Scaling, stretching and shifting sinusoids

This is a brief and simple [1] explanation of how to adjust the standard sinusoid to change its amplitude, frequency and phase shift. More precisely, given the general function: We’ll see how adjusting the parameters , and affect the shape of . Each section below covers one of these aspects mathematically, and you can use the demo at the bottom to experiment with the topic visually. Scaling Scaling is conceptually the simplest change; we adjust to increase or decrease the amplitude (maximal height) of . Setting will make the value twice as large (in both the positive and negative direction) as the original function. Stretching Stretching changes the frequency of , which is inverse proportional to its period. The baseline function has a period of , meaning it repeats every . In other words, for any . If we set , we get . This function repeats itself twice as fast as , because is multiplied by 2 before being fed into the sinusoid. If changes by , the sinusoid’s input changes by .…