1. FLIPPED CLASSROOM on Discrete time signal processing - II
Dr. Sunil Karamchandani Ashish Khodwe
RC 1016_001
IDP in Educational Technology – IIT Bombay

2. Sunil Karamchandani RC 1016_001 Ashish Khodwe
Characteristics of Discrete Time Systems
Digital Signal Processing
EXTC
Third Year UG Students in EXTC
DJSCE, University of Mumbai
IDP in Educational Technology, IIT Bombay

3. Out-of-class Activity Design -1
Learning Objective(s) of Out-of-Class Activity:
At the end of watching the videos student should be able to,
Describe a discrete time system in terms of its impulse
response
Identify the characteristics of Discrete time systems such as
time invariance and linearity.
Interpret causality in discrete time signals.
Key Concept(s) to be covered:
Time Invariance
Linearity
Causal Systems
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4. Out-of-class Activity Design - 2
Uploaded Video URL
   
License of Video
Creative-Commons License
CONCEPT
VIDEO
SEGMENT
DURATION
(min)
Discrete Time System
V – 1.10 1
Time Invariance of a discrete time system
V – 2.55
1. 42
Linearity property of a discrete time signal
V3- 3 – 7 4
Causality of a discrete time system
V – 9.03
1.53
Creative-Commons License
Duration of Screencast
9 m 12s
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5. Out-of-class Activity Design - 3
Aligning Assessment with Learning Objective
Learning Objective
Assessment Strategy
Expected duration
(in min)
Additional Instructions (if any)
Time Invariance
Q1. Examine the following systems y(n) with respect to time invariance with proper working
Cos [x(n)]
x(-n+2)
(c) x(2n)
(a) 2 min
(b) 2 min
(c) 2 min
To be attempted after video v2.
Linearity
Q2. Examine the following systems y(n) with respect to linearity with proper working
x(n) + n x(n+1)
x(-n)
(c) sign[x(n)]
(d) x(n) + 3x(n+4)
2 min
To be attempted after video v3.
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6. Out-of-class Activity Design - 3
Aligning Assessment with Learning Objective
Learning Objective
Assessment Strategy
Expected duration
(in min)
Additional Instructions (if any)
Causality
Q3. Examine the following systems y(n) with respect to causality with proper working
ex(n)
a x(n)
(c) x(n) – x(n-1)
(d) x(n2)
(a) 2 min
(b) 2 min
2min
2 min
To be attempted after video v4
Discrete time system
Q3. Explain a discrete time system with respect to its characteristics of shift invariance, linearity and causality.
8 min
At the end of the screencast
Expected activity duration
30 min
IDP in Educational Technology, IIT Bombay

7. In-Class Activity Design
This section helps you design the in-class segment of Flipped Classroom Strategy
IDP in Educational Technology, IIT Bombay

8. In-class Activity Design -1
Learning Objective(s) of In-Class Activity:
Students will be able to
Estimate the response of a discrete time system as a convolution operation.
Interpretation of a discrete time signal as summation of impulse responses.
Justify the role of Linear Time Invariant systems for discrete time signal processing.
Key Concept(s) to be covered:
Linear Convolution
Signal Decomposition
Linear Time Invariant Systems
IDP in Educational Technology, IIT Bombay

9. In-class Activity Design -2
Active Learning activities
Peer Instruction Phase:
Tutor would present a Screencast to understand the concept of convolution which represents the response/output of linear time invariant discrete time system.
Think-Pair-Share Phase:
Students will be shown a short screencast on discrete time signals. The students will be required to recall the concept of shift and fold of a signal. The tutor will pose a problem to the students after the viewing of the screencast. The pair phase involves the application of the convolution procedure to a discrete time input. The tutor assists the students to recuperate the characteristics of discrete time systems. The pair phase will be a discussion on the procedure followed by each pair for implementing the convolution formulae.
IDP in Educational Technology, IIT Bombay

10. In-Class Activity Design- 2
Deliverables
Instructor: Prepare a screencast and to front a problem denoting the significance of convolution.
Student: Perform the operation of convolution to obtain y(n) the response of the system with an impulse response h(n) and an input x(n).
Facilitate higher level cognitive actions as a
Think – Pair- Share activity
The students will be able to (understand) the reason why convolution is required to obtain the output of linear time invariant discrete time systems (apply and evaluate).
Total Activity Duration : 27 min
IDP in Educational Technology, IIT Bombay

