A short post on how to understand Convolution

Convolution is one of the first concepts every student of communications engineering learns. It is so fundamental to the study of signals and systems, and yet, is given out as an equation with explanations that focus on how to convolve rather than why.

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The way we teach and learn convolution is convoluted :)

Remember how we learnt it? If x[n] in the input to an LTI system with impulse response h[n], the output y[n] is given by convolution operation:

y[n] = ∑ₖ h[k] x[n-k]

Gee, nice equation, but what does it mean, we asked. And we got the visual flip, slide and multiply accumulate!

Say I give you two sequences:

x1 = [1, 2, 1, 0, 0, 2, 1, 2]
x2 = [3, 0, 0, 3, 0, 0, 1]

And I ask you for the convolution output. What would you do? Especially if you don’t have Matlab or Octave or Python. Would you evaluate the y[n] = ∑ₖ h[k] x[n-k] equation for the above two sequences? …


Video Tutorial

A quick look at the different neural network architectures, their advantages and disadvantages.

Video Tutorial

Experimental Machine learning is turning out to be so much fun! After my investigations on replacing some signal processing algorithms with deep neural network, which for the interested reader has been documented in the article “Machine Learning and Signal Processing”, I got around to trying the other two famous neural network architectures: LSTM and CNN.

Introducing CNN and LSTM

Before we get into the details of my comparison, here is an introduction to, or rather, my understanding of the other neural network architectures. We all understand deep neural network, which are simply a set of neurons per layer interconnected sequentially to another set of neurons in the next layer and so on. …


A physical layer comparison of cellular evolution with WiFi over the last three decades.

There are a lot of similarities between the cellular and WiFi evolution, especially for the physical layer. Today, both are ubiquitous and indispensable: a rare case of two competing technologies carving a niche for themselves and co-existing. Let us take a look at their interesting history!

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The cellular story started in the early 90s when the Global System for Mobile Communications (GSM) became the standard for wireless communication. …

About

Prasanna Sethuraman

It has been two decades of building Systems using Signal Processing, but the learning never stops!

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