DFT full form

What is the full form of DFT?

Answer:

• Discrete Fourier Transform 

What does DFT mean?

In digital signal processing, the DFT as the name implies the discrete Fourier transform is purely discrete. The discrete-time data is a set that is converted into a discrete frequency representation. This is in exact contrast to the DTFT that uses discrete-time but converts to continuous frequency.

Explore more information:

1. Full form of DSP
2. Full form of DTFT
3. Full form of LTI
4. Full form of FIR
5. Full form of DM
6. Full form of STFT
7. Full form of IIR
8. Full form of ROC
9. Full form of FFT

DFT meaning

In the digital communication system, the DFT stands for Discrete Fourier transform, it is a finite duration frequency sequence which is obtained by sampling one period of Fourier transform. Sampling is done at 'N' equally spaced points, over the period extending from o to around range of 2π.

Mathematical equations :

The DFT of discrete sequence sequence is x(n) and  is denoted by X(k). It is given by,

            N-1

X(K) = ∑    x(n) . e ^–j2πkn/N

              n=0

Here k = 0,1,2,3.......N-1

Since this summation is taken for N point, it is called as N point of discrete Fourier transform called DFT.

We can obtain a discrete sequence x(n) from its DFT. It is called an inverse discrete Fourier transform. It is given by, 

                 N-1

X(n) =1/N ∑    x(k) . e ^–j2πkn/N

                    k=0

Here n = 0,1,2,3.......N-1

This is called as N point IDFT.

Properties of DFT

Before we learn about properties of DFT first we learn about the exact meaning terms of DFT. The Fourier transform can be used for the analysis of a signal. It used for transformation from the time domain to the frequency domain. Here this article gives information about properties of  DFT to know more details or learn about DFT. 

Linearity : 

Periodic signals : A x(n) + B y(n)

Fourier series coefficients : A a_k + B b_k

Time shifting :

Periodic signals : x(n - n₀)
Fourier series coefficients: a_k e^-jk(2π/N)n      

Frequency Shifting :

Periodic signals : x(n) e^jm(2π/N)n      

Fourier series coefficients : X(k - m) 

Conjugation :

Periodic signals : x*(n)       

Fourier series coefficients : ^a*_-k

Time Reversal :

Periodic signals : x(-n)       
Fourier series coefficients : ^a_-k

Thyristor chopper circuit

Actually, a chopper consists of a main power semiconductor types of device together with their turn on as well as turn off mechanisms. Here we have already learned about different types of chopper circuit like type A, type B, type C, type E etc. Now let us check it out the information about thyristor chopper circuit to know more details about chopper circuitry design.

In chopper definition, the low power chopper circuit; power transistors and also a GTOs terms. are being used widely. In high power level, however thyristor definition are in most commonly use. So here we have to learn the object of this section is to study the thyristor chopper circuit along with their commutation circuitry.

Forced commutation: 

In the method of forced commutation called, the external elements L and C which do not carry the load current continuously, are used to turn off a conducting Thyristor. Forced commutation can be achieved in the following ways :

1. Voltage commutation : 

• In this scheme, a conducting thyristor is commutated by the application of a pulse of a large reverse type of voltage. This reverse voltage is applied by switching a previously charged capacitor of the circuit device. 
• The sudden application of the reverse voltage across the conducting Thyristor reduces the anode to zero rapidly.
• Then the presence of a reverse voltage across the SCR stands aids in the completion of its turn off process.

2. Current commutation :

• In this scheme, an external pulse of current greater than the load current is passed in the reversed direction through the conducting SCR. When the current pulse attains a value equal to the load current, net pulse current through thyristor becomes zero and the device turn off. So the current pulse is usually generated by an initially charged capacitor.
• An important feature of current commutation is the connection of a diode in anti-parallel with the main thyrostor so that voltage drop across the diode reverse biases the main SCR. Since this voltage drop is of the order of is 1 volt only, the commutation time in current commutation is more as compared to that in voltage commutation.
• In both voltage and current commutation schemes, commutation is initiated by gating an auxiliary SCR called thyristor.

