This document is a compilation of my notes for ELE 792: Digital Signal Processing at TMU. All information comes from my professor’s lectures, as well as the course textbook Discrete-Time Signal Processing, 3rd Edition by A.V. Oppenheim and R.W. Schafer.
Adam Szava - 2tor.ca
F2023
This lecture was all basic review of ELE 532/632. See my notes for the courses.
Only thing to note is the following different definition of the unit step function:
$$ u[n]=\sum_{m=-\infty}^n\delta[m] $$
When sampling a continuous time sinusoid in the form:
$$ x(t)=A\cos(2\pi Ft+ \theta) $$
If $t$ is discretized as $t = nT$, T being the sampling time, related to the sampling rate by $f_s = 1/T$, then the discrete time sampled signal can be written as:
$$ x[n]=x(nT)=A\cos(2\pi \frac{F}{f_s}n + \theta) $$
We can define $f = F/f_s$ to be the relative or normalized frequency. Because of the repetition of frequencies in discrete time, we have that $-1/2 < f < 1/2$.
For proper reconstruction of the continuous signal, we have that:
$$ |F|<f_S/2 $$
Analog to digital conversion is illustrated by the following:
The role of the sampler is as follows: