Butterfly diagram

Contents • • • • What is FFT? • We use N-point DFT to convert an N-point time-domain sequence x(n) to an N-point frequency domain sequence x(k). • The purpose of performing a DFT operation is so that we get a discrete-time signal to perform other processing like filtering and spectral analysis on it. • However, the process of calculating DFT is quite complex. • It requires NxN complex multiplications and N(N+1) complex additions. • Cooley and Turkey were two mathematicians who came up with • To be precise, the FFT took down the complexity of complex multiplications from to N . • Thus, the FFT (Fast Fourier Transform) is nothing but a more efficient way of calculating the DFT (Discrete Fourier Transform). • The FFT is basically two algorithms that we can use to compute DFT. • Decimation in Time algorithm (DIT). • Decimation in Frequency algorithm (DIF). • The gist of these two algorithms is that we break up the signal in either time and frequency domains and calculate the DFTs for each and then add the results up. • We have taken an in-depth look into both of these algorithms in this How can we use the FFT algorithm to calculate inverse DFT (IDFT)? Check out the formulae for calculating DFT and inverse DFT below. DFT: x(k) = IDFT: x(n) = As you can see, there are only three main differences between the formulae. • In DFT we calculate discrete signal x(k) using a continuous signal x(n). Whereas in the IDFT, it’s the opposite. • In the IDFT formula, we have two different mult...

Equation 12 The N Log N savings Remember, for a straight DFT you needed N*N multiplies. The N Log N savings comes from the fact that there are two multiplies per Butterfly. In the 4 input diagram above, there are 4 butterflies. so, there are a total of 4*2 = 8 multiplies. 4 Log(4) = 8. This is how you get the computational savings in the FFT! The log is base 2, as described earlier. See equation 1. In the next part I provide an 8 input butterfly example for completeness.

Butterfly Life Cycle The butterfly and moth develop through a process called metamorphosis. This is a Greek word that means transformation or change in shape. Insects have two common types of metamorphosis. Grasshoppers, crickets, dragonflies, and cockroaches have incomplete metamorphosis. The young (called a nymph) usually look like small adults but without the wings. Butterflies, moths, beetles, flies and bees have complete metamorphosis. The young (called a larva instead of a nymph) is very different from the adults. It also usually eats different types of food. There are four stages in the metamorphosis of butterflies and moths: egg, larva, pupa, and adult. Egg Eggs are laid on plants by the adult female butterfly. These plants will then become the food for the hatching caterpillars. Eggs can be laid from spring, summer or fall. This depends on the species of butterfly. Females lay a lot of eggs at once so that at least some of them survive. Butterfly eggs can be very small. Caterpillar: The Feeding Stage The next stage is the larva. This is also called a caterpillar if the insect is a butterfly or a moth. The job of the caterpillar is to eat and eat and eat. As the caterpillar grows it splits its skin and sheds it about 4 or 5 times. Food eaten at this time is stored and used later as an adult. Caterpillars can grow 100 times their size during this stage. For example, a monarch butterfly egg is the size of a pinhead and the caterpillar that hatches from this tiny egg ...

The Butterfly Diagram accentuates the continuous flow of materials in the circular economy. Its ambition is to showcase the difference between technical and organic cycles through their ‘value circles’. Popularized by the Ellen MacArthur Foundation, the butterfly diagram takes into consideration 3 driving principles, namely the effective use of finite resources, enhancing the utility of raw materials and minimizing waste generation. Topics in this article Source: The Ellen MacArthur Foundation As authors Ed Weenk MSc PDEng and Rozanne Henzen mention in their book, ‘ • The Biological Cycle (left side of the diagram) – focuses on materials which are biodegradable • The Technical Cycle (right side of the diagram) – focuses on materials which are non-biodegradable. The first step towards a Technical Cycle: circular strategies and the R-Ladder The technical cycle consists of products which are not biodegradable. However, that does not mean that they should lose their value after use. In fact, this is where the technical aspect of product manufacturing comes into play. At its inception, the product must be put together with raw materials that can be reused, like valuable metals and polymers. This cycle requires a proper management of finite material stocks, so that after restoring the product, its components, and the materials can flow back into the cycle. This cycle consists of products that are maintained so that they retain their value for the longest time. It compels compani...

