Assignment 1

by

Shridevi kotta

This write up involves the
understanding of the function y = a sin(2fx+n). This is a sine wave function. Some of the
terms involved in the function have the following terminologies: a is called
the amplitude of the wave, n is the phase control parameter and f is frequency
control parameter.

A sine function is a
periodic function where the values of the function repeat at a regular interval
called the period. The period is determined by the frequency factor and is
inversely proportional to frequency.

LetÕs look at some graphs
and see how each of these parameters vary the graph.

First lets look at
amplitude. Consider the equation

y = a sin(2fx).
In this equation we set f =1. And phase is set to 0. So the period is 2. Y takes on a maximum value = a which we call the amplitude.

The following is some sample
waveforms for the given equations with change in amplitude.

When we vary the frequency,
we see that period varies inversely proportional. For example we make frequency
f =2. Then the period reduces by half to and if we reduce
the frequency to 0.5, we see period doubles to 4.

Click here
to see the variation in phase: c takes values from Š10 to 10.

And also see the graphs
below. Phase shifts the graph to right or left. And since it is a periodic
function we see that maximum shift we could make is equal to that of the
period. Any shift in multiples of period will be the original graph itself.