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Name :- Smit Shah -140410109096
S.Y electrical 2 Sem 4
Subject:-SS
Topic :- Frequency spectrum of periodic
signal..
Representation of periodic signals:
Frequency spectrum of periodic
signal..
 Spectrum : The entire range over which some
measurable property of a physical system can vary,
such as a frequency of sound , the wavelength etc. Its
also called as a graphic or photographic representation
of such measurable range..
Frequency Domain Representation
 All the signal till now were drawn with respect to time.
That representation of signal with respect to time is
called as its time domain representation.
 The time domain representation of the signal is not
sufficient for its analysis. Hence we have to use the
frequency domain representation of the signal for the
sake of analysis.
 In the frequency domain representation , the variable
plotted on the X-axis is frequency “f” rather than “t”.
 The signal represented in the frequency domain is
called as the line spectrum. The line spectrum consists
of two graphs mainly.
 1. Amplitude spectrum: A graph of amplitude on Y-axis
versus frequency on X-axis.
 2. Phase Spectrum : A graph of phase on Y-axis versus
frequency on X-axis.
 The signal x(t) and its line spectrum is show in above
fig.
 The graph of Instantaneous signal voltage plotted on
y-axis versus time plotted on X-axis is called as time
domain representation.
 The time domain representation gives us the following
information:
 1. Shape of the signal
 2. Its frequency
 3. Type of the signal (periodic or nonperiodic )
 4. One cycle peroid
 But we do not know anything about what frequency
components are present and in what proportion they
have been mixed in order to obtain the particular
shape of signal.
 All this information can be obtained from the line
spectrum of a signal.
 Line spectrum is the representation of the same signal
x(t), now in the frequency domain.
 It can be obtained by using either Fourier series or
Fourier Transform. It consists of the amplitude and
phase spectrum of the signal.
 The line spectrum indicates the amplitude and phase
of various frequency components present in the given
signal. The line spectrum enables us to analyze and
synthesize a signal….
Frequency Domain Representation of Sinusoids:
Continuous Time
Consider a sinusoid in continuous time:
tFjjtFjj
ee
A
ee
A
tFAtx
00 22
0
22
)2cos()(

















Frequency Domain Representation:
0F
2
A

0F

2
A
magnitude
phase
radians
)(HzF
)(HzF
Example
Consider a sinusoid in continuous time:
    tjjtjj
eeee
ttx


200015.0200015.0
55
)15.02000cos(10)(



Represent it graphically as:
000,1
5
15.0
magnitude
phase
15.0
radians
5
000,1 )(HzF
)(HzF
Frequency Domain Representation of Sinusoids:
Discrete Time
Same for a sinusoid in discrete time:
njjnjj
ee
A
ee
A
nAnx
00
22
)cos(][ 0

















2
A
magnitude
phase
0


2
A
0 )(rad
)(rad
Frequency Domain Representation:
Example
Consider a sinusoid in discrete time:
    njjnjj
eeee
nnx


45.035.045.035.0
44
)35.045.0cos(8][



Represent it graphically as:
45.0
4
35.0
magnitude
phase
35.0
radians
4
45.0 )(rad
)(rad
 So as we show in above example for real periodic signal
the amplitude spectrum is even symmetric & phase
spectrum is odd symmetric…
Frequency spectrum of periodic signal..

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Frequency spectrum of periodic signal..

  • 1. Name :- Smit Shah -140410109096 S.Y electrical 2 Sem 4 Subject:-SS Topic :- Frequency spectrum of periodic signal..
  • 2. Representation of periodic signals: Frequency spectrum of periodic signal..  Spectrum : The entire range over which some measurable property of a physical system can vary, such as a frequency of sound , the wavelength etc. Its also called as a graphic or photographic representation of such measurable range..
  • 3. Frequency Domain Representation  All the signal till now were drawn with respect to time. That representation of signal with respect to time is called as its time domain representation.  The time domain representation of the signal is not sufficient for its analysis. Hence we have to use the frequency domain representation of the signal for the sake of analysis.
  • 4.  In the frequency domain representation , the variable plotted on the X-axis is frequency “f” rather than “t”.  The signal represented in the frequency domain is called as the line spectrum. The line spectrum consists of two graphs mainly.
  • 5.  1. Amplitude spectrum: A graph of amplitude on Y-axis versus frequency on X-axis.
  • 6.  2. Phase Spectrum : A graph of phase on Y-axis versus frequency on X-axis.
  • 7.  The signal x(t) and its line spectrum is show in above fig.  The graph of Instantaneous signal voltage plotted on y-axis versus time plotted on X-axis is called as time domain representation.  The time domain representation gives us the following information:
  • 8.  1. Shape of the signal  2. Its frequency  3. Type of the signal (periodic or nonperiodic )  4. One cycle peroid  But we do not know anything about what frequency components are present and in what proportion they have been mixed in order to obtain the particular shape of signal.
  • 9.  All this information can be obtained from the line spectrum of a signal.  Line spectrum is the representation of the same signal x(t), now in the frequency domain.  It can be obtained by using either Fourier series or Fourier Transform. It consists of the amplitude and phase spectrum of the signal.
  • 10.  The line spectrum indicates the amplitude and phase of various frequency components present in the given signal. The line spectrum enables us to analyze and synthesize a signal….
  • 11. Frequency Domain Representation of Sinusoids: Continuous Time Consider a sinusoid in continuous time: tFjjtFjj ee A ee A tFAtx 00 22 0 22 )2cos()(                  Frequency Domain Representation: 0F 2 A  0F  2 A magnitude phase radians )(HzF )(HzF
  • 12. Example Consider a sinusoid in continuous time:     tjjtjj eeee ttx   200015.0200015.0 55 )15.02000cos(10)(    Represent it graphically as: 000,1 5 15.0 magnitude phase 15.0 radians 5 000,1 )(HzF )(HzF
  • 13. Frequency Domain Representation of Sinusoids: Discrete Time Same for a sinusoid in discrete time: njjnjj ee A ee A nAnx 00 22 )cos(][ 0                  2 A magnitude phase 0   2 A 0 )(rad )(rad Frequency Domain Representation:
  • 14. Example Consider a sinusoid in discrete time:     njjnjj eeee nnx   45.035.045.035.0 44 )35.045.0cos(8][    Represent it graphically as: 45.0 4 35.0 magnitude phase 35.0 radians 4 45.0 )(rad )(rad
  • 15.  So as we show in above example for real periodic signal the amplitude spectrum is even symmetric & phase spectrum is odd symmetric…