Signals and Systems : Important interview question Part-2

1. Why we use only sinusoid wave and no other signals for signal analysis?

Ans. we use only sinusoid wave because:

(i) The response of a sine wave to an LTI (linear time-invariant) system is also sinusoidal.

(ii) The sinusoidal analysis of electric network is simple and convenient.

1. Why do we Fourier Transform in the signal analysis?

Ans. By Fourier we can represent the signal from the time domain to frequency domain, thus we can find the various frequency component in the present signal helping us to find total Bandwidth required for the transmission of the given signal.

1. Explain the difference between the Laplace transform and Fourier transform.

Ans. Laplace transform and z-transform can be applied to the analysis of many unstable systems and consequently play an important role in the investigation of the stability or the instability of systems, whereas we cannot apply Fourier Transform.

1. Is there any difference between digital and discrete signals?

Ans. A digital signal is sampled in both the amplitude and time axis while a discrete signal is sampled in time axis only.

1. What are even signals and odd signals? Give their expressions.

Ans. Odd signals are symmetric in the first and third quadrant.

Given as              f(-t) = -f(t)

Even signals are symmetric in first and second quadrant.

Given as              f(-t) = f(t)

1. What will be the value of odd signals at the origin?

Ans. An odd signal must pass through origin since they are symmetric about first and third quadrant, Hence the value should be zero.

1. Define a memoryless system.

Ans. A system is memoryless if the output at any time instant depends only on the input at that particular instant, it is also called as static system.

1. What do you mean by causality? Give an example?

Ans. A system is causal if its output is a function of the current or previous sample values of input and output doesn’t depend on future values.

1. What condition must be satisfied by a function f(t) for its Fourier Transform representation?

Ans. Dirichlet condition needs to be satisfied:

• F(t) must be absolutely integrable
• It must have a finite number of maxima and minima in any given bounded interval.
• It must have a finite number of discontinuity in the bounded interval.

1. Give properties of Fourier transform used in Analog modulation?

Ans. Modulation property: A function is modulated by another function if they are multiplied in time.

Since multiplication in time domain leads to convolution in frequency domain.

              F{f(t) g(t)} = F(f) *G(f)

In DSB-SC, the signal is multiplied with ‘cos(ω ₀t)’

F(t) cos(ω₀ t) ↔ [F (ω -ω ₀) + F(ω + ω₀)]

1. What is the bandwidth required for unit impulse function?

Ans. F{δ(t)} = 1 ; -∞ < f < ∞

Hence infinite bandwidth is required for transmission of unit impulse function.

1. Define Parseval’s Theorem.

Ans.  Parseval’s relation states that the total energy may be determined by computing the energy per unit time [|x(t)|²] and integrating over all time or by calculating energy per unit frequency. [|X(jω|²] and integrating over all frequencies.

The above equation holds true as each signal has unique Fourier representation.

1. What is the advantage of active filters?

Ans. Advantages of active filters are Gain and frequency adjustment flexibility, No loading problem, Non-floating and output, Less cost.

1. Is there any difference between analog signals and continuous time signals?

Ans. Analog signals are those which can take the infinite number of potential values. (No break in amplitude level) whereas Continuous signals are those which have a finite value at any point in time (no break on time axis). Analog signals may be continuous and discontinuous.

1. What do you understand by region of convergence for Laplace transform and z-transform?

Ans. The range variation of the real part of 's' for which the Laplace transform converges is called the region of convergence. The range variation of ‘|z|’ for which the z-transform converges is called ROC for z-transform.

Region of Convergence (ROC) Whether the Laplace transform of a signal exists or not depends on the complex variable as well as the signal itself. All complex values of for which the integral in the definition converges form a region of convergence (ROC) in the s-plane.

1. What is the Laplace transform? Why it is used? How is it different from the fourier transform?

Ans. For a continuous time signal x(t). the Laplace transform is defined as

Where ‘s’ is a complex frequency which is given as

              S = σ  + jω

Where, σ  = Re {s} is damping factor

              ω = Im {s} is oscillation frequency in ‘rad/s’

The Fourier transform is not applicable for a signal that is not absolutely integrable. This problem could be resolved by generalizing Fourier transform which leads to the development of Laplace transform. The Laplace transform can be applied to a broader class of signals compared to Fourier transform and analysis of many unstable systems.

