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# MCQs on Fourier Theory

A sine wave whose frequency is some integer multiple of a fundamental sine wave is called?

a) Complex wave

b) Square wave

c) Harmonic

d) Digital pulses

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c

Explanation: A harmonic is a sine wave whose frequency is some integer multiple of a fundamental sine wave. The third harmonic of a 2-kHz sine wave is a sine wave of 6 kHz.

What is the duty cycle of a square wave with equal duration positive and negative alterations?

a) 100%

b) 50%

c) 200%

d) 25%

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b

Explanation: Duty cycle is the ratio of the duration of the positive alteration t1 to the period T expressed as percentage. D= t1⁄T*100 = t1⁄2t1 * 100 = 50%.

What is the frequency of 7th harmonic of a 2KHz sine wave?

a) 14Khz

b) 9KHz

c) 5KHz

d) 2KHz

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a

Explanation: The frequency of 7th harmonic sine wave = 7 x 2KHz = 14KHz

An infinite number of odd harmonics are present in a sine wave.

a) True

b) False

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a

Explanation: A square wave is made up of a sine wave at the fundamental frequency of the square wave plus an infinite number of odd harmonics. For example, if the fundamental frequency of the square wave is 1 kHz, the square wave can be synthesized by adding the 1-kHz sine wave and harmonic sine waves of 3 kHz, 5 kHz, 7 kHz, 9 kHz, etc.

What is the peak value of 5th harmonic if the square wave has a peak voltage of 3v and a frequency of 48Khz?

a) 0.74

b) 0.52

c) 0.76

d) 1.5

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c

Explanation:

Which instrument produces frequency domain information?

a) Oscilloscope

b) Spectrum analyzer

c) Frequency divider

d) Beam analyzer

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b

Explanation: The test instrument for producing a frequency-domain display is the spectrum analyzer. Like the oscilloscope, the spectrum analyzer uses a cathode-ray tube for display, but the horizontal sweep axis is calibrated in hertz and the vertical axis is calibrated in volts or power units or decibels.

What is the band width required to pass a signal with t0=75×10-9 without excessive distortions?

a) 14MHz

b) 53.7MHz

c) 13.33MHz

d) 11.56MHz

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c

Explanation:

A pulse train has a rise time of 6 ns. What is the minimum bandwidth to pass this pulse train faithfully?

a) 58.3MHz

b) 42.6MHz

c) 812MHz

d) 41.5MHz

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a

Explanation:

A circuit has a bandwidth of 200 kHz. What is the fastest rise time this circuit will pass?

a) 1.5μs

b) 2.3μs

c) 1.2μs

d) 1.75μs

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d

Explanation:

Fourier analysis helps us to determine how much bandwidth a particular signal occupies.

a) True

b) False

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a

Explanation: Fourier analysis allows us to determine not only the sine wave components in any complex signal but also how much bandwidth a particular signal occupies. Although a sine or cosine wave at a single frequency theoretically occupies no bandwidth, complex signals obviously take up more spectrum space.