Now, if
${X}_{c}()$ is bandlimited to
$\left[-\left(\frac{{}_{s}}{2}\right) , \frac{{}_{s}}{2}\right]$ and we use the usual lowpass reconstruction filter in the
D/A,
:
For bandlimited signals sampled at or above the Nyquist
rate, we can relate the input and output of the DSP systemby:
${Y}_{c}()={G}_{\mathrm{eff}}(){X}_{c}()$
where
$${G}_{\mathrm{eff}}()=\begin{cases}G(T) & \text{if $\left|\right|< \frac{{}_{s}}{2}$}\\ 0 & \text{otherwise}\end{cases}$$
Note
${G}_{\mathrm{eff}}()$ is LTI if and only if the following two
conditions are satisfied:
$G()$ is LTI (in DT).
${X}_{c}(T)$ is bandlimited and sampling rate equal to or
greater than Nyquist. For example, if we had a simplepulse described by
$${X}_{c}(t)=u(t-{T}_{0})-u(t-{T}_{1})$$ where
${T}_{1}> {T}_{0}$ . If the sampling period
$T> {T}_{1}-{T}_{0}$ ,
then some samples might "miss" the pulse while othersmight not be "missed." This is what we term
time-varying behavior .
If
$\frac{2\pi}{T}> 2B$ and
${}_{1}< BT$ , determine and sketch
${Y}_{c}()$ using
.
Unfortunately, in real-world situations electrodes also pick
up ambient 60 Hz signals from lights, computers,
etc. . In fact, usually this "60 Hz noise"
is much greater in amplitude than the EKG signal shown in
.
shows the EKG signal; it is barely noticeable
as it has become overwhelmed by noise.
Dsp solution
Sampling period/rate
First we must note that
$\left|Y()\right|$ is
bandlimited to60 Hz.
Therefore, the minimum rate should be 120 Hz. In order toget the best results we should set
$${f}_{s}=\mathrm{240}\mathrm{Hz}$$ .
$${}_{s}=2\pi 240\frac{\mathrm{rad}}{s}$$
Digital filter
Therefore, we want to design a digital filter that will
remove the 60Hz component and preserve the rest.
Questions & Answers
Is there any normative that regulates the use of silver nanoparticles?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?