Statistical Signal Processing

By Prof. Prabin Kumar Bora   |   IIT Guwahati
Learners enrolled: 480
Many practical signals are random in nature or modelled as random processes. Statistical Signal Processing involves processing these signals and forms the backbone of modern communication and signal processing systems.This course will the three broad components of statistical signal processing: random signal modelling, estimation theory and detection theory.

PRE- REQUISITES : A Basic Course in Probability 
Course Status : Completed
Course Type : Core
Duration : 12 weeks
Category :
  • Electrical, Electronics and Communications Engineering
  • Communication and Signal Processing
  • Control and Instrumentation
Credit Points : 3
Level : Postgraduate
Start Date : 24 Jan 2022
End Date : 15 Apr 2022
Enrollment Ends : 07 Feb 2022
Exam Date : 23 Apr 2022 IST

Note: This exam date is subjected to change based on seat availability. You can check final exam date on your hall ticket.

Page Visits

Course layout

Week 1 & 2 : Introduction; Stationary processes: Strict sense and wide sense stationarity; Correlation and spectral analysis of discrete-time wide sense stationary processes, white noise, response of linear systems to wide-sense stationary inputs, spectral factorization
Week 2, 3 & 4 : Parameter estimation: Properties of estimators, Minimum Variance Unbiased Estimator (MVUE Cramer Rao bound, MVUE through Sufficient Statistics, Maximum likelihood estimation- properties. Bayseaen estimation-Minimum Mean-square error(MMSE) and Maximum a Posteriori(MAP) estimation
Week 5 : Signal estimation in white Gaussian noise– MMSE, conditional expectation; Linear minimum mean-square error( LMMSE ) estimation-–, orthogonality principle and Wiener Hoff equation 
Week 6 : FIR Wiener filter, linear prediction-forward and backward predictions, Levinson-Durbin Algorithm, application –linear prediction of speech
Week 7 : Non-causal IIR wiener filter, Causal IIR Wiener filtering
Week 8, 9 & 10: Iterative and adaptive implementation of FIR Wiener filter: Steepest descent algorithm, LMS adptive filters, convergence analysis, least-squres(LS) method, Recursive LS (RLS) adaptive filter, complexity analysis, application- neural network 
Week 10 & 11: Kalman filters: Gauss -Markov state variable models; innovation and Kalman recursion, steady-state behaviour of Kalman filters
Week 12: Review; Conclusions.

Books and references

1.M. H. Hayes, Statistical Digital Signal Processing and Modeling, John Wiley & Sons, Inc., 2002.
2.S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory, Prentice Hall,1993.
3.D.G. Manolakis, V.K. Ingle and S.M. Kogon, Statistical and Adaptive Signal Processing, McGraw Hill, 2000

Instructor bio

Prof. Prabin Kumar Bora

IIT Guwahati
Ph.D. IISc Bangalore Designation: Professor,IIT Guwahati P.K. Bora joined the institute in 1997.

Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
Date and Time of Exams: 23 April 2022 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
Registration url: Announcements will be made when the registration form is open for registrations.
The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.
Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.


Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Guwahati .It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team

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