The Butterfly Diagram The Butterfly Diagram builds on the Danielson-Lanczos Lemma and the twiddle factor to create an efficient algorithm. The Butterfly Diagram is the FFT algorithm represented as a diagram. First, here is the simplest butterfly. It's the basic unit, consisting of just two inputs and two outputs. That diagram is the fundamental building block of a butterfly. It has two input values, or N=2 samples, x(0) and x(1), and results in two output values F(0) and F(1). The diagram comes form the D-L Lemma for two inputs. This can be shown by taking equation 7 above and plugging in for values n=0 and n=1, thus:

What is the Life Cycle of a Butterfly The series of changes in shape, form, and activities that a butterfly goes through during its lifetime is the life cycle, while the complex biological process involved in the transformation from caterpillars to adult butterflies is called metamorphosis. Butterflies undergo complete metamorphosis in which the young differs from the adult in What are the Life Stages of a Butterfly Butterflies go through four different stages in their life cycle, with each having a different goal. The caterpillars, for example, eat a lot, whereas adults reproduce. Depending on the butterfly species, these stages last from several weeks to a year. The life cycle starts with the adult female butterfly laying a cluster of small, round eggs on plants, which become food for the tiny worm-like caterpillars that hatch 4-6 days after they are laid. It is the larval stage during which the caterpillar emerges from the egg. It is also called the feeding stage because, at this stage, a caterpillar has only one job to do that is to eat. After a caterpillar attains its full-grown size, it stops eating and enters its chrysalis for the pupal stage. Fourth Stage: Adult In this stage, the chrysalis opens, and the adult butterfly or imago comes out. The adult butterfly has long antennae, long legs, and compound eyes. When it first emerges from the chrysalis, its long, colorful wings are damp, soft, and are folded against the body. The butterfly rests and waits for the wings...

The Ellen MacArthur Foundation was one of the pioneers in promoting the Circular Economy. The theoretical framework that we use for explaining the Circular Built Environment in this course is based on its principles. Below you can see the Circular Economy concept illustrated by the “butterfly diagram”. Both sides of the diagram are relevant to the built environment: the right side illustrates the technical cycle and closing the loops of resources facilitated by circularity strategies such as reuse, refurbish and recycling; the left side of the diagram shows the biological cycle and the loops and cascades assuring the sustainable management of biological resources and creating renewable flows and stocks. The ultimate aim of this economic model is to minimize the extraction of raw materials and waste generation. You can access a larger image of the diagram

Learn to create beautiful butterfly chart in PowerPoint for your business presentations. Discover creative variations of the diagram to convey your message with impact.This tutorial has been updated with step by step video on creating the Butterfly Diagram. The butterfly diagram you will learn today is: The diagram is as useful as it is beautiful. Before we learn to create the diagram, let us understand a bit more about the application of the diagram in business presentations. Applications of the diagram: A typical Butterfly diagram has the shape of a butterfly. The body of the butterfly represents the core concept. The wings represent ideas emerging from the core. You can use the diagram to represent: • Two sides of an argument • Two sets of outcomes from an action • Cause and effect relationship • Comparison etc. Let us learn to create the diagram in a simple step by step way. Watch the video below to create this diagram Now the rectangle is a freeform shape, which is easy to edit. You can use this simple feature to play with create interesting PowerPoint shapes. Step 2: Create Wedge Shape Right click on the shape and go to ‘Edit points’. Drag the corner point in the bottom left of the rectangle to your left till you get a wedge shape as shown below. Select the shapes -> got to ‘Shape effects’ in PowerPoint ribbon -> Presets -> Preset 2. This gives a nice bevel to the shapes. Add necessary text to the shapes. Group the shapes and add ‘reflection’. Add a rectangle with a ...