GATE ECE 2017 Paper 1 — page 11

Questions 31–33 of 65. Imported answers require review unless explicitly marked reviewed.

Let

be a continuous time periodic signal with fundamental period

seconds. Let

be the complex Fourier series coefficients of

, where

is integer valued. Consider the following statements about

I. The complex Fourier series coefficients of

are

where

is integer valued II. The complex Fourier series coefficients of

are

where

is integer valued III. The fundamental angular frequency of

rad/s

For the three statements above, which one of the following is correct?

Your answerChoose one option.

only II and III are true

only I and III are true

only III is true

only I is true

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Two discrete-time signals

and

are both non-zero only for

, and are zero otherwise. It is given that

Let

be the linear convolution of

and

. Given that

and

, the value of the expression

is __________.

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Let

be the impulse response of a discrete-time linear time invariant (LTI) filter. The impulse response is given by

Let

be the discrete-time Fourier transform (DTFT) of

, where

is the normalized angular frequency in radians. Given that

and

, the value of

(in radians) is equal to __________.

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2017 · Paper 1