MCQs based on the topics related to Signal Systems and Digital Signal Processing

 

8.Signal System and Digital Signal Processing

 8.1 Signal and system:

Here are some multiple-choice questions (MCQs) based on the topics related to Signal Systems and Digital Signal Processing. These questions are designed to test fundamental concepts that are crucial for an Engineering license exam.

 

### MCQ 1: Signal Definition

Which of the following is true for a continuous-time signal?

- A) It is defined only at discrete time intervals.

- B) It can take values only at integer times.

- C) It is defined for every possible time instance.

- D) It can only have non-negative values.

 

**Answer:** C) It is defined for every possible time instance.

 

### MCQ 2: Impulse Response

The impulse response of an LTI system is:

- A) The output when the input is a unit step function.

- B) The output when the input is a delta function.

- C) The Fourier transform of the input signal.

- D) The convolution of the input with the system's transfer function.

 

**Answer:** B) The output when the input is a delta function.

 

### MCQ 3: Convolution

Which of the following is the correct formula for convolution of two continuous-time signals $x(t)$ and $h(t)$?

A) $y(t) = \int_{-\infty}^{\infty} x(\tau) h(\tau - t) d\tau$

 

### MCQ 4: Fourier Series

The Fourier series of a signal decomposes the signal into:

- A) A sum of sine and cosine functions with discrete frequencies.

- B) A sum of exponential functions with continuous frequencies.

- C) A single sine wave of varying amplitude.

- D) A sum of step functions.

 

**Answer:** A) A sum of sine and cosine functions with discrete frequencies.

 

### MCQ 5: Fourier Transform

Which of the following signals has a Fourier Transform that is purely imaginary?

- A) A unit step function.

- B) A signum function.

- C) A sinc function.

- D) A delta function.

 

**Answer:** B) A signum function.

 

### MCQ 6: Sinc Function

The sinc function is defined as:

A) $\text{sinc}(t) = \frac{\sin(\pi t)}{t}$

D) $\text{sinc}(t)=\frac{\sin (\pi t)}{t+\pi \mathrm{<br>}\mathrm{<br>}\mathrm{<br>}}$

​Answer: C) 

 

### MCQ 7: Hilbert Transform

The Hilbert transform of a signal results in:

- A) A phase shift of 90 degrees for all frequency components.

- B) A phase shift of 180 degrees for all frequency components.

- C) No change in phase but an amplitude change.

- D) Both phase and amplitude changes.

 

**Answer:** A) A phase shift of 90 degrees for all frequency components.

 

### MCQ 8: LTI System

For an LTI system, the output $y(t)$ in response to an input $x(t)$ is given by:

A) The product of $x(t)$ and $h(t)$.

B) The convolution of $x(t)$ and $h(t)$.

C) The addition of $x(t)$ and $h(t)$.

D) The division of $x(t)$ by $h(t)$.

Answer: B) The convolution of $x(t)$ and $h(t)$.

 

### MCQ 9: Energy Spectral Density (ESD)

Energy Spectral Density (ESD) is used to measure:

- A) The distribution of signal power across different frequencies.

- B) The total energy of the signal in the time domain.

- C) The distribution of signal energy across different frequencies.

- D) The peak value of a signal in the frequency domain.

 

**Answer:** C) The distribution of signal energy across different frequencies.

 

### MCQ 10: Power Spectral Density (PSD)

Power Spectral Density (PSD) is typically used for which type of signals?

- A) Finite energy signals.

- B) Periodic signals.

- C) Aperiodic signals.

- D) Transient signals.

 

**Answer:** B) Periodic signals.

 

These questions cover various aspects of the topics you are studying and should be useful for practice as you prepare for your licensing exam. If you need more questions or different types of questions, feel free to ask!