GATE EC ||SIGNALS AND SYSTEMS ||FOURIER SERIES & FOURIER TRANSFORM || PYQs

One period (0, T) each of two periodic waveforms W₁ and W₂ are shown in the figure. The magnitudes of the n^th Fourier series coefficients of W₁ and W₂, for n ≥ 1, n is odd, are respectively proportional to

(GATE 2000 || EC || PYQ || MCQ || 2 MARKS)

A periodic g(t) is shown in figure. Determine the PSD of g(t).

(GATE 2001 || EC || PYQ || NAT || 5 MARKS)

Which of the following cannot be the Fourier series expansion of a periodic signal?

(GATE 2001 || EC || PYQ || MCQ || 1 MARKS)

The Fourier series expansion of a real periodic signal with fundamental frequency f₀ is given by:

[Tex]g_p(t) = \sum_{n=-\infty}^{\infty} C_n e^{j2\pi n f_0 t}[/Tex]

It is given that C₃ = 3 + j5. Then C_–3 is

(GATE 2003 || EC || PYQ || MCQ || 1 MARKS)

Choose the function f(t), –∞< t <∞, for which a Fourier series cannot be defined?

(GATE 2005 || EC || PYQ || MCQ || 1 MARKS)

A function is given by f(t) = sin²t + cos 2t. Which of the following is true?

(GATE 2009 || EC || PYQ || MCQ || 1 MARKS)

The Fourier series of a real periodic function has only

• P. Cosine terms if it is even
• Q. Sine terms if it is even
• R. Cosine terms if it is odd
• S. Sine terms if it is odd

Which of the above statements are correct?

(GATE 2009 || EC || PYQ || MCQ || 1 MARKS)

The trigonometric Fourier series for the waveform f(t) shown below contains

(GATE 2010 || EC || PYQ || MCQ || 1 MARKS)

The trigonometric Fourier series of an even function does not have the:

(GATE 2011 || EC || PYQ || MCQ || 1 MARKS)

Consider the periodic square wave in the figure shown.

The ratio of the power in the 7^th harmonic to the power in the 5^th harmonic for this waveform is closest in value to _____.

(GATE 2014 || EC || PYQ || NAT || 1 MARKS)