Spectrum Estimation: Presentation by Dr. K.Muthumeenakshi Asso - Prof / ECE SSN College of Engineering
Spectrum Estimation: Presentation by Dr. K.Muthumeenakshi Asso - Prof / ECE SSN College of Engineering
Spectrum Estimation: Presentation by Dr. K.Muthumeenakshi Asso - Prof / ECE SSN College of Engineering
Presentation by
Dr. K.Muthumeenakshi Asso.Prof / ECE
SSN College of Engineering
Spectral Estimation
• Non Parametric Methods
– Periodogram method
– Modified periodogram method
– Bartlett’s method
– Welch method
– Blackmann Tukey method
• Parametric Methods
– ARMA model
– AR model
– MA model
Spectral Estimation
• Non parametric method /Classical method
– Find autocorrelation from the data set
– Use Wiener Khinchine theorem to find its power
spectrum
• Parametric / Non classical method
– Use of a model to estimate the power spectrum
– ARMA
– AR
– MA
Performance of an Estimator
• Based on
– Bias
– Variance
Performance of an Estimator
• Based on
– Bias
– Variance
• Bias
Bias is defined as,
where,
Periodogram Estimator
Thus the periodogram is proportional to the squared magnitude of the DTFT of
xN(n) and may be computed using a DFT as follows:
Example 1
white noise process
amplitude 5
-5
0 5 10 15 20 25 30 35 40 45 50
samples
autocorrelation
100
amplitude
50
-50
-50 -40 -30 -20 -10 0 10 20 30 40 50
samples
power spectrum
magnitude(dB)
-2
-4
-5
0 20 40 60 80 100 120 140 160 180 200
samples
autocorrelation
200
amplitude
100
-100
-200 -150 -100 -50 0 50 100 150 200
samples
power spectrum
2
magnitude(dB)
-2
-4
-2
0 10 20 30 40 50 60 70 80 90 100
samples
autocorrelation
100
amplitude
50
-50
-100 -80 -60 -40 -20 0 20 40 60 80 100
samples
power spectrum
0.06
magnitude(dB)
0.04
0.02
0
0 50 100 150 200 250 300 350 400 450 500
frequency
Example 2
sine (200Hz) + white noise process
amplitude 2
-2
0 50 100 150 200 250 300 350 400 450 500
samples
autocorrelation
500
amplitude
-500
-500 -400 -300 -200 -100 0 100 200 300 400 500
samples
power spectrum
0.2
magnitude(dB)
0.1
0
0 50 100 150 200 250 300 350 400 450 500
frequency
Performance of the Periodogram
• Mean square convergence,
Performance of the Periodogram
• Mean square convergence,
which implies,
Periodogram bias
• To compute the bias, we first evaluate the
expected value of
Periodogram bias
• To compute the bias, we first evaluate the
expected value of
Periodogram bias
• To compute the bias, we first evaluate the
expected value of
Periodogram bias
• Using the conjugate symmetry of
Periodogram bias
• Using the conjugate symmetry of
Periodogram bias
• Using the conjugate symmetry of
• Setting
Performance of the Periodogram