Q3(a) Suggest any two limitations of Fourier Series.(b)A full-wave rectified sinusoidal signal has a peak amplitude A of 6 V anda time period of 2 ms. Using Fourier Series,(i) calculate the frequencies and the amplitudes (magnitudes) for thefirst four even harmonics and dc;(ii) sketch the magnitude spectrum of this signal for the first four evenharmonics and dc.2Af (t) =4A (cos2wtcos4wt+3 x 5cos6wt+cos8wt+7 x 91х35 x 7π(c)Obtain the Compact trigonometric Fourier series of 6sin8t + 3cos8t.(d)Obtain the Fourier transform of a rectangular function. Also sketch itsmagnitude spectrum.

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Suggest any two limitations of Fourier Series.

Introductory Circuit Analysis (13th Edition)

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ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

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Concept explainers

Fourier Transform

In mathematics, the Fourier transformation is a mathematical transformation that rotates responsibilities by using region or time into tasks depending on the local or temporal frequency, such as the rendering of a musical track in step with existing volumes and frequencies. The term Fourier amendment refers to each illustration of the frequency range and the mathematical functionality related to the representation of the frequency domain and the function of space or time.

Question

Q3(a) Suggest any two limitations of Fourier Series.
(b)
A full-wave rectified sinusoidal signal has a peak amplitude A of 6 V and
a time period of 2 ms. Using Fourier Series,
(i) calculate the frequencies and the amplitudes (magnitudes) for the
first four even harmonics and dc;
(ii) sketch the magnitude spectrum of this signal for the first four even
harmonics and dc.
2A
f (t) =
4A (cos2wt
cos4wt
+
3 x 5
cos6wt
+
cos8wt
+
7 x 9
1х3
5 x 7
π
(c)
Obtain the Compact trigonometric Fourier series of 6sin8t + 3cos8t.
(d)
Obtain the Fourier transform of a rectangular function. Also sketch its
magnitude spectrum.

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