GATE EC Continuous-time Signals questions

Practise Continuous-time Signals questions for GATE EC. Explore official PYQs and original topic-wise quizzes, check answers and view available solutions. Free, no sign-in.

Identify whether the signal and system are continuous-time or discrete-time. Check linearity, time invariance and stability before selecting a transform or response method.

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SubjectTopicYearType

The baseband signal

m(t)

shown in the figure is phase-modulated to generate the

PM

\varphi(t)=\cos(2\pi f_{c}t+ k\:\: m(t)).

t

x-

axis in the figure is in milliseconds. If the carrier frequency is

f_{c}=50\:kHz

k=10 \pi,

then the ratio of the minimum instantaneous frequency (in kHz) to the maximum …

In the circuit shown, the clock frequency, i.e., the frequency of the ClK signal, is

12\:kHz

. The frequency of the signal at

Q_{2}

is _______ kHz.

\text{x(t)}

be a periodic function with period

\text{T = 10}

.The Fourier series coefficients for this series are denoted by

a_{k},

x\left ( t \right )=\sum ^{\infty }_{k=-\infty }a_{k}e^{jk\:\frac{2\pi }{T}t}

The same function

x(t)

can also be considered as a periodic function with period

{T}'=40.

b_{k}

4\sin c(2t)

is fed to a Hilbert transformer to obtain

y( t),

as shown in the figure below: Here

\sin c \left ( x\right )=\dfrac{\sin\left ( \pi x \right )}{\pi x}.

The value (accurate to two decimal places) of

\int ^{\infty }_{-\infty } \mid y( t ) \mid ^{2}dt

A band limited low-pass signal

x(t)

5\:kHz

is sampled at a sampling rate

f_{s}

x(t)

is reconstructed using the reconstruction filter

H(f)

whose magnitude response is shown below: The minimum sampling rate

f_{s}(\text{in}\: kHz)

for perfect reconstruction of

x(t)

A periodic signal

x(t)

has a trigonometric Fourier series expansion

x( t )= a_{0}+\sum_{n=1}^{ \infty } ( a_{n} \cos n\omega _{0}t+b_{n}\sin n\omega _{0}t )

x(t)= -x(-t)=-x(t-\frac{\pi }{\omega _{0}})

, we can conclude that

x(t)

be a continuous time periodic signal with fundamental period

T=1

{a_{k} }

be the complex Fourier series coefficients of

x(t)

k

is integer valued. Consider the following statements about

x(3t)

: The complex Fourier series coefficients of

x(3t)

{a_{k}}

k

is integer valued The complex …

x(t)=\sin (14000\pi t)

t

is in seconds, is sampled at a rate of

9000

samples per second. The sampled signal is the input to an ideal lowpass filter with frequency response

H(f)

H(f)=\begin{cases} 1, & \mid f \mid \leq 12 kHz .\\ 0,& \mid f \mid> 12 kHz. \end{cases}

What is the number of sinusoids …

A continuous-time function

x(t)

is periodic with period

T

. The function is sampled uniformly with a sampling period

T_s

. In which one of the following cases is the sampled signal periodic?

A continuous-time sinusoid of frequency

33 Hz

is multiplied with a periodic Dirac impulse train of frequency

46Hz

. The resulting signal is passed through an ideal analog low-pass filter with a cutoff frequency of

23Hz

. The fundamental frequency (in

Hz

) of the output is _______

The amplitude of a sinusoidal carrier is modulated by a single sinusoid to obtain the amplitude modulated signal

s(t) = 5 \cos1600 \pi t + 20 \cos 1800 \pi t + 5 \cos 2000 \pi t

. The value of the modulation index is _________

The energy of the signal

x(t)= \frac{\sin(4\pi t)}{4\pi t}

2 \cos(\frac{2\pi}{3}t)-\cos(\pi t)

is the input to an LTI system with the transfer function

H(s)=e^s+e^{-s}.

C_k

k^{th}

coefficient in the exponential Fourier series of the output signal, then

C_3

The waveform of a periodic signal

x(t)

is shown in the figure. A signal

g(t)

g(t) = x \big( \frac{t-1}{2} \big)

. The average power of

g(t)

A sinusoidal signal of

2

kHz frequency is applied to a delta modulator. The sampling rate and step-size

\Delta

of the data modulator are

20,000

samples per second and

0.1

V, respectively. To prevent slope overload, the maximum amplitude of the sinusoidal signal (in Volts) is

Consider the signal

s(t)=m(t) \cos(2 \pi \: f_ct)+ \hat{m}(t) \sin(2 \pi f_c t)

\hat{m}(t)

denotes the Hilbert transform of

m(t)

and the bandwidth of

m(t)

is very small compared to

f_c

s(t)

The magnitude and phase of the complex Fourier series coefficients ܽ

a_{k}

of a periodic signal

x(t)

are shown in the figure. Choose the correct statement from the four choices given. Notation:

C

is the set of complex numbers, ܴ

R

is the set of purely real numbers, and

P

ܲis the set of purely imaginary numbers.

A sinusoidal signal of amplitude

A

is quantized by a uniform quantizer. Assume that the signal utilizes all the representation levels of the quantizer. If the signal to quantization noise ratio is

31.8\: dB,

the number of levels in the quantizer is __________.

\cos \left(10\pi t + \dfrac{\pi}{4}\right)

is ideally sampled at a sampling frequency of

15 Hz.

The sampled signal is passed through a filter with impulse response

\left(\dfrac{\sin (\pi t)}{\pi t}\right)\cos\left(40\pi t – \dfrac{\pi}{2}\right)

The filter output is

A message signal

m(t) = A_{m} \sin(2πf_{m}t)

is used to modulate the phase of a carrier

A_{c} \cos(2πf_{c}t)

to get the modulated signal

y(t) = A_{c} \cos(2πf_{c}t + m(t)).

The bandwidth of

y(t)