11. In-class Activity Design -2(a)
Active Learning activities
Peer Instruction Phase:
Students will be shown a short screencast on response of discrete time systems which will enable them to interpret the concept of linear convolution to obtain the response of linear time invariant discrete time system.
Uploaded Video URL
License of Video
Creative-Commons License
IDP in Educational Technology, IIT Bombay

12. In-class Activity Design – 2(a)
Uploaded Video URL
License of Video
Creative-Commons License
CONCEPT
VIDEO
SEGMENT
DURATION
(min)
System Response of a Discrete Time Signal
V – 2.30
1.37
Decomposition of a Discrete Time Signal
V2 – 2.31 – 4.18
1.13
Linear Time Invariant Systems
V – 7.12
2. 52
Response of a discrete time signal as a convolution operation
V4 – 7.14 – 8.37
1.23
Creative-Commons License
Duration of Screencast
8 m 38s
IDP in Educational Technology, IIT Bombay

13. In-Class Activity Design- 2(b)
Think Phase
Role of the instructor: Front a problem on linear convolution
Compute the convolution of the following signal. Also show that summation of y(n) is equal to the product of the summations of x(n) and h(n).
x (n) = {1,2,4} and h(n) = {1,1,1,1,1}
Role of student: Reminisce the signal properties of shift and fold of a signal which will aid in the convolution operation. Relate these properties to interpret the convolution formula
Deliverables: The student can now interpret the convolution formula analytically and apply it to calculate the system response. (Analyze and Interpret)
Time Duration - 3 min.
IDP in Educational Technology, IIT Bombay

14. In-Class Activity Design- 2(c)
Pair Phase
Role of the instructor: Assure active participation of each student in every pair to decipher the posed question in the Think Phase.
Role of student: within the groups the students will jot down the steps to be performed for the convolution operation. (fold, shift, multiply and add ) in that order. Estimate the output y(0), y(1), ……y(n) after each shift.
Deliverables: Learning objectives of Apply and Evaluate.
Time Duration - 7 min.
IDP in Educational Technology, IIT Bombay

15. In-Class Activity Design- 2(d)
Share Phase
Role of the instructor: Tutor will move across the classroom to the individual groups and ask students to share their procedure thy have followed. At the end of the tour he asks each group leader to mention the individual steps which he writs down on the board.
Role of student: Share their solutions and fine-tune them if any inconsistencies arise from given solution. Observe and follow the review comments of the instructor.
Deliverables: Relate and authenticate the solutions of the students (verify).
Time Duration - 9 min.
IDP in Educational Technology, IIT Bombay

16. In-Class Activity Design- 3
End of class summary, conclusion and lee way
Think Pair Share is then followed by a rapid recap of the necessary formulae required.
The instructor concludes that sampling of continuous time signal is an important prerequisite to understand the use of discrete time signals in discrete time systems. The manipulation of these signals aid in the understanding of time invariance, linearity and causality of discrete time signals.
The instructor proposes an extension of signals to discrete time systems which would be discussed in the next lecture.
Activity Duration: 19 min.
IDP in Educational Technology, IIT Bombay

17. In-Class Activity Design – 4
The trio of think-pair-share as a cumulative repository aids in the understanding the response of linear time invariant systems. TPS serves as a platform of active learning strategy for discrete time sampling of as it allows the students to analyze, assess and apply. The students would participate in interpretation and validation of the convolution procedure.
Review:
The instructor at the end of share phase gets sufficient feedback whether the in-class activity has succeeded in justifying the taxonomy of analyze, interpret assess and apply.
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18. In-class Activity Design - 5
Aligning Assessment with Learning Objective
Learning Objective
Assessment Strategy
Expected duration
(in min)
Additional Instructions (if any)
Convolution operation
Q1. Consider the following operations
Multiply the integers 131 and 122
Compute the convolution of the signals {1,3,1} and {1,2,2}.
Comment on your results
Q1. 9 min.
2 min.
4 min.
3 min
Submit these to the tutor at the beginning of the next lecture
Tabular Convolution
Q2. Compute the convolution of the signals using the tabular method.
Q2. 6 min.
Activity Duration: 15 min.
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19. END OF CONSTRUCTOR
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