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QUESTION: 1

If x(n) is a discrete-time signal, then the value of x(n) at non integer value of ‘n’ is:

Solution:

Explanation: For a discrete time signal, the value of x(n) exists only at integral values of n. So, for a non- integer value of ‘n’ the value of x(n) does not exist.

QUESTION: 2

The discrete time function defined as u(n)=n for n≥0;=0 for n<0 is an:

Solution:

Explanation: When we plot the graph for the given function, we get a straight line passing through origin with a unit positive slope. So, the function is called as unit ramp signal.

QUESTION: 3

The phase function of a discrete time signal x(n)=a^{n}, where a=r.e^{jθ} is:

Solution:

Explanation: Given x(n)=a^{n}=(r.e^{jθ})^{n} =r^{n}.e^{jnθ}

=>x(n)=r^{n}.(cosnθ+jsinnθ)

Phase function is tan^{-1}(cosnθ/sinnθ)=tan^{-1}(tan nθ)=nθ.

QUESTION: 4

The signal given by the equation is known as:

Solution:

Explanation: We have used the magnitude-squared values of x(n), so that our definition applies to complex-valued as well as real-valued signals. If the energy of the signal is finite i.e., 0<E<∞ then the given signal is known as Energy signal.

QUESTION: 5

x(n)*δ(n-k)=?

Solution:

Explanation: The given signal is defined only when n=k by the definition of delta function. So, x(n)*δ(n-k)= x(k)*δ(n-k).

QUESTION: 6

A real valued signal x(n) is called as anti-symmetric if:

Solution:

Explanation: According to the definition of anti-symmetric signal, the signal x(n) should be symmetric over origin. So, for the signal x(n) to be symmetric, it should satisfy the condition x(n)=-x(-n).

QUESTION: 7

The odd part of a signal x(t) is:

Solution:

Explanation: Let x(t)=xe(t)+xo(t)

=>x(-t)=xe(-t)-xo(-t)

By subtracting the above two equations, we get

xo(t)=(1/2)*(x(t)-x(-t)).

QUESTION: 8

Time scaling operation is also known as:

Solution:

Explanation: If the signal x(n) was originally obtained by sampling a signal xa(t), then x(n)=xa(nT). Now, y(n)=x(2n)(say)=xa(2nT). Hence the time scaling operation is equivalent to changing the sampling rate from 1/T to 1/2T, that is to decrease the rate by a factor of 2. So, time scaling is also called as down-sampling.

QUESTION: 9

What is the condition for a signal x(n)=Brn where r=eαT to be called as an decaying exponential signal?

Solution:

Explanation: When the value of ‘r’ lies between 0 and 1 then the value of x(n) goes on decreasing exponentially with increase in value of ‘n’. So, the signal is called as decaying exponential signal.

QUESTION: 10

The function given by the equation x(n)=1, for n=0;=0, for n≠0 is a:

Solution:

Explanation: According to the definition of the impulse function, it is defined only at n=0 and is not defined elsewhere which is as per the signal given.

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