Question 1. Define Discrete Time Signal?

Answer :

A discrete time signal x (n) is a function of an impartial variable this is an integer. A discrete time signal isn't always described at immediate among successive samples.

Question 2. Define Discrete Time System?

Answer :

A discrete or an algorithm that performs some prescribed operation on a discrete time signal is called discrete time machine.

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Question 3. What Are The Elementary Discrete Time Signals?

Answer :

Unit sample collection (unit impulse)

δ (n)= 1 n=0

zero Otherwise

Unit step sign

U (n) = 1 n>=0

0 Otherwise

Unit ramp sign

Ur(n)=n for n>=0

zero Otherwise

Exponential sign

x (n)=an in which a is actual

x(n)-Real signal

Question 4. State The Classification Of Discrete Time Signals?

Answer :

The kinds of discrete time signals are:

Energy and electricity indicators

Periodic and Aperiodic indicators

Symmetric(even) and Antisymmetric (abnormal) signals

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Question five. Define Periodic And Aperiodic Signal?

Answer :

A signal x (n) is periodic in period N, if x (n+N) =x (n) for all n. If a signal does no longer fulfill this equation, the signal is referred to as aperiodic sign.

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Question 6. Define Symmetric And Antisymmetric Signal?

Answer :

A actual value sign x (n) is known as symmetric (even) if x (-n) =x (n). On the opposite hand the signal is referred to as antisymmetric (unusual) if x (-n) =x (n).

Question 7. State The Classification Of Systems?

Answer :

Static and dynamic gadget.

Time invariant and time version machine.

Causal and anticausal gadget.

Linear and Non-linear device.

Stable and Unstable system.

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Question eight. Define Dynamic And Static System?

Answer :

A discrete time machine is referred to as static or reminiscence less if its output at any immediately n depends almost on the enter sample at the equal time but no longer on beyond and destiny samples of the input.

E.G. Y(n) =a x (n)

In anyother case the machine is said to be dynamic and to have reminiscence.

E.G. (n) =x (n)+three x(n-1)

Question 9. Define Time Variant And Time Invariant System?

Answer :

A device is known as time invariant if its output , enter traits dos now not change with time.

E.G.Y(n)=x(n)+x(n-1)

A machine is called time variant if its input, output characteristics modifications with time.

E.G.Y(n)=x(-n).

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Question 10. Define Stable And Unable System?

Answer :

A gadget is stated to be solid if we get bounded output for bounded enter.

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Question 11. Define Region Of Convergence?

Answer :

The location of convergence (ROC) of X(Z) the set of all values of Z for which X(Z) reap final fee.

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Question 12. State Properties Of Roc.?

Answer :

The ROC does not include any poles.

When x(n) is of finite duration then ROC is entire Z-aircraft besides Z=zero or Z=∞.

If X(Z) is causal,then ROC consists of Z=∞.

If X(Z) is anticasual,then ROC consists of Z=0.

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Question 13. State The Methods For Evaluating Inverse Z-remodel.?

Answer :

Direct valuation by way of contour integration.

Expansion into series of phrases within the variable Z and Z-1.

Partial fraction growth and appearance up desk.

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Question 14. State The Properties Of Dft?

Answer :

Periodicity

Linearity and symmetry

Multiplication of two DFTs

Circular convolution

Time reversal

Circular time shift and frequency shift

Complex conjugate

Circular correlation

Question 15. How To Obtain The Output Sequence Of Linear Convolution Through Circular Convolution?

Answer :

Consider finite duration sequences x(n) and h(n) of length L samples and M samples. The linear convolution of these two sequences produces an output collection of length L+M-1 samples, whereas , the circular convolution of x(n) and h(n) give N samples in which N=max(L,M).In order to acquire the number of samples in round convolution equal to L+M-1, both x(n) and h(n) should be appended with appropriate variety of 0 valued samples. In different words via growing the length of the sequences x(n) and h(n) to L+M-1 factors after which circularly convolving the ensuing sequences we reap the same result as that of linear convolution.

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Question sixteen. What Is Zero Padding?What Are Its Uses?

Answer :

Let the collection x(n) has a duration L. If we need to locate the N-factor DFT(N>L) of the series x(n), we need to add (N-L) zeros to the series x(n). This is referred to as zero padding.

The uses of zero padding are:

We can get better display of the frequency spectrum.

With 0 padding the DFT can be used in linear filtering.

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Question 17. Define Sectional Convolution?

