Sampling theorem:


  • A continuous time signal can be represented as samples and can be recovered back when sampling frequency fis greater than or equal to twice the highest frequency component of message signal.
  • If this condition does not satisfy, it leads to aliasing.
  • Aliasing is an effect   that causes different signals to become indistinguishable when sampled.

Visualizing using python:

import matplotlib.pyplot as plt #  to plot

import numpy as np

#numerical python to get array of float values and for sine operation

t = np.arange(0, 2e-3, 10e-6) # x axis time period

# sampling at fs =10kHz in time domain ts=1/fs (0.1ms)

ts = np.arange(0,2e-3,0.1e-3)

f = 1000 # message signal fm

b = np.sin(2*np.pi*f*t) #phase for sinewave

c = np.sin(2*np.pi*f*ts)

plt.plot(t,b,”g”) # plot of message signal (1kHz)

plt.plot(ts,c,”k*”) # plot of sampled message signal (1kHz)

fs>=2fm:      Input frequency= 1kHz          sampling frequency = 10kHz


b = -np.sin(2*np.pi*f*t)

c = -np.sin(2*np.pi*f*ts)

plt.plot(t,b) # plot of message signal (9kHz)

plt.plot(ts,c,’r+’)  # plot of sampled message signal (9kHz)

fs<2fm:      Input frequency = 9kHz        sampling frequency = 10kHz

Sampled output of 1kHz and 9kHz :

Aliasing of 1kHz and 9kHz

part1: https://youtu.be/og-Pn2oOqP4

Relief work with migrant laborers

During this lock-down period, the migrant laborers struggled a lot for food and shelter. At STEM land we had an opportunity to work with an NGO called Coast India for helping migrant people. Ten of us volunteered for this NGO. The NGO had collected a database from the state government on migrant laborers who had earlier called in for help and put this information in an app. Our responsibility was to call the concerned people and verify the data and update their current specific requirements of migrant laborers. We spent about 2hrs per day for about a month. We worked with the migrants who were from Jharkhand in Tamil Nadu.

We called around 600 contacts and through them we reached nearly 2000 others. It was a difficult task for us to communicate since most of us do not know Hindi and most migrants could communicate with limited Tamil, but we still managed to understand and help them get food , shelter and transportation to get home by working in tandem with the NGOs on the ground in their areas.

Initially the government had promised that with updated data the migrants will have money transferred to their accounts. However, this did not happen and many of them were frustrated when they didn’t get the support committed by their government and additionally the situation at hand was also hard. The calls were hard to take as they were emotional and it even affected some of us as we were expected to continue to follow up for updated information. Nonetheless, our team members consoled them and helped them by sending many emails to the NGOs for follow up. All this struggle and emotional stress was wiped away when many of the migrant people sent us messages that they have safely reached home or got the rations they needed. We would like to thank Coast India NGO for creating this opportunity to help in relief for those who were stranded during the Carona.

Some insights

Working on COVID-19 relief work with Bindu and team was one such experience which made me realize one of the most pressing issues in our society – migrant workers. This issue was invisible to many of us till we got the intensity of it – the number of migrants, many unregistered, working in most hostile conditions thousands of kilometres from their homes, away from family.

As Bindu planned, we were given contact details and basic data from initial calls (mostly state government call centres). We had to reach out to the people on our list and get the latest status regarding their food, stay, health and any other essential things. There were mainly two phases:

1) initial phase when our migrant friends were having difficulties getting food, dry ration etc. Though we used to take note of their needs, many times it wasn’t possible to reach out to them with the help considering strict lockdown and resources at hand, both financial and human. Bindu was working hard to manage the ration/food for those who are in urgent needs, even with the scarce resources at hand.

2) In the second phase, there was a shift from getting food to getting transportation to their home states. This was the time when I realized that though many don’t have enough food to twice a day, they were not asking for it but for transportation.

Many times, it happened that they were frustrated by filling up different forms of the two states, with changed rules over every week. I experienced that through phone calls but wasn’t able to do anything about their travel. Eventually some of them started walking to their home with no hope of governments and administration managing their travel.

In all this chaos and helpless situation, I just started to listen to them. Some of them couldn’t control their tears, some just having hopes in their eyes. Some just needed to know the status of travel, and some of them were hopeful that someone is at least listening to what they are facing. Though I couldn’t contact all the people from cases assigned to me, I had contacted many of other migrants and could share some important updates with them as my number was being circulated by many of them among their other friends.

I couldn’t work from the last two weeks on this issue as it was very time consuming (I used to get calls all day) and I had other responsibilities. I still feel I could at least help some of them if not as many as I would have liked.

It moved me to see these many friends of ours have to go through these difficult times but there are people like Bindu who are working tirelessly to help them. Glad to be part of this initiative.

– Ganesh Shelke

When I called them, I came to know most of them are facing problems with food, shelter and many have to go back to Jharkhand. Hearing their problems and helping them to go back to their hometown gives me satisfaction. Thanks for giving me this opportunity.

