Sampling Flashcards
what does f(t) and F(s) represent
the * represents the sampled signal in either time or frequency domain
in terms of number of smaples and sampling period, f*(t) is given by
f*(t) = f(nT)
- n=no. of samples
- T=Sampling period
what is the equation for sampling frequency fs
fs = 1/T = Ws/2pi
f*(t) can be written as what autosum equation
f*(t) = sum[f(n).delta(t-nT)] starting from n=0 to n=n-1
what is the laplace of the f*(t)
F*(s) = sum[f(nT) * e^-nsT] from n = 0-infinity
what is MacLaurin’s theorem
L{deltaT(nT)} = sum[e^-nsT] from 0-infinity = 1/(1- e^-sT)
if f*(t) = sum[f(t) * delta(t-nT)] (-inf - +inf), what is the equivalent fourier expression
by subbing in Ws=2pi/T and laplacing f(t),
we get F(s) = 1/T sum[F(s - jnWs)] (-inf - +inf)
where s = jw
in fourier sampling, the convolution of f(t) being sampled at T to f*(nT) gives
deltaT(nT) = sum[delta(t - nT)] (n=0 - +inf)
in fourier sampling, deltaT(nT) can be rewritten as
deltaT(nT) = 1/T sum[e^jnWst] (n=-inf - n=+inf)
what is aliasing and how is it avoid
the phenomoen that occurs when some information from the original signal f(t) is lost during the sampling operation
-avoid by chosing the correct frequenvy so that Ws >= 2*bandwidth
recite the shannon nyquist theorem
To be able to reconstruct F(jw) from F*(jw), the sampling frequency ‘fs’ must be chosen to be at least twice as high as the highest frequency pertaining to the signal F(jw)
in closed loop systems, bandwidth ir referred to what and defined in terms of what
- desired bandwidth
- defined interms of closed loop specs such rise time, settling time, overshoot etc
- sampling time, T is determined by T= (1/10 / 1/20) Tc, where Tc = predominant time constant of plant
define the phenomenon of folding back and how can be it be prevented
- if noise (high freq) is present in the original signal, sampling it will cause folding back where the signal is altered and we have interference
- avoid via analogue low pass filter before sampling
