Signal and Systems Set 1

1. The term 'bandwidth' represents the quantitative measure of a signal.

True

False

Explanation: In addition to the relatively broad frequency domain classification of signals, it is often desirable to express quantitatively the range of frequencies over which the power or energy density spectrum is concentrated. This quantitative measure is called the ‘bandwidth’ of a signal.

Explanation

Explanation: In addition to the relatively broad frequency domain classification of signals, it is often desirable to express quantitatively the range of frequencies over which the power or energy density spectrum is concentrated. This quantitative measure is called the ‘bandwidth’ of a signal.

2. In general, a digital system designer has better control of tolerances in a digital signal processing system than an analog system designer who is designing an equivalent analog system.

True

False

Analog signal processing operations cannot be done very precisely either, since electronic components in analog systems have tolerances and they introduce noise during their operation. In general, a digital system designer has better control of tolerances in a digital signal processing system than an analog system designer who is designing an equivalent analog system.

Explanation

Analog signal processing operations cannot be done very precisely either, since electronic components in analog systems have tolerances and they introduce noise during their operation. In general, a digital system designer has better control of tolerances in a digital signal processing system than an analog system designer who is designing an equivalent analog system.

3. The system described by the equation y(n)=ay(n-1)+b x(n) is a recursive system.

True

False

Explanation: Since the present output depends on the value of the previous output, the system is called as Recursive system.

Explanation

Explanation: Since the present output depends on the value of the previous output, the system is called as Recursive system.

4. The output signal when a signal x(n)=(0,1,2,3) is processed through an 'Identical' system is:

(3,2,1,0)

(1,2,3,0)

(0,1,2,3)

None of the mentioned

An identical system is a system whose output is same as the input, that is it does not perform any operation on the input and transmits it.

Explanation

An identical system is a system whose output is same as the input, that is it does not perform any operation on the input and transmits it.

5. Which of the following condition is to be satisfied for the Fourier transform of a sequence to be equal as the Z-transform of the same sequence?

|z|=1

|z|

|z|>1

Can never be equal

Let us consider the signal to be x(n)

Explanation

Let us consider the signal to be x(n)

6. Which of the following electromagnetic signals has a frequency range of 30kHz-3MHz?

Radio broadcast

Shortwave radio signal

RADAR

Infrared signal

Explanation: Radio broadcast signal is an electromagnetic signal which has a frequency range of 30kHz-3MHz.

Explanation

Explanation: Radio broadcast signal is an electromagnetic signal which has a frequency range of 30kHz-3MHz.

7. If x(n) is a stable sequence so that X(z) converges on to a unit circle, then the complex cepstrum signal is defined as:

X(ln X(z))

Ln X(z)

X-1(ln X(z))

None of the mentioned

Let us consider a sequence x(n) having a z-transform X(z). We assume that x(n) is a stable sequence so that X(z) converges on to the unit circle. The complex cepstrum of the signal x(n) is defined as the sequence cx(n), which is the inverse z-transform of Cx(z), where Cx(z)=ln X(z)
=> cx(z)= X-1(ln X(z))

Explanation

Let us consider a sequence x(n) having a z-transform X(z). We assume that x(n) is a stable sequence so that X(z) converges on to the unit circle. The complex cepstrum of the signal x(n) is defined as the sequence cx(n), which is the inverse z-transform of Cx(z), where Cx(z)=ln X(z)
=> cx(z)= X-1(ln X(z))

8. What is the frequency range(in Hz) of Electroencephalogram(EEG)?

10-40

1000-2000

0-100

None of the mentioned

Explanation: Electroencephalogram(EEG) signal has a frequency range of 0-100 Hz.

Explanation

Explanation: Electroencephalogram(EEG) signal has a frequency range of 0-100 Hz.

9. If a signal x(n) is passed through a system to get an output signal of y(n)=x(n+1), then the signal is said to be:

Delayed

Advanced

No operation

None of the mentioned

Explanation: For example, the value of the output at the time n=0 is y(0)=x(1), that is the system is advanced by one unit.

Explanation

Explanation: For example, the value of the output at the time n=0 is y(0)=x(1), that is the system is advanced by one unit.

10. What is the impulse response of the system described by the second order difference equation y(n)-3y(n-1)-4y(n-2)=x(n)+2x(n-1)?

[-1/5 (-1)n-6/5 (4)n]u(n)

[1/5 (-1)n – 6/5 (4)n]u(n)

[ 1/5 (-1)n+ 6/5 (4)n]u(n)

[- 1/5 (-1)n+ 6/5 (4)n]u(n)

The homogenous solution of the given equation is yh(n)=C1(-1)n+C2(4)n—-(1)
To find the impulse response, x(n)=δ(n)
now, for n=0 and n=1 we get
y(0)=1 and
y(1)=3+2=5
From equation (1) we get
y(0)=C1+C2 and
y(1)=-C1+4C2
On solving the above two set of equations we get
C1=- 1/5 and C2= 6/5
=>h(n)= [-1/5 (-1)n + 6/5 (4)n]u(n).

Explanation

The homogenous solution of the given equation is yh(n)=C1(-1)n+C2(4)n—-(1)
To find the impulse response, x(n)=δ(n)
now, for n=0 and n=1 we get
y(0)=1 and
y(1)=3+2=5
From equation (1) we get
y(0)=C1+C2 and
y(1)=-C1+4C2
On solving the above two set of equations we get
C1=- 1/5 and C2= 6/5
=>h(n)= [-1/5 (-1)n + 6/5 (4)n]u(n).

Signal And Systems Set 1