[link] shows how this
sequence of signals portrays the signal more accuratelyas more terms are added.
We need to assess quantitatively the accuracy of theFourier series approximation so that we can judge how rapidly
the series approaches the signal. When we use a
-term series, the error—the difference between
the signal and the
-term series—corresponds to the unused terms from
the series.
To find the rms error, we must square this expression and
integrate it over a period. Again, the integral of mostcross-terms is zero, leaving
[link] shows how the error in the
Fourier series for the half-wave rectified sinusoid decreases asmore terms are incorporated. In particular, the use of four
terms, as shown in the bottom plot of
[link] , has a rms error (relative
to the rms value of the signal) of about 3%. The Fourier seriesin this case converges quickly to the signal.
We can look at
[link] to
see the power spectrum and the rms approximation error for thesquare wave.
Because the Fourier coefficients decay more slowly here than for
the half-wave rectified sinusoid, the rms error is notdecreasing quickly. Said another way, the square-wave's
spectrum contains more power at higher frequencies than does thehalf-wave-rectified sinusoid. This difference between the two
Fourier series results because the half-wave rectifiedsinusoid's Fourier coefficients are proportional to
while those of the square wave are proportional to
. If fact, after 99 terms of the square wave's
approximation, the error is bigger than 10 terms of theapproximation for the half-wave rectified sinusoid.
Mathematicians have shown that no signal has an rmsapproximation error that decays more slowly than it does for the
square wave.
Questions & Answers
Ayele, K., 2003. Introductory Economics, 3rd ed., Addis Ababa.
what's the difference between a firm and an industry
Abdul
firm is the unit which transform inputs to output where as industry contain combination of firms with similar production 😅😅
Abdulraufu
Suppose the demand function that a firm faces shifted from
Qd 120 3P
to
Qd 90 3P
and the supply function has shifted from
QS
20 2P
to
QS
10 2P .
a) Find the effect of this change on price and quantity.
b) Which of the changes in demand and supply is higher?
Demand curve shows that how supply and others conditions affect on demand of a particular thing and what percent demand increase whith increase of supply of goods
Israr
Hi Sir please how do u calculate Cross elastic demand and income elastic demand?
Abari
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