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# 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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900

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Flow in Cumec
Time
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