Load commutation : 

In load commutation, a conducting thyristor is turned off when load current flowing through a thyristor either :

1. It becomes to zero due to the nature of load circuit parameters 

2.Transferred to another device from the conducting thyrostor

Types of chopper circuits

before we learn about different types of chopper circuit first let we check it out what is a chopper and how it used in power electronics application.

Chopper definition :

A chopper device is one type of electronic circuit used to refer to numerous types of electronic switching devices and used in power control and signals applications. 

In power electronics, the much industrial application requires power from dc voltage sources. Several of these types of applications, however, perform better in case these are fed variable dc voltage source. 

In power electronic the conversion from fixed dc voltage to an adjustable dc type of output voltage, through the use of semiconductor devices, can be carried out by the two types of dc to dc converters  are as listed below :

1. AC link chopper
2. DC chopper

Here this article gives information about the different types of chopper circuit, to how to convert the dc output voltage.

1. AC link chopper 

shows in the circuit diagram of an ac link chopper to, dc are first converted to ac by an inverter. AC is then stepped down by a transformer which is then converted back to dc by a diode rectifier, As the conversion is in two stages, dc to ac to dc. So Ac link chopper is costly, bulky, and less efficient.

2. DC chopper 

To show in the figure here DC  chopper is a static device that converts fixed dc input voltage to a variable dc output voltage directly.

A chopper may be thought of as dc equivalent of an ac transformer so that it can behave like is an identical manner. As a state that the chopper involves that one stage conversion, these are more efficient for a circuit, so is the one of the most useful compared to AC link chopper.

Chopper is now being all over for rapid transits systems. Chopper systems offer too much fast response, smooth control, high efficiency, and also regeneration.

The power semiconductor devices are used for a chopper circuit can be force commutative thyristor, and also power BJT full form, IGBT full form, power MOSFET full form. As we stated above, a chopper is dc equivalent to an ac transformer having continuously variable turn ratio. 

As an alike transformer, a chopper can be used to step up or step down for the fixed dc input voltage. As a step-down dc chopper are more common,  then the term dc chopper would mean a step-down dc chopper.

What is chopper

First of all, we should check what chopper exactly means and after that where it mostly used.

What is a chopper?

As we know that a chopper is one type of electronic circuit used to refer numerous types of electronic switching devices and used in power control and signals applications. 

A chopper is a static device and it converts fixed dc input voltage to a voltage to a variable dc output voltage directly.

A chopper is basically a DC to DC converter whose main function is to create an adjustable DC voltage from a fixed DC voltage source through the use of semiconductors.

A chopper is more efficient as they involved in only one stage conversion. The future electric automobiles are likely to use the chopper for their speed control and also braking.

A chopper is considered as a DC equivalent of an AC transformer since it behaves in an identical manner.

The chopper used in trolley cars, marine hoists, forklift trucks, and also a mine hauler. The chopper is the dc equivalent to an ac transformer having continuously variable to a turn ratio. Like a transformer, a chopper can be used to step up or step down with the fixed DC input voltage.

In power electronic system the conversion from fixed dc voltage to an adjustable dc output voltage, through the use of semiconductor devices, can be carried out by the two types of dc to dc converters like ac link chopper and also a dc chopper. 

Chopper circuits are very widely used in power electronics as also numerous electronics circuits as given below. 

• SMPS terms
• DC DC converters
• Amplifiers
• Filters
• DC motor speed control
• VFD drives motors

Applications of chopper : 

• Switched mode power supply 
• DC to DC converter 
• Class D electronic amplifier 
• Switched capacitor filter 
• Variable frequency drive
• DC voltage boosting 
• Battery operated electric cars
• Battery chargers 
• Railway traction 

FIR filter block diagram

In the digital signal processing system, the use of  FIR short form is one type of filter whose impulse response is of finite duration, the reason of it settles zero in finite time. This is a contrast to IIR filter design, which has internal feedback and may continue to respond indefinitely. 