Answer :

If the statistics collection x(n) is of long length it's miles very tough to attain the output series y(n) due to constrained reminiscence of a digital laptop. Therefore, the facts series is split up into smaller sections. These sections are processed separately one by one and managed later to get the output.

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Question 18. What Are The Two Methods Used For The Sectional Convolution?

Answer :

The two techniques used for the sectional convolution are:

The overlap-upload method and

Overlap-keep approach.

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Question 19. What Is Overlap-add Method?

Answer :

In this method the size of the input statistics block xi(n) is L. To every statistics block we append M-1 zeros and carry out N factor circular convolution of xi(n) and h(n). Since every facts block is terminated with M-1 zeros the closing M-1 factors from each output block must be overlapped and introduced to first M-1 points of the succeeding blocks.This approach is known as overlap-add approach.

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Question 20. What Is Overlap-keep Method?

Answer :

In this method the statistics sequence is split into N point sections xi(n).Each segment carries the remaining M-1 statistics factors of the previous phase accompanied by L new records factors to form a records collection of length N=L+M-1.In round convolution of xi(n) with h(n) the first M-1 points will not consider the linear convolution of xi(n) and h(n) because of aliasing, the remaining points will trust linear convolution. Hence we discard the first (M-1) points of filtered segment xi(n) N h(n). This method is repeated for all sections and the filtered sections are abutted together.

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Question 21. Why Fft Is Needed?

Answer :

The direct evaluation DFT calls for N2 complicated multiplications and N2 –N complicated additions. Thus for big values of N direct assessment of the DFT is hard. By the usage of FFT set of rules the wide variety of complex computations may be decreased. So we use FFT.

Question 22. What Is Fft?

Answer :

The Fast Fourier Transform is an algorithm used to compute the DFT. It makes use of the symmetry and periodicity homes of twiddle aspect to efficaciously reduce the DFT computation time.It is based on the essential precept of decomposing the computation of DFT of a sequence of period N into successively smaller DFTs.

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Question 23. How Many Multiplications And Additions Are Required To Compute N Point Dft Using Radix-2 Fft?

Answer :

The quantity of multiplications and additions required to compute N point DFT the use of radix-2 FFT are N log2 N and N/2 log2 N respectively,.

Question 24. What Is Meant By Radix-2 Fft?

Answer :

The FFT set of rules is most efficient in calculating N factor DFT. If the number of output points N may be expressed as a energy of 2 that is N=2M, wherein M is an integer, then this algorithm is called radix-2 algorithm.

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Question 25. What Is Dit Algorithm?

Answer :

Decimation-In-Time algorithm is used to calculate the DFT of a N factor collection. The concept is to interrupt the N factor sequence into two sequences, the DFTs of which may be combined to provide the DFt of the

unique N point sequence.This set of rules is called DIT because the collection x(n) is regularly splitted into smaller sub- sequences.

Question 26. What Dif Algorithm?

Answer :

It is a famous shape of the FFT algorithm. In this the output series X(k) is divided into smaller and smaller sub-sequences , this is why the name Decimation In Frequency.

Question 27. What Are The Applications Of Fft Algorithm?

Answer :

The packages of FFT algorithm consists of:

Linear filtering

Correlation

Spectrum analysis

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Question 28. Why The Computations In Fft Algorithm Is Said To Be In Place?

Answer :

Once the butterfly operation is performed on a couple of complicated numbers (a,b) to provide (A,B), there's no want to shop the enter pair. We can shop the result (A,B) inside the same locations as (a,b). Since the same garage locations are used troughout the computation we say that the computations are performed in place.

Question 29. Distinguish Between Linear Convolution And Circular Convolution Of Two Sequences?

Answer :

Linear convolution:

If x(n) is a chain of L quantity of samples and h(n) with M quantity of samples, after convolution y(n) could have N=L+M-1 samples.

It may be used to find the reaction of a linear filter.

Zero padding isn't always vital to find the response of a linear filter.

Circular convolution:

If x(n) is a chain of L range of samples and h(n) with M samples, after convolution y(n) will have N=max(L,M) samples.

It cannot be used to discover the reaction of a filter.

Zero padding is vital to discover the reaction of a filter out.

Question 30. What Are Differences Between Overlap-keep And Overlap-upload Methods?