– Sharat Kumar.N

I felt connected when I talked to people. Language was an issue for me. I was not able to speak in Hindi and was not able to reach people easily. They were asking for support and used so many “please” it was hard for me at that time to listen to their queries. Some of them were physically not well, didn’t get ration items, had to pay rent, wanted to go home and so on. Most of the time I had this question within me that, is what I do really useful and does it reach the one in need. I had this question when many of them said that it has been 20 days since I have requested, but still we didn’t receive anything. But I processed it within myself and took it as an opportunity of my growth and others.


I feel content and happy that I was able to support others during their difficult situation. It was great that their government (Jarkhand) took so much effort to give their support to the migrant people through this NGO (coast India) and Jarkhand Sahayta App. When people informed me that they received support from NGOs I was very happy. When some people did not receive any help at that time, we sent an email to NGO people to give support to the migrant people. The NGO people took an effort and gave their support to the migrant people. It was a great and new experience

– Saranya

Initially I had a willingness to help people, so I called them and asked about their needs, and I was happy by doing this. For two weeks, I was supporting people by registering their basic needs in our portal and bringing some urgent issues to the team. But after two weeks most people asked me to help them to reach their hometown.

I shared the information both in Hindi and English regarding special trains and e-pass. Later I realized that I was creating expectations in people’s mind that they can travel to their hometown when the government allowed only one or two trains. So, I stopped calling new cases, and only supported the old cases which have been assigned to me.


Even though I have been very busy in my work, I separately allocated time for calling migrants. When I was calling them, they were at the stage of losing hope, my words consoled them. I felt very happy. Working with the unknown people was new for me and I hope I have given my best.

-Vasantharaj gandhi

It was a different and challenging experience, because of the language which plays a medium for communication. I did this for my inner satisfaction. But because of some other works and self-development activities, I was not able to continue further. I appreciate and acknowledge all the others who did this service for a good cause.



Train the trainers – Interaction with Delhi Government Mentors

~Ganesh, Poovizhi, Saranya

Delhi Government Mentor teachers wished to visit Auroville to learn about the initiatives and steps that Auroville has taken in the field of education.

Mentor teachers is a core group of teachers looking for the academic quality and improvement of Delhi Government schools. As a part of capacity building  tour, mentors visited Pondicherry and surrounding areas to learn about alternate pedagogies in teaching and learning.
Due to government mandate of not having large gatherings  the group couldn’t visit STEM land schools but they were enthusiastic enough to learn more about STEM land, leadership capacity and stewardship qualities. We met them in Pondicherry where the group learnt about the activities we do in STEM land. They asked about preparing project material and learnt how students create projects in STEM land. We showed them different projects created by students on software like Scratch, Alice etc. They were also keen to know how to motivate teachers to adapt these pedagogies and how to balance both theoretical and practical learning.

Archana Shekar’s experience in STEM land

Archana Shekar who conducts ten days residential Vipassana retreats, children’s meditation courses and is in charge of it for Karnataka state. After completing her Masters at IITKGB and MBA at XLRI she worked with Price Waterhouse, Synovate and also wrote for Hong Kong based “Asian Business”. She prefers to work on inner development, Yoga and therapies,  Spirituality and Integral yoga.

She volunteered with STEM land and supported children in Isai Ambalam school on their English. Here is a short video of her experience in STEM land with Sanjeev Ranganathan.


STEM land meeting

~Poovizhi, Abilash

Yesterday we had STEM land meeting with all the coordinators of different STEM land and STEM land math teachers. Sundar presented a scratch program for fraction. Later we were all given small booklets by Azim Premji University on each topic like Addition, subtraction, multiplication, measurement. It had different activities that could be done with children in learning the concept. We agreed to read the booklet and present what we learnt from it make a model of it and present it to others in the next session. For some time we all read our booklet in silence and took notes.

Then shared about cyclic number which he read from his book which was new and interesting for all of us. The cyclic number is the following

1/7 = 0.142857

142857 x 2 = 285714

142857 x 3 = 428571

142857 x 4 = 571428

142857 x 5 = 714285

142857 x 6 = 857142

142857 x 7 = 999999

And the other one was to find the pattern and come up with an equation

1 = 1

3+5 = 8

7+9+11 = 27

What is the pattern and will the next line be?

1       = 1       : 1^3

3+5       = 8      : 2^3

7+9+11      = 27   : 3^3

13+ 15+17+19  = 64   : 4^3

n(n-1)+1 is the equation

STEM land meeting with Swati Sircar

~Poovizhi, Murali and Arun

This week it was a large group of people in the meeting. Coordinators from Aikiyam, Udavi, Isai ambalam and AITI joined the meeting. Swati Sircar joined the meeting online. At first Sundar demonstrated Scratch projects on finding LCM created by 8th grade and program on Graph created by 9th grade children which asks the user to find the point and completes by drawing a bear. Then we listed few topics to discuss with Swati. Swati explained about Trignometry. She said we can ask children to come up with 6 possible ratios from a right angle triangle and map the names.

