Convolution in DSP

Updated on Friday, December 30, 2011 at 7:38PM by Darran

One of the problems that I've encountered in trying to teach myself DSP has been that most textbooks contain questions with no answers. Having been booked to take part in a 3 day course at Oxford Uni that was cancelled due to insufficient take-up, I've picked up the textbook that they were to use. It's a great book and has self assessment questions throughout with answers in the back, but the end of chapter exams don't. Some have a numerical answer which is fine for me to check I'm getting the right end of the stick, but not much help if I'm completely lost. Hopefully someone who knows what they're talking about will take pity on me and let me know if I've got this one right or not...

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An exploration of the effect of the number of coefficients used in a trigonometric Fourier series

Following on from the earlier post allowing you to manually enter different coefficients for a trigonometric Fourier series and visualise the resulting signal, I got to wondering how much of an effect the number of coefficients used had. So, playing around with a bit more jQuery, I came up with this. Choose either a square wave or a triangle wave and vary the number of coefficients used by dragging the slider. The chart updates in realtime so that you can see how quickly the signal converges to the true desired x(t).

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Trigonometric Fourier Series

With the Christmas study period (apparently some people mistakenly call it a holiday) now fully underway, I've started working my way through Digital Signal Processing: Concepts and Applications. One of the first concepts covered is the trigonometric Fourier series - the fact that any periodic power signal can be decomposed into a series of sine and cosine waves.

To demonstrate this, and brush up on my JavaScript, I put together this example of the trigonometric Fourier series in practice.

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Royal Institution lecture videos

I have many happy memories of whiling away my Christmas holidays watching the Royal Institution Christmas lectures. Now, I ican relive those captivating moments as the RI have launched richannel.org. The site holds not only Christmas lectures from recent years, but even some from 1973 (The Language of Animals with Sir David Attenborough), but many other lectures too covering various engineering, technology, mathematics and other subjects. Wonderful stuff.

It's sprouting peripherals

A quick session with the soldering iron, some female headers on the m3pi board and some right angle headers on the peripherals, and my Pololu is starting to look a little different. At the front is a 4D Systems uCAM serial JPEG camera module with the ability to also output RAW images as a simple stream of uncompressed pixel data; ideal for further processing. Just behind this, to give some visual feedback, is a Sparkfun Nokia 6100 breakout board. Thankfully, getting up and running is accelerated nicely by the kind contributors at mbed.org who have published code to interface with the m3pi, the Nokia LCD and the uCAM. With this rich source of code to build upon, it wasn't too difficult to get camera taking a 128x128 pixel, 8 bit greyscale image and display it on the LCD. An hour longer and it was first performing horizontal or vertical edge detection using a simple 2 pixel additive filter kernel. The next task is to build on the edge detection to be able to perform a full, convoluted gradient filter to detect vertical and horizontal edges without needing another 16kB buffer as the mbed doesn't have enough free RAM for that simplistic and inefficient approach.