Sinusoidal Signals Exercises

Frequency is $\_\_\_\_\_\_\_\_\_\_\_$  proportional to fundamental period.

Continuous-time sinusoids with distinct frequencies are

$\_\_\_\_\_\_\_\_\_\_\_$.

Discrete-time sinusoids with distinct frequencies are $\_\_\_\_\_\_\_\_\_\_\_$.

Discrete-time frequency is measured in units of $\_\_\_\_\_\_\_\_\_\_\_$.

A complex sinusoid $x[n] = Ae^{j\pi n/8}$ has real part given by a $\_\_\_\_\_\_\_\_\_\_\_$.

Find the fundamental frequency of the signal depicted below.

Select the two following discrete-time sinusoids that are identical.

A continuous-time sinusoid $x(t) = 4\cos(\Omega_o t + \pi/8)$ is sampled to produce a discrete-time sinusoid $x[n] = x(nT)$.  Find the frequency $\omega_o$ in rads of the discrete-time sinusoid for $\Omega_o = 4\pi$ rads/sec,  $T = 0.1$ secs.

The fundamental frequency of a trumpet note $x(t)$ is $f_c$ Hz.

Find the fundamental frequency in units of rads/sec if $f_c =880$ Hz.

The fundamental frequency of a trumpet note $x(t)$ is $f_c$ Hz.

You sample $x(t)$ at an interval $T = 10^{-4}$ sec to obtain $x[n]$. What is the fundamental frequency of $x[n]$ if $f_c = 880$ Hz.

Find the fundamental period of $x(t) = \cos(\pi t)$.

Find the fundamental period of $y(t) = \sin(2\pi t/3)$.

Find the fundamental period of $z(t) = \cos(\pi t) + \sin(2\pi t/3)$.

Hint: if a signal $x(t)$ has fundamental period $T_x$, then it also is periodic with period $mT_x$ where $m = 1, 2, 3, \ldots$.

The sound file SaxA.wav contains a brief recording of an alto saxophone playing the musical note A.  Listen to the sound.  A 22.65 ms section of this note is depicted below.

SaxA.wav

Use the graph to find the fundamental frequency of this note in Hz.  Hint:  measure the time for multiple periods and divide by the number of periods.

Problem statements in pdf file here.  Note there are some differences from the quiz questions to map them onto the quiz tool.

MATLAB code SaxAapprox.m and MATLAB file SaxA_note.mat for extra question in pdf file.