Signals and Systems
Fourier Series
Practice questions from Fourier Series.
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IncorrectA time-limited waveform is specified as follows:
A new waveform is constructed from as follows:
The sum of the coefficients of the third harmonics of the sine and cosine terms in the trigonometric Fourier series expansion of is .
What is the value of ?
1
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Sign in to UnlockThe discrete time Fourier series representation of a signal x[n] with period N is written as . A discrete time periodic signal with period N = 3, has the non-zero Fourier series coefficients: and . The signal is
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Sign in to UnlockWhich of the following is true for all possible non-zero choices of integers m, n; m ≠ n, or all possible non-zero choices of real numbers p, q; p ≠ q as applicable?
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Sign in to UnlockA periodic function f(t), with a period of , is represented as its Fourier series,
.
If
,
The Fourier series coefficients and of f(t) are
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Sign in to UnlockConsider
.
Here, represents the largest integer less than or equal to t and denotes the smallest integer greater than or equal to t. The coefficient of the second harmonic component of the Fourier series representing is ___________
No harmonics can be determined
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Sign in to UnlockLet f(x) be a real, periodic function satisfying . The general form of its Fourier series representation would be
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Sign in to UnlockThe signum function is given by
The Fourier series expansion of sgn has
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Sign in to UnlockFor a periodic square wave, which one of the following statements is TRUE?
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Sign in to UnlockA 10 kHz even-symmetric square wave is passed through a band-pass filter with center frequency at 30 kHz and 3dB pass-band of 6 kHz. The filter output is
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Sign in to UnlockFor a periodic signal
, the fundamental frequency in rad/s is
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Sign in to UnlockThe Fourier series expansion of the periodic signal shown below will contain the following nonzero terms
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Sign in to UnlockThe second harmonic component of the periodic waveform given in the figure has amplitude of
0
1
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Sign in to UnlockThe Fourier Series coefficients, of a periodic signal x(t), expressed as are given by ; ; ; ; ; and for . Which of the following is true?
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Sign in to UnlockLet x(t) be a periodic signal with time period T, Let for some . The Fourier Series coefficients of y(t) are denoted by . If for all odd k, then can be equal to
2T
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Sign in to UnlockA signal x(t) is given by
Which among the following gives the fundamental Fourier term of x(t)?
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Sign in to Unlockx(t) is a real valued function of a real variable with period T. Its trigonometric Fourier Series expansion contains no terms of frequency ω = 2π (2k)/T; k = 1, 2,…… Also, no sine terms are present. Then x(t) satisfies the equation
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Sign in to UnlockThe Fourier series for the function is:
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Sign in to UnlockFourier Series for the waveform, f(t) shown in Figure is
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Sign in to UnlockConsider the voltage waveform v, shown in figure.
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Sign in to UnlockIf an ac voltage wave is corrupted with an arbitrary number of harmonics, then the overall voltage waveform differs from its fundamental frequency component in terms of
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Sign in to UnlockCompute the amplitude of the fundamental component of the waveform given in figure
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Sign in to UnlockA periodic rectangular signal, x(t) has the wave form shown in figure. Frequency of the fifth harmonic of its spectrum is
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