratory S2. See also the FAQ on power spectrum. 2 (a) (b) 3 (a)
Hints to Problem Set 4
1 (a) Simplify the signal first when = 3 .
(b) Does the reddish component have a larger power? 2 (a) What is the impulse response? Is it likely that an extremely high voltage pulse will damage the speaker of the system? Impul
Hints to Problem Set 3
1 (a) See if the signal is periodic. Try to write down its spectrum.
(b) Assume that the triangles seen on the spectrum analyzer correspond to actual impulses. See FAQ on power spectrum. Recall what you see on the analyzer in
Hints to Problem Set 2
1 (a) Recall the result from tutorial and laboratory experiment S1 that relates the spectrum of a single pulse to that when the pulse is made periodic. The book has a problem that plots the spectrum of a periodic square wavefor
Hints to Problem Set 1
1 (a) Note that the signal is periodic. It is better to work out the spectrum of just 1 pulse and then use the results from tutorial and laboratory experiment S1. Note also that convolving two rectangular pulses gives a triangu
Signal
x( t ) = F
1
Spectrum
{ X ( f )} =  X ( f ) e
jt
df
X ( f ) = F{ x( t )} = x( t ) e  jt dt

x1 ( t ) = real = [ x1 ( t ) ]
X 1 ( f ) = [ X 1 (  f )]
X 1 ( f ) = symmetric = X 1 (  f ) arg[ X 1 ( f ) ] = anti  symmetric =
What is meant by the implementation complexity of a digital system?
In general, implementation complexity is the amount of hardware and software or standard operations that is needed to realize some sort of processing in real time. Consider, for exam
Are the real Fourier series using sines and cosines equivalent to the complex Fourier series using complex sinusoids?
No. The complex Fourier series based on the complex sinusoid e jk0t can be regarded as the superset. The complex Fourier series incl
How are loudspeakers, amplifier and equalizer used in an audio system?
A loudspeaker is a transducer that converts electrical into acoustic signals. Most loudspeakers work like a motor. However, instead of rotating, the motion is linear. The load tha
EE2009/EE2009E Signals / page 1
NATIONAL UNIVERSITY OF SINGAPORE
EXAMINATION FOR Semester I: 2005/2006
EE2009/EE2009E SIGNALS November/December 2005 Time Allowed: 2 Hours
INSTRUCTIONS TO CANDIDATES: 1. This paper contains SIX (6) questions and
EE2009/EE2009E Signals / page 1
NATIONAL UNIVERSITY OF SINGAPORE
EXAMINATION
Semester II: 2004/2005
EE2009 SIGNALS April 2005 Time Allowed: 2 Hours
INSTRUCTIONS TO CANDIDATES: 1. This paper contains SIX (6) questions and comprises NINETEEN (19
NATIONAL UNIVERSITY OF SINGAPORE
EXAMINATION FOR
Semester I: 2004/2005
EE2009/EE2009E SIGNALS November/December 2004 Time Allowed: 2 Hours
INSTRUCTIONS TO CANDIDATES: 1. This paper contains SIX (6) questions and comprises NINETEEN (19) printed
NATIONAL UNIVERSITY OF SINGAPORE
EXAMINATION FOR THE DEGREE OF
B.ENG. (ELECTRICAL) / B.ENG. (COMPUTER ENG.)
(Semester II: 2003/2004)
EE2009  SIGNALS
April 2004 Time Allowed: 2 Hours
INSTRUCTIONS TO CANDIDATES: 1. This paper contains SIX (6) q
NATIONAL UNIVERSITY OF SINGAPORE
EXAMINATION FOR THE DEGREE OF
B.ENG. (ELECTRICAL) / B.ENG. (COMPUTER ENG.) / B.TECH. (ELECTRONICS)
(Semester I: 2003/2004)
EE2009/EE2009E  SIGNALS
November 2003 Time Allowed: 2 Hours
INSTRUCTIONS TO CANDIDATES
NATIONAL UNIVERSITY OF SINGAPORE
EXAMINATION FOR THE DEGREE OF
B.ENG. (ELECTRICAL) / B.ENG. (COMPUTER ENG.)
(Semester II: 2002/2003)
EE2009  SIGNALS
May 2003 Time Allowed: 2 Hours
INSTRUCTIONS TO CANDIDATES: 1. This paper contains SIX (6) que
NATIONAL UNIVERSITY OF SINGAPORE
EXAMINATION FOR THE DEGREE OF
B.ENG. (ELECTRICAL) / B.ENG. (COMPUTER ENG.)
(Semester II: 2002/2003)
EE2009  SIGNALS
May 2003 Time Allowed: 2 Hours
INSTRUCTIONS TO CANDIDATES: 1. This paper contains SIX (6) que
NATIONAL UNIVERSITY OF SINGAPORE
EXAMINATION FOR THE DEGREE OF
B.ENG. (ELECTRICAL) / B.ENG. (COMPUTER ENG.) / B.TECH. (ELECTRONICS)
(Semester I: 2002/2003)
EE2009/TE2009  SIGNALS
November 2002  Time Allowed: 2 Hours
INSTRUCTIONS TO CANDIDATES
EE2009/EE2009E Signals / page 1
NATIONAL UNIVERSITY OF SINGAPORE
EXAMINATION FOR
(Semester I: 2006/2007)
EE2009/EE2009E SIGNALS November 2006 Time Allowed: 2 Hours
INSTRUCTIONS TO CANDIDATES: 1. This paper contains SIX (6) questions and compri