Introduction to Microservice Architecture Using SpringBoot - Part 1

What is a signal and system?

A function of one or more independent variables which contain some information is called signal.
A system is a set of elements or functional blocks that are connected together and produces an output in response to an input signal.

Define a causal system.

The causal system generates the output depending upon present &past inputs only. A causal system is non anticipatory.

What is meant by linear system?

A linear system should satisfy superposition principle i.e, additive property and scaling or homogeneity property. A linear system should satisfy F[ax1(t)+bx2(t)] =ay1(t)+by2(t)

y1(t)=F[x1(t)]
y2(t)=F[x2(t)]

Define time invariant system.

A system is time invariant if the behavior and characteristics of the system are fixed over time. A system is time invariant if a time shift in the input signal results in an identical time shift in the output signal. For example ,a time invariant system should produce y(t-t0)as the output when x(t-to) is the input.

 Define stable system?

When the system produces bounded output for bounded input, then the system is called bounded input& bounded output stable. If the signal is bounded, then its magnitude will always be finite.

Define memory and memoryless system.

The output of a memory system at any specified time depends on the inputs at that specified time and at other times. Such systems have memory or energy storage elements. The system is said to be static or memoryless if its output depends upon the present input only.

Define invertible system?

A system is said to be invertible if there is unique output for every unique input.

What are passive and active filters?

 A passive filter is a kind of electronic filter that is made only from passive elements – in contrast to an active filter, it does not require an external power source (beyond the signal). An active filter is a type of analog electronic filter, distinguished by the use of one or more active components and require an external power source.

What is the difference between deterministic and random signals?

A deterministic signal can be completely represented by mathematical equation at any time whereas a signal which cannot be represented by any mathematical equation is called random signal.

Define periodic signal. and non periodic signal.

A signal is said to be periodic ,if it exhibits periodicity .i.e., X(t +T)=x(t), for all values of t.
Periodic signal has the property that it is unchanged by a time shift of T. A signal that does not satisfy the above periodicity property is called an aperiodic signal.

What are analog and digital signals?

Analog signals use a continuous range of values to represent the data and information.

Digital signals use discrete values (or discontinuous values), i.e. discrete 0 and 1, to represent the data and information.

What are even and odd signals?

A signal is said to be even signal if inversion of time axis does not change the amplitude. i.e, x(t) = x(-t)
A signal is said to be odd signal if inversion of time axis also inverts amplitude of the signal. i.e, x(t) = -x(-t)

What is meant by sampling

A sampling is a process by which a CT signal is converted into a sequence of discrete samples with each sample representing the amplitude of the signal at the particular instant of time.

State Sampling theorem

A band limited signal of finite energy, which has no frequency components higher than the W hertz, is completely described by specifying the values of the signal at the instant of time separated by 1/2W seconds and A band limited signal of finite energy, which has no frequency components higher than the W hertz, is completely recovered from the knowledge of its samples taken at the rate of 2W samples per second.

Can you able to reconstruct the original signal from sampled signal if it has been sampled at Nyquist rate?

No original signal cannot be reconstructed because in order to reconstruct the original signal from sampled signal when it is sampled at Nyquist rate, an ideal low pass filter is required which is impossible in real life to construct.

What is the difference between power signal and energy signal in terms of energy and power?

Energy of the power signal is infinite whereas power of the energy signal is zero.

What is the significance of unit impulse or unit sample functions?

Unit impulse or unit sample functions are used to determine impulse response of the system. It also contains all the frequencies from -∞ to ∞.

Define Aliasing effect

Aliasing is an effect that causes different signals to become indistinguishable (or aliases of one another) when sampled. It also refers to the distortion or artifact that results when the signal reconstructed from samples is different from the original continuous signal.

What is the significance of unit ramp function?

The ramp function indicates linear relationship. It also indicates constant current charging of the capacitor.

What are the applications of convolution?

The applications of convolution are:

It is used for system analysis such as causality, stability, step response, impulse response, invertibility etc.
It is used to determine output of the system if input and impulse response is given.
It relates input output and impulse response.
Convolution helps to represent system in frequency domain using Fourier, Laplace and z-transform.
This is used to study pole-zero plots, stability, filtering etc.

What is autocorrelation?

When we calculate correlation function of the signal with itself, then it is called autocorrelation. Thus if x1(t) = x2(t), then correlation becomes autocorrelation.

Why do we do Fourier Transform?

By Fourier Transform we can represent the signal from time domain to frequency domain, thus we can find the various frequency components contained in the given signal. Helping us to find the total bandwidth required for the transmission of the given signal.

What Is Dft ?

DFT stands for discrete fourier transform. it converts a finite list of equally spaced samples of a function into the list of coefficients of a finite combination of complex sinusoidal.

What are the limitations of Fourier transform and use of Laplace transform?

They are:Fourier transform can be calculated only for the signals which are absolutely integrable. But Laplace transform exists for signals which are not absolutely integrable.
Fourier transform is calculated only on the imaginary axis, but Laplace transform can be calculated over complete s-plane. Hence Laplace transform is more broader compared to Fourier transform.

What is the significance of region of convergence (ROC) of Z transform?

The significance of region of convergence (ROC) of Z transform are:

ROC gives an idea about values of z for which Z-transform can be calculated.
ROC can be used to determine causality of the system.
ROC can be used to determine stability of the system.

What is the similarity between Laplace transform and z-transform?

 Z-transform is the discrete time counter part of Laplace transform with negative real axis mapped within unit circle, jω axis mapped on unit circle and right half mapped on outside a unit circle.

What is the difference between DTFT and DFT?

In DTFT the discrete signal is assumed to be aperiodic so the frequency domain signal is periodic and continuous whereas in DFT, the discrete signal is assumed to be periodic so frequency domain signal is periodic and discrete.

What are the advantages of digital filter over analog filters?

Digital filters have the following advantages compared to analog filters:

Digital filters are software programmable, which makes them esay to build and test.
Digital filters require only the arithmetic operations of addition, subtraction and multiplication.
Digital filters do not drift with temperature or humidity or require precision components.
Digital filters have a superior performance to cost ratio.
Digital filters do not suffer from manufacturing variations or aging

Define FIR system.

 If the system has finite duration impulse response then the system is said to be finite impulse response (FIR) system.

Define IIR system.

If the system has infinite duration impulse response then the system is said to be infinite impulse response (IIR) system.

Give one example of FIR and IIR filters?

 Windowed sinc filters are the examples of FIR filters and moving average filters are the example of IIR filters.

Which filter (FIR or IIR filters) is always stable and why?

FIR filters are always stable because they do not contain poles.