Page 73 - Fundamentals of Communications Systems

Signals and Systems Review 2.25

■ sqrt — square root function
■ log10 — log base ten, this is useful for working in dB
■ max — maximum of a vector
■ sum — sum of the elements of a vector

Complex signals
■ abs — |•|
■ angle — arg(•)
■ real —
[•]
■ imag — [•]
■ conj —(•) ∗

Input and Output
■ plot — 2D plotting
■ xlabel, ylabel, axis — formatting plots
■ sound,soundsc — play vector as audio
■ load — load data
■ save — save data

Frequency Domain and Linear Systems
■ fft — computes a discrete Fourier transform (DTF)
■ fftshift — shifts an DFT output so when it is plotted it looks more like a
Fourier transform
■ conv — convolves two vectors

2.5 Homework Problems

Problem 2.1. Let two complex numbers be given as

z 1 = x 1 + jy 1 = a 1 exp( j θ 1 ) z 2 = x 2 + jy 2 = a 2 exp( j θ 2 ) (2.85)

Find

(a)
[z 1 + z 2 ]
(b) |z 1 + z 2 |
(c) [z 1 z 2 ]
(d) arg[z 1 z 2 ]
(e) |z 1 z 2 |