Introduction to signals - Continuous and Discrete Time Signals and Systems - page 60

(i) x ( t ) = exp( − 2 t ) sin(10 π t ) for t ≤ 1 .
(ii) A periodic signal x ( t ) with fundamental period T

= 5. The value

over one period is given by

x ( t ) = 5 t 0 ≤ t < 5 .

Use the sawtooth function available in M ATLAB to plot five
periods of x ( t ) over the range − 10 ≤ t < 15 .
(iii) The unit step function u ( t ) over [ − 10, 10] using the sign function
available in M ATLAB .
(iv) The rectangular pulse function rect( t )

t
10

1 − 5 < t < 5

rect =

0 elsewhere

using the unit step function implemented in (iii).
(v) A periodic signal x ( t ) with fundamental period T

= 6. The value

over one period is given by

3 t ≤ 1
01 < t ≤ 3 .

x ( t ) =

Use the square function available in M ATLAB .

1.32 (M ATLAB exercise) Write a M ATLAB function mydecimate with the
following format:

function [y] = mydecimate(x, M)
% MYDECIMATE: computes y[k] = x[kM]
% where
% x is a column vector containing the DT input
% signal
% M is the scaling factor greater than 1
% y is a column vector containing the DT output time
% decimated by M

In other words, mydecimate accepts an input signal x [ k ] and produces
the signal y [ k ] = x [ kM ].

1.33 (M ATLAB exercise) Repeat Problem 1.30 for the transformation y [ k ] =
x [ k / N ]. In other words, write a M ATLAB function myinterpolate
with the following format:

function [y] = myinterpolate(x, N)
% MYINTERPOLATE: computes y[k] = x[k/N]
% where
% x is a column vector containing the DT input
% signal
% N is the scaling factor greater than 1