Phase Shift of Sine and Cosine Waves Review

Phase Shift of Sine and Cosine Waves

Review • y = a*sin(b*x) • y = a*cos(b*x) • a amplitude • Vertical stretch/shrink • b frequency • Horizontal stretch/shrink

This time • y = a*sin(b*x+c) • y = a*cos(b*x+c) • What is c?

What is c? • y = a*sin(b*x+c) • c is called the phase angle, and it affects horizontal shift or displacement of the graph

Phase shift • y = a*sin(b*x+c) • c phase angle • Phase shift = -c/b • Displacement graph is shifted by • Note that phase angle and phase shift are not the same thing

Phase shift • y =a*sin(b*x+c) • y = sin(x+π) • Phase shift = -c/b = -π/1 = -π • y = sin(3 x-π) • Phase shift = -c/b = π/3 • y =12*sin(2*x+π/4) • Phase shift = -c/b = (-π/4)/2 = -π/8

Phase Shift • Consider y = sin(x) and y = sin(x + π/4) • Phase shift = -c/b = -π/4

Phase Shift • Consider y = sin(x) and y = sin(x – π/2) • Phase shift = -c/b = π/2

Phase Shift • Notice: • y = a* sin(b*x+c) shift by c/b in negative direction • y = a* sin(b*x-c) shift by c/b in positive direction

Why do we care? • Applications of sine waves in sciences, medical fields, engineering • National Academy of Engineering Grand Challenge. Reverse-Engineer the Brain • Neurons in the brain have electrical activity even after paralysis • This activity can be recorded, and often is periodic like sine waves

Why do we care? • Complex signals can be broken down into simpler sine waves • Pattern recognition methods applied to find motor commands within the recorded signal • Motor commands can be translated to robotic arms • http: //www. youtube. com/watch? v=QRt 8 QCx 3 BCo