Answer :

Overlap-keep method:

In this method the size of the input statistics block is N=L+M-1

Each data block consists of the remaining M-1 records points of the preceding statistics block observed through L new records points

In each output block M-1 factors are corrupted due to aliasing as circular convolution is employed

To shape the output series the primary

M-1 records points are discarded in each output block and the last information are geared up collectively

Overlap-add technique:

In this technique the dimensions of the enter information block is L

Each information block is L points and we append M-1 zeros to compute N point DFT

In this no corruption because of aliasing as linear convolution is carried out using circular convolution

To form the output series the closing

M-1 factors from every output block is delivered to the first M-1 factors of the succeeding block

Question 31. What Are The Differences And Similarities Between Dif And Dit Algorithms?

Answer :

Differences:

The input is bit reversed while the output is in natural order for DIT, while for DIF the output is bit reversed even as the enter is in herbal order.

The DIF butterfly is slightly one of a kind from the DIT butterfly, the difference being that the complicated multiplication takes place after the add-subtract operation in DIF.

Similarities:

Both algorithms require identical range of operations to compute the DFT.Both algorithms can be executed in region and both want to carry out bit reversal at some location at some point of the computation.

Question 32. What Are The Different Types Of Filters Based On Impulse Response?

Answer :

Based on impulse response the filters are of two types:

IIR filter

FIR filter out

The IIR filters are of recursive kind, wherein the prevailing output sample relies upon on the prevailing input, past input samples and output samples.

The FIR filters are of non recursive type, wherein the existing output sample relies upon on the present input sample and previous enter samples.

Question 33. What Are The Different Types Of Filters Based On Frequency Response?

Answer :

Based on frequency reaction the filters may be categorized as:

Lowpass filter out

Highpass filter out

Bandpass clear out

Bandreject filter out

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Question 34. Distinguish Between Fir Filters And Iir Filters?

Answer :

FIR clear out:

IR filter

These filters can be without difficulty designed to have flawlessly linear section.

FIR filters may be found out recursively and non-recursively.

Greater flexibility to govern the shape of their significance reaction.

Errors because of spherical off noise are much less extreme in FIR filters, especially due to the fact comments isn't always used.

IIR clear out:

These filters do now not have linear section.

IIR filters are without difficulty realized recursively.

Less flexibility, usually restricted to specific kind of filters.

The round off noise in IIR filters is greater.

Question 35. What Are The Design Techniques Of Designing Fir Filters?

Answer :

There are 3 widely known methods for designing FIR filters with linear segment .They are (1.)Window approach (2.)Frequency sampling method (3.)Optimal or minimax layout.

Question 36. What Is Gibb’s Phenomenon?

Answer :

One possible way of finding an FIR filter out that approximates H(ejw) might be to truncate the countless Fourier series at n=±(N-1/2).Direct truncation of the collection will lead to constant percent overshoots and undershoots before and after an approximated discontinuity inside the frequency reaction.

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Question 37. What Are The Desirable Characteristics Of The Window Function?

Answer :

The appropriate traits of the window are:

The relevant lobe of the frequency response of the window must include most of the strength and need to be slim.

The highest facet lobe level of the frequency response must be small.

The facet lobes of the frequency reaction should lower in power rapidly as ω tends to ?.

Question 38. Give The Equations Specifying The Following Windows?

Answer :

Rectangular window

Hamming window

Hanning window

Bartlett window

Kaiser window

1. Rectangular window:

The equation for Rectangular window is given via

W(n)= 1 zero ≤ n ≤ M-1

0 in any other case

2. Hamming window:

The equation for Hamming window is given through

WH(n)= 0.Fifty four-0.Forty six cos 2?n/M-1 zero ≤ n ≤ M-1

0 otherwise

three. Hanning window:

The equation for Hanning window is given with the aid of

WHn(n)= 0.Five[1- cos 2?n/M-1 ] 0 ≤ n ≤ M-1

0 in any other case

four. Bartlett window:

The equation for Bartlett window is given by means of

WT(n)= 1-20 ≤ n ≤ M-1

M-1

zero otherwise

five. Kaiser window:

The equation for Kaiser window is given byn0 in any other case

wherein α is an impartial parameter.

Question 39. What Is The Necessary And Sufficient Condition For Linear Phase Characteristic In Fir Filter?

Answer :

The essential and enough situation for linear phase characteristic in FIR filter out is, the impulse response h(n) of the system have to have the symmetry property i.E.,

H(n) = h(N-1-n)

wherein N is the period of the series.

Question 40. What Are The Advantages Of Kaiser Window?

