![]() The process of getting from the time domain to the frequency domain, and from the frequency domain back to the time domain, is called the Fourier Transform. It’s important to remember that the top graph only represents frequency and not time it is merely another way of looking at the signal. ![]() On the frequency graph, the three spikes would represent the low, medium and high tones of the voice. It’s a summary of the signal’s frequency over that time period. The line on the top graph is the same signal represented in the frequency domain. Below, the bottom graph is a signal similar to the voice signal in the time domain. In the frequency domain, the frequency of the signal is on the x-axis, while the amplitude (or loudness) of the signal is still on the y-axis. While plotting a signal in the time domain is often a nice way to visualise it, Engineers find it useful to deal with a signal in the frequency domain. This means that along the x-axis of this graph (left to right) is time, while on the y-axis (up and down) is the amplitude of the voice – how loud it is. The picture of the voice is a signal in the time domain. ![]() Basically think of a signal as a squiggly line on a graph, like above. It could also be an image, a video, a word file, a graph or a multitude of other things. For instance it could be a clip of a voice recording, like the graph below (altered from this website) In Engineering, a signal is usually something you want to send or record. As it is a very broad overview of the subject there are some big simplifications, but hopefully you’ll get something from it. This blog post does not have much maths in it, but it does deal with concepts that might be slightly beyond someone with no mathematical background. It ends by describing how wavelets can be used for transforms and why they are sometimes preferred because they give better resolution. It then goes on to talk about the limitations of the Fourier Transform and Heisenberg’s uncertainty principle. ![]() ![]() First it describes how and why Engineers de/reconstruct a signal using the Fourier transform. What are these transforms then and why are they so important? How are Wavelet Transforms different/better than Fourier Transforms? That’s the subject of this blog post. These little waves are shaking things up because now Wavelet Transforms are available to Engineers as well as the Fourier Transform. However they all take the form of a ‘mini wave’, fading to zero quickly. Rather than being a wave that goes on forever, like sin() or cos(), wavelets are a short ‘burst’ of waves that quickly die away, like the picture below:īecause there are very few rules about what defines a wavelet, there are hundreds of different types. In doing this they are opening up a new way to make sense of signals, which is the bread and butter of Information Engineering.Īt their most basic, wavelets are quite literally ‘mini waves’. What’s interesting about wavelets is that they are starting to undermine a staple mathematical technique in Engineering: the Fourier Transform. Wavelets have recently migrated from Maths to Engineering, with Information Engineers starting to explore the potential of this field in signal processing, data compression and noise reduction. ![]()
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