Then different methods of teaching multiplications

7×9 = 7×10-7

To explain and use multiplication in

  1. Scaling
  2. Repeated addition
  3. Cartesian product (Choices of combinations)
  4. Area (rows and column)
  5. Rate (price and qty)

Then we moved to Division and she explained how to spit 11/3. For example to draw three circles and draw apples in each circle equally and the remaining is the reminder.

Then we discussed about simplification. For simplification children need to learn divisibility rules for 2,3,4,5,9,10 and 11

Followed with we had a conversation on negative exponential

2^-x = 1/2^x

(1/2)^-5 = (2)^5

2^3 = 8

2^2 = 4

2^1 = 2

2^0 = 1

2^-1 = 1/2

2^-2 = 1/4

2^-3 = 1/8

STEM land meeting with all STEM coordinators

~ Murali and Poovizhi

Sundar (Udavi school STEM land coordinator) gave a demonstration on learning Algebra using weighing scale. He used few sketch pens and weighing cubes (1gm) . For example one side had 10 grams and the other side had 5 sketch pens when both were weighing equal. He asked us to find the weight of each sketch pen. Then we discussed and solved few such examples in solveme and came up with all possible algebraic equations.

Saravanan from Aikiyam school had brought a star tetrahedron in which children had learnt about pyramids and triangles.

Arun who is coordinating with AIIT explained about parallelogram and showed how a rectangle can be formed by bisecting the angles of the parallelogram.


STEM land in Thamarai learning center

~Poovizhi, Saranya

There were around 20 kids from 6th std above. Thamarai facilitators said that they wanted to teach mathematics using materials. To start with basics we used Dienes block to visualize the arithmetic operations. Children learnt about cube, rod and plate and recalled place values .  I wrote the numbers and the operator on the board and asked children to find the answer for it using Dienes block. Children were split into four teams and worked as a team. Facilitators also learnt along with the children. Through this, children got clarity of how carry over works and why do we carry over , borrow and whether we carry over ones, tens or hundreds based on the place value.

Scaling up STEM land

~Poovizhi, Prabha, Arun

STEM land is being scaled to different schools in and around Auroville. We had a meeting with all the STEM land coordinators from Isai ambalam school, Udavi school, Thamarai night school, Auroville ITI, TLC and  Aikiyam school.

We shared what we did in each STEM land. We discussed about algebraic identities, powers and how children can understand visually. One of the STEM coordinator solved it blindfolded. When we blindfold the cube size feels like it’s the same but when we compare it with the other cube it is a bit easier to figure it out. It was fun to learn.

Next meet : Link

Research on how Alumni use or retain what they learn in STEM land

Poovizhi, Murali and Saranya

As explained in the previous blog http://www.auraauro.com/uncategorized/2017-2018-batch-childrens-reflection-on-stem-land/

We did a research on how children use or retain what they learn in STEM land. We conducted a survey in the following methodology
a) a group sharing of the alumni of how each of them are doing and what they have retained and use from their experience at STEM land.
b) This was followed by a review of the intention of each of the 20 questions of the
survey that explored each of these aspects
c) The children then filled out the survey individually
d) Four children who were not able to attend the group sharing filled out just the survey.
The conversation and the responses were analysed to understand what the children have found
special, useful and what continues to be useful and impacts them about STEM land.

This paper records reflections of alumni of STEM land two years after they
graduated from STEM land and pursuing their further studies in other schools. We review if
and how they found their time in STEM land useful and what role their experience in STEM
land continues to play in their lives:
1) If they found their time in STEM land useful and in what way.
2) What they retained and its application in higher education.
3) How interventions at STEM land that made the learning environment different from
what they experienced otherwise at school has shaped their attitude in further studies.
Specifically, we examine:
 the freedom to plan their work
 peer learning
 access to puzzles and strategy and logic games that give a broader perspective of
Mathematics and are joyful
 access and use of materials in Mathematics to make abstract ideas concrete
 creating projects that provide opportunity to own one’s work

Following is the graph which shows how useful was STEM land for them.

The survey and conversations indicate that children not only learned Mathematical concepts
but also learned skills like programming and logical thinking. The children were left with a
comfort with these areas and all of them took up these subjects in higher education took up
computer science as an elective even those who took up Arts as a stream. They also continued
supporting their peers even in environments that are not entire conducive to peer learning.
The children not only understood what they had learned, but also had clarity in the
development of logical thinking, strategies and multiple methodologies of solving questions.

They also shared that they find a learning environment joyful and they appreciate is one that
gives them responsibility to plan their learning and work and gives them access to resources
and peer learning.
We believe these interventions if introduced as part of Mathematics could support children
taking responsibility of their learning and develop a deeper sense of learning beyond what is
expected in their Mathematics curriculum across India.

We have submitted our paper in epiSTEME8 it is available in the following link.