1. What is the reliability of the system?

Ans. Reliability of a system is defined as the probability that a device/system will perform its intended function during a specified period of time under stable condition.

1. Where is the impulse response and step response used?

Ans. Impulse response and step response can be used for transient state analysis of a dynamic system.

1. What is the sampling theorem?                             

Ans. According to sampling theorem “A band limited signal of finite energy can be completely reconstructed from its samples taken uniformly at a rate ω_s ≥ 2ω_m samples/rad/sec (or, f_s ≥ 2f_m sample/sec)ⁿ where ω_m  = message signal bandwidth, ω_s =sampling frequency

1. What is the significance of impulse response? Why impulse response is calculated?

Ans. The impulse response is the output of a system when it is subjected to a unit impulse input. Generally, an impulse response gives the reaction of any dynamic system in response to some external change and system analysis is done.

1. Explain difference between Fourier series, Fourier Transform, Laplace Z-transform.

Ans. Fourier series is used represent a periodic function by a sum of the complex exponential, while the Fourier transform is used to represent a general, non-periodic function of the complex exponential.

The z-transform is essentially discrete version of the Laplace transform and can be used to solve difference equations, the discrete version of differential equations.

Fourier is a subset of Laplace. Laplace is a more generalized transform. 

Fourier is used primarily for steady state signal analysis, while Laplace is used for transient signal analysis. Laplace is good at looking for the response to pulses, step functions, delta functions, while Fourier is good for continuous signals.

1. What is doublet? Explain it.

Ans. A unit doublet is the derivative of Dirac Delta function, it can be used to differentiate signals. 

Where    → Unit doublet function.

1. Give few differences between FIR and IIR filter.

Ans. Finite Impulse Response (FIR) filter uses only current and past input digital samples to obtain the current output sample value. It does not utilize past output samples.

Infinite Impulse Response (IIR) filter user current input sample value, past input and output samples to obtain current output sample value transfer function of FIR will have only zeros, will need more memory, while transform function of IIR filter will have both zeros and poles and will require less memory compared to FIR.

1. What is image processing?

Ans. Image processing is a method to convert an image into digital form and perform some operation on it, in order to get enhanced image or to extract some useful information from it.

digital image processing is the use of computer algorithms to perform image processing on digital images. As a subcategory or field of digital signal processing, digital image processing has many advantages over analog image processing.

1. What are various types of signals known to you?

Ans. Types of signals:

• Continuous time signal
• Discrete-time signal.
• Periodic Signal
• Energy signal
• Power signal
• Random signal
• Deterministic signal

1. Is there any difference between signal & wave?

Ans. A signal is anything having associated information with it. A wave is a disturbance or variation that transfer energy from one point to another.

1. What do you mean by Gibbs phenomenon?

Ans. Gibbs phenomenon says that whenever there is an abrupt discontinuity in the signal which is being sampled, the reconstructed signal will always have high, frequency oscillations and as the number of samples increases the oscillations compress towards discontinuity but their maximum value remains the same.

The n^th partial sum of the Fourier series has large oscillations near the jump, which might increase the maximum of the partial sum above that of the function itself. The overshoot does not die out as n increases but approaches a finite limit.

1. What are the effects of aliasing?

Ans.  Aliasing is an effect that causes different signals to become indistinguishable (or aliases of one another) when sampled. It also refers to the distortion that results when the signal reconstructed from samples is different from the original continuous signal. Due to aliasing, both high frequency and low frequency contents are lost.

1. What is the location of poles in Chebyshev and Butterworth filters?

Ans.  In Chebyshev, filters poles lie on an ellipse in the complex plane while in Butterworth filter poles lie on a circle.

1. Why windowing necessary for a sampled signal?

Ans. When a signal is sampled and FFT is performed directly then the first side lobe is only 14 dB less than the main lobe i.e. the SNR is very poor. Windowing of sampled signal is done to improve the ratio between main lobe and the first side-lobe.

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