Answer :

It gives flexibility for the designer to choose the aspect lobe stage and N

It has the attractive assets that the aspect lobe level can be various continuously from the low cost within the Blackman window to the high value within the rectangular window

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Question 41. What Is The Principle Of Designing Fir Filter Using Frequency Sampling Method?

Answer :

In frequency sampling approach the desired value reaction is sampled and a linear segment reaction is specific .The samples of favored frequency response are recognized as DFT coefficients. The filter coefficients are then decided because the IDFT of this set of samples.

Question 42. For What Type Of Filters Frequency Sampling Method Is Suitable?

Answer :

Frequency sampling technique is attractive for narrow band frequency selective filters wherein only a few of the samples of the frequency reaction are non 0.

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Question 43. When Cascade Form Realization Is Preferred In Fir Filters?

Answer :

The cascade form cognizance is preferred while complex zeros with absolute significance is less than one.

Question forty four. State The Equations Used To Convert The Fir Filter Coefficients To The Lattice Filter Coefficient.

Answer :

For an M_stage clear out , αm-1(zero) =1 and km = αm(m)??

αm-1(okay) = αm(k) - αm(m)?? • αm(m-ok) , 1≤okay≤m-1

1-αm2 (m)

Question forty five. State The Structure Of Iir Filter?

Answer :

IIR filters are of recursive kind whereby the prevailing o/p pattern relies upon on gift i/p, beyond i/p samples and o/p samples. The design of IIR filter out is realizable and strong.

The impulse reaction h(n) for a realizable filter out is

h(n)=zero for n≤0

Question 46. State The Advantage Of Direct Form ΙΙ Structure Over Direct Form Ι Structure.?

Answer :

In direct form ΙΙ shape, the number of memory locations required is less than that of direct form Ι structure.

Question forty seven. How One Can Design Digital Filters From Analog Filters?

Answer :

Map the desired digital clear out specs into the ones for an equal analog filter out.

Derive the analog switch function for the analog prototype.

Transform the switch feature of the analog prototype into an equivalent digital filter transfer function.

Question forty eight. Mention The Procedures For Digitizing The Transfer Function Of An Analog Filter.?

Answer :

The critical strategies for digitizing the transfer function of an analog clear out are:

Impulse invariance approach.

Bilinear transformation technique.

Question 49. What Do You Understand By Backward Difference?

Answer :

One of the simplest method for converting an analog clear out right into a virtual clear out is to approximate the differential equation via an equal distinction equation.

D/dt y(t)=y(nT)-y(nT-T)/T

The above equation is called backward distinction equation.

Question 50. What Is The Mapping Procedure Between S-plane & Z-aircraft In The Method Of Mapping Differentials? What Are Its Characteristics?

Answer :

The mapping process among S-plane & Z-aircraft inside the technique of mapping of differentials is given by way of

H(Z) =H(S)the following characteristics:

The left half of S-aircraft maps interior a circle of radius ½ centered at Z= ½ inside the Z-aircraft.

The proper 1/2 of S-aircraft maps into the vicinity outside the circle of radius ½ within the Z-plane.

The j ?-axis maps onto the perimeter of the circle of radius ½ in the Z-aircraft.

Question 51. What Is Meant By Impulse Invariant Method Of Designing Iir Filter?

Answer :

In this method of digitizing an analog filter out, the impulse reaction of resulting digital filter is a sampled version of the impulse reaction of the analog filter.The switch function of analog filter out in partial fraction form.

Question fifty two. Give The Bilinear Transform Equation Between S-aircraft And Z-aircraft?

Answer :

S=2/T(1-Z-1/1+Z-1)

Question fifty three. What Is Bilinear Transformation?

Answer :

The bilinear transformation is a mapping that transforms the left half of of S-aircraft into the unit circle inside the Z-aircraft simplest once, therefore fending off aliasing of frequency additives.

The mapping from the S-plane to the Z-plane is in bilinear transformation is

S=2/T(1-Z-1/1+Z-1)

Question 54. What Are The Properties Of Bilinear Transformation?

Answer :

The mapping for the bilinear transformation is a one-to-one mapping this is for every factor Z, there is exactly one corresponding point S, and vice-versa.

The j ?-axis maps on tozhalf of the s-aircraft maps to the indoorszhalf of of the s-aircraft maps on to the outdoorsz55. Write A Short Note On Pre-warping.

Answer :

The effect of the non-linear compression at excessive frequencies can be compensated. When the desired significance reaction is piece-wise steady over frequency, this compression can be compensated by introducing a appropriate pre-scaling, or pre-warping the essential frequencies through the usage of the method.

