In filter design you will be asked to use hyper-bolic functions. In this problem we relate these functions to sinusoids and obtain a definition of these functions so that we can actually plot them.

(a) Consider computing the cosine of an imaginary number, i.e., use

let x = jθ and find cos(x). The resulting function is called the hyper-bolic cosine or

cos(jθ) = cosh(θ)

(b) Consider then the computation of the hyperbolic sine sinh(θ), how would you do it? Carefully plot it as a function of θ.

(c) Show that the hyperbolic cosine is always positive and bigger than 1 for all values of θ

(d) Show that sinh(θ) = −sinh(−θ)

(e) Write a MATLAB script to compute and plot these functions between −10 and 10.

Transcribed Image Text:

ei* +ei* -jx cos(x) 2