Problems


OWN 1.26b Is the discrete-time signal $x[n] = \cos \left(\frac{n}{8}\right)$ periodic? If it is, what is the time period?

OWN 1.26c Is the discrete-time signal $x[n] = \cos \left(\frac{\pi n^2}{8}\right)$ periodic? If it is, what is the time period?


OWN 1.27a Is the system $y(t) = x(t-2)+x(2-t)$ memoryless, linear, stable, time-invariant and causal?
OWN 1.27c Is the system $y(t) = \int_{-\infty}^{2t} x(\tau) \ d \tau$ memoryless, linear, stable, time-invariant and causal?
OWN 1.27d Is the system $y(t) = \begin{cases} 0, \ \ t < 0 \\ x(t)+x(t-2), t \geq 0 \end{cases}$ memoryless, linear, stable, time-invariant and causal?
OWN 1.27g Is the system $y(t) = \frac{d}{dt}x(t)$ memoryless, linear, stable, time-invariant and causal?
Consider the system defined by $y(t) = x(t) \ u(t)$. Is this linear, time invariant, stable, invertible?

OWN 2.4 Compute the convolution of

(1)
\begin{align} x[n] = \left\{ \begin{array}{ll} 1, & 3 \leq n \leq 8 \\ 0, & \hbox{otherwise.} \end{array} \right. \ \hbox{and} \ h[n] = \left\{ \begin{array}{ll} 1, & 4 \leq n \leq 15 \\ 0, & \hbox{otherwise.} \end{array} \right. \end{align}

OWN 2.6 Compute the convolution of $x[n] = \left(\frac{1}{3} \right)^{-n} \ u[-n-1]$ and $h[n] = u[-n-1]$


Bandpassfromoldexam
DTFS
Phasefunction
Two systems
Problem5fromoldexam - There is a small mistake in the solutions to the last part. The correct answer is 450Hz,500Hz,550 Hz


Review done on Sunday, December 10, 2017 before the final exam

Fall 2017 Midterm2 Question1 - Fourier Series
Fall 2017 Midterm2 Question4
Fall 2017 Midterm2 Question5
Oppenheim Wilsky and Nawab 4.21f

Compute Discrete-time Fourier transform of $x[n] = \sin \left( \frac{\pi n/5}{\pi n}\right) \ \cos \left(\frac{5 \pi n}{2} \right)$

Problem on sampling from old exam- Part 1
Part2

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