Frequency Domain Analysis (2) Notes | EduRev

: Frequency Domain Analysis (2) Notes | EduRev

 Page 1


STOCHASTIC HYDROLOGY 
Lecture -14 
Course Instructor :  Prof. P. P. MUJUMDAR 
                                     Department of Civil Engg., IISc. 
 
INDIAN	
  INSTITUTE	
  OF	
  SCIENCE	
  
Page 2


STOCHASTIC HYDROLOGY 
Lecture -14 
Course Instructor :  Prof. P. P. MUJUMDAR 
                                     Department of Civil Engg., IISc. 
 
INDIAN	
  INSTITUTE	
  OF	
  SCIENCE	
  
2	
  
Summary	
  of	
  the	
  previous	
  lecture	
  
•? Frequency domain analysis 
–? Spectral density 
–? Test for significance of periodicities 
–? Removing periodicities 
–? Standardizing the data 
 
 
Page 3


STOCHASTIC HYDROLOGY 
Lecture -14 
Course Instructor :  Prof. P. P. MUJUMDAR 
                                     Department of Civil Engg., IISc. 
 
INDIAN	
  INSTITUTE	
  OF	
  SCIENCE	
  
2	
  
Summary	
  of	
  the	
  previous	
  lecture	
  
•? Frequency domain analysis 
–? Spectral density 
–? Test for significance of periodicities 
–? Removing periodicities 
–? Standardizing the data 
 
 
Frequency Domain Analysis 
3	
  
•? Spectral density (I
k
) is the amount of variance per 
interval of frequency 
•? Spectral analysis helps indentify the significant 
periodicities themselves 
•? A peak in the spectrum indicates an important 
contribution to variance at frequencies close to the 
peak 
•? Prominent spikes indicate periodicity 
•? Line spectrum - inconsistent estimate 
•? Power spectrum - consistent estimate ?
k
	
  	
  	
  
I(k)
	
  
Page 4


STOCHASTIC HYDROLOGY 
Lecture -14 
Course Instructor :  Prof. P. P. MUJUMDAR 
                                     Department of Civil Engg., IISc. 
 
INDIAN	
  INSTITUTE	
  OF	
  SCIENCE	
  
2	
  
Summary	
  of	
  the	
  previous	
  lecture	
  
•? Frequency domain analysis 
–? Spectral density 
–? Test for significance of periodicities 
–? Removing periodicities 
–? Standardizing the data 
 
 
Frequency Domain Analysis 
3	
  
•? Spectral density (I
k
) is the amount of variance per 
interval of frequency 
•? Spectral analysis helps indentify the significant 
periodicities themselves 
•? A peak in the spectrum indicates an important 
contribution to variance at frequencies close to the 
peak 
•? Prominent spikes indicate periodicity 
•? Line spectrum - inconsistent estimate 
•? Power spectrum - consistent estimate ?
k
	
  	
  	
  
I(k)
	
  
Example – 1 
(Spectral Analysis) 
4	
  
Monthly Stream flow (in cumec) statistics(1979-2008) for a 
river is selected for the study. (Part data shown below) 
Year Month S.No. Flow 
1979 June 1 54.6 
July 2 325.4 
August 3 509.5 
September 4 99.4 
October 5 53.5 
November 6 25.8 
December 7 12.5 
1980 January 8 5.6 
February 9 3.1 
March 10 2.2 
April 11 0.9 
May 12 0.81 
N = 348	
  
Page 5


STOCHASTIC HYDROLOGY 
Lecture -14 
Course Instructor :  Prof. P. P. MUJUMDAR 
                                     Department of Civil Engg., IISc. 
 
INDIAN	
  INSTITUTE	
  OF	
  SCIENCE	
  
2	
  
Summary	
  of	
  the	
  previous	
  lecture	
  
•? Frequency domain analysis 
–? Spectral density 
–? Test for significance of periodicities 
–? Removing periodicities 
–? Standardizing the data 
 
 
Frequency Domain Analysis 
3	
  
•? Spectral density (I
k
) is the amount of variance per 
interval of frequency 
•? Spectral analysis helps indentify the significant 
periodicities themselves 
•? A peak in the spectrum indicates an important 
contribution to variance at frequencies close to the 
peak 
•? Prominent spikes indicate periodicity 
•? Line spectrum - inconsistent estimate 
•? Power spectrum - consistent estimate ?
k
	
  	
  	
  
I(k)
	
  
Example – 1 
(Spectral Analysis) 
4	
  
Monthly Stream flow (in cumec) statistics(1979-2008) for a 
river is selected for the study. (Part data shown below) 
Year Month S.No. Flow 
1979 June 1 54.6 
July 2 325.4 
August 3 509.5 
September 4 99.4 
October 5 53.5 
November 6 25.8 
December 7 12.5 
1980 January 8 5.6 
February 9 3.1 
March 10 2.2 
April 11 0.9 
May 12 0.81 
N = 348	
  
Example – 1 (contd.) 
 (Spectral Analysis) 
5	
  
The time series plot 
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Flow in Cumec 
Time 
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