An Analysis Approach: Chap 8

Reading Questions

At any point, you can submit your answers by collecting them and uploading them to the class site.

No answers yet collected

Link to upload site

If requested by your instructor, please identify here the people from whom you received assistance on this assignment.

If the answers that have been loaded automatically are not yours, press this button before starting your work:

Reading Question 8. 1 What is the role of coefficients in building a linear combination?

Reading Question 8. 2 Imagine you have three functions \(f()\), \(g()\), and \(h()\) each of which takes a single argument. (They might, for instance, be input-scaled storybook functions.) Here are some different ways of composing a new function out of them:

  1. \(one( ) \equiv f(x) g(y) + h(z)\)
  2. \(two( ) \equiv g(h(y)) + f(y)\)
  3. \(three( ) \equiv g(y) (h(x) + f(y))\)
  4. \(four(z, y) \equiv f(g(z)) h(y)\)

We have given names to the newly constructed functions: \(one()\), \(two()\), \(three()\) and \(four\). But the definitions are incomplete for the first three functions since there are no argument names given in the parentheses on the left side of \(\equiv\). On the other hand, \(four()\) is defined with argument names.

For each of \(one()\), \(two()\), and \(three()\), say what the argument names should be to have a sensible function definition.

Reading Question 8. 3 For each of the four functions in (2), list each of the methods—linear combination, function multiplication, and pipelining—that have been used when defining the function.

Reading Question 8. 4 The sound wave following tapping a tuning fork looks something like this (although the oscillation is much faster than shown):

The tuning-fork function shown is different from any of the storybook functions. Pick the storybook function that is most similar and explain how the tuning-fork function differs from it.