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This document contains 5 exercises involving determining the frequency response and Fourier components of various periodic signals using Fourier series analysis and MATLAB programs. The exercises involve proving properties of square waves and filtering signals, including determining the power in different harmonics and the amplitudes after filtering.

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59 views2 pages

Sheet

This document contains 5 exercises involving determining the frequency response and Fourier components of various periodic signals using Fourier series analysis and MATLAB programs. The exercises involve proving properties of square waves and filtering signals, including determining the power in different harmonics and the amplitudes after filtering.

Uploaded by

b5fc94cdd3
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Exercise-2

1. Determine using Fourier series - the frequency response of the


periodic signal shown. Prove that the coefficients are sinc function.
Write the MATLAB program to find the Fourier components.

Fig. (P 2.1 )
2. Determine using Fourier series - the frequency response of the
periodic signals shown. Draw the frequency response of each.
Write the MATLAB program to find the Fourier transform of each.

Fig. (P 2.2 a)

Fig. (P 2.2 b)

Fig. (P 2.2 c)

Fig. (P 2.2 d)
3. For the square wave shown in Fig. (P 2.3 ) has a duty cycle D = /T.

Prove that the k th. harmonic is zero if k = 1/D = T/ . Assume k is


an integer. Assume k = 3 and write MATLAB program to prove.

Fig. (P 2.3 )
4. For the waveform shown in Fig. (P 2.4 ) show that
(a) 91 % of the total power is included in the fundamental.
(b) The third harmonic doesn't exist.
(c) If this signal is passed through a filter whose characteristics is

1
H(j ) =
f 4
1 ( )
fC
Determine the amplitude of the fundamental and 5 th. harmonic
at the output of the filter.

Fig. (P 2.4 )
5. For a symmetrical square wave (50 % duty cycle) swinging
between zero and A volts, prove that
(a) Half the power is included in the DC component.
(b) 40 % of the power is included in the fundamental.
(c) Write the MATLAB program to find (a) and (b).

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