Question 56. What Are The Advantages & Disadvantages Of Bilinear Transformation?

Answer :

Advantages:

The bilinear transformation provides one-to-one mapping.

Stable continuous structures can be mapped into realizable, strong virtual systems.

There isn't any aliasing.

Disadvantage:

The mapping is incredibly non-linear generating frequency, compression at high frequencies.

Neither the impulse response nor the phase reaction of the analog clear out is preserved in a digital filter received via bilinear transformation.

Question fifty seven. What Is The Advantage Of Cascade Realization?

Answer :

Quantization errors may be minimized if we recognize an LTI gadget in cascade form.

Question fifty eight. Define Signal Flow Graph?

Answer :

A signal go with the flow graph is a graphical representation of the relationships between the variables of a hard and fast of linear difference equations.

Question 59. What Is Transposition Theorem & Transposed Structure?

Answer :

The transpose of a structure is described by way of the following operations:

Reverse the guidelines of all branches inside the signal flow graph

Interchange the enter and outputs.

Reverse the jobs of all nodes in the waft graph.

Summing factors turn out to be branching factors.

Branching points end up summing factors.

According to transposition theorem if we reverse the directions of all branch transmittance and interchange the enter and output within the flowgraph, the machine function stays unchanged.

Question 60. What Are The Different Types Of Arithmetic In Digital Systems.?

Answer :

There are 3 kinds of arithmetic utilized in virtual structures. They are fixed point mathematics, floating point ,block floating factor mathematics.

Question sixty one. What Is Meant By Fixed Point Number?

Answer :

In constant point number the position of a binary factor is constant. The bit to the proper represent the fractional component and people to the left is integer part.

Question 62. What Are The Different Types Of Fixed Point Arithmetic?

Answer :

Depending at the poor numbers are represented there are 3 kinds of constant point arithmetic. They are signal magnitude,1’s supplement,2’s complement

Question sixty three. What Is Meant By Sign Magnitude Representation?

Answer :

For sign significance representation the main binary digit is used to symbolize the signal. If it is equal to one the variety is terrible, otherwise it's far nice.

Question 64. What Is Meant By 1’s Complement Form?

Answer :

In 1,s complement shape the fine wide variety is represented as in the signal importance form. To obtain the negative of the effective wide variety ,complement all of the bits of the nice variety.

Question sixty five. What Is Meant By 2’s Complement Form?

Answer :

In 2’s complement form the advantageous quantity is represented as inside the signal importance form. To achieve the bad of the tremendous variety ,complement all the bits of the wonderful quantity and add 1 to the LSB.

Question sixty six. What Is Meant By Floating Pint Representation?

Answer :

In floating factor form the wonderful variety is represented as F =2CM,wherein is mantissa, is a fraction such that1/2<M<1and C the exponent can be either superb or bad.

Question 67. What Are The Advantages Of Floating Point Representation?

Answer :

Large dynamic range

Overflow is not going.

Question sixty eight. What Are The Quantization Errors Due To Finite Word Length Registers In Digital Filters?

Answer :

Input quantization errors

Coefficient quantization errors

Product quantization errors

Question sixty nine. What Is Input Quantization Error?

Answer :

The filter out coefficients are computed to countless precision in theory. But in digital computation the filter coefficients are represented in binary and are saved in registers. If a b bit register is used the clear out coefficients ought to be rounded or truncated to b bits ,which produces an errors.

Question 70. What Is Product Quantization Error?

Answer :

The product quantization errors get up on the out positioned of the multiplier. Multiplication of a b bit records with a b bit coefficient results a product having 2b bits. Since a b bit register is used the multiplier output can be rounded or truncated to b bits which produces the mistake.

Question 71. What Are The Different Quantization Methods?

Answer :

Truncation and Rounding

Question 72. What Is Truncation?

Answer :

Truncation is a procedure of discarding all bits much less massive than LSB that is retained

Question 73. What Is Rounding?

Answer :

Rounding quite a number to b bits is achieved via deciding on a rounded end result because the b bit wide variety closest quantity being unrounded.

Question 74. What Are The Two Types Of Limit Cycle Behavior Of Dsp?

Answer :

Zero restrict cycle conduct

Over drift restriction cycle conduct

Question 75. What Are The Methods To Prevent Overflow?

Answer :

Saturation mathematics and

Scaling

Question 76. State Some Applications Of Dsp?

Answer :

Speech processing ,Image processing, Radar sign processing.