A discrete time FIR filter of N number of order and the top part is an N stage delay line with total N+1 taps to shown in the figure. Each of unit delay is a Z^-1 type of operator in the Z transform notation. 

The output y of a linear time-invariant system is determined by conveying its input signal x with its impulse response b. 

For a discrete-time FIR filter, the output is depend on a weighted sum of the current and finite number of previous values of the input signal.

The operation is described by the following equation, which defines the output sequence of y[n] in terms of its input sequence of x [n] given below.

Y[n] = b₀ x[n] + b₁ x[n-1]  + b₂ x[n-2] …………b_n x[n-N]

           N

Y[n] =  ∑ b_i x[n-i]

          I=0

Where, 

x[n] = input signal

y[n] = output signal

DC chopper

A chopper is a static device that converts fixed dc input voltage to a variable dc output voltage directly.

A chopper may be thought of as dc equivalent of an ac transformer so that they behave in an identical manner. As chopper involve that one stage conversion, these are more efficient for the circuit.

Chopper is now being all over for rapid transits systems. Chopper systems offer smooth control,  fast response, high efficiency, and regeneration.

The power semiconductor devices used for a chopper circuit can be force commutative thyristor, power BJT, IGBT, power MOSFET. 

As stated above, a chopper is dc equivalent to an ac transformer having continuously variable turn ratio. 

A  transformer, a chopper can be used to step up or step down for the fixed dc input voltage. As a step-down dc chopper is more common, the term dc chopper or chopper would mean a step-down dc chopper.

Chopper application

A  terms chopper is considered as DC equivalent of an AC transformer since it behaves in an identical manner. It can be used many more electrical device like the electric car, mine hauler, Forklift trucks etc. Here this articles gives information about chopper application to know more details about it.

• Chopper is used for DC motor control
• Solar and wind energy conversion
• It has more efficient as they involve in one or more stage conversion
• Dynamic  break
• Forklift trucks, mine hauler, trolley cars
• HVDT
• It also used in the electric car
• Speed control and braking
• Airplane and spaceships, where onboard regulated DC power supplies are required
• Chopper supply circuit are used as power supplies in computers, commercial electronics, electronics instruments
• DC voltage boosting
• Battery chargers
• Onboard regulated the dc power supply

Type E chopper

As we that a chopper is one type of electronic circuit used to refer numerous types of electronic switching devices and used in power control and signals applications. This characteristic of their operation in any four quadrants form the basis of their classification as class A, class B, class C, Class D, class E, etc. Now let us check it out the information about type E chopper to know more details about the chopper.

The power diagram for a four-quadrant chopper is shown in the figure. 

• It consists of four semiconductor switches CH1 to CH4 and also four diode D1 to D4 in anti-parallel.
• The numbering of chopper CH1,...CH4  corresponds to their respective quadrant operation.
• For example for first quadrant operation, only chopper CH1 is operated for second quadrant operation, only CH2 is operated and so on. 
• Working of this chopper in the four quadrants is explained as under four quadrants is given below.

First quadrant :

• For 1st quadrant operation of the figure shown chopper CH4 is kept ON, CH3 is kept off and chopper CH1 is operated.
• With chopper CH1, CH4 on load voltage V₀ = V_s and load current I0 begins to flow. 
• Here both voltage, as well as current V0 and I0, are positive giving first quadrant operation.
• When CH1 is turn off positive current freewheels through chopper CH4, D2.
• In this manner, both voltage and current V₀, I₀ can be controlled in the first quadrant.

Second quadrant :

• Here CH2 is operated and CH1, CH3, and CH4 kept off.
• With CH2 on, reverse current flows through L, CH2, D4, and E inductance L stores energy during the time CH2 is on.
• When CH2 is turn off current is fed back to the source through diodes D1, D4. 
• Note that here the voltage (E+L di/dt) is more than the source voltage of Vs.
• As load voltage V₀ is positive and I₀ is negative, it is the second quadrant operation of the chopper, Also power is fed back from load to source.
• So this quadrant, configuration operates as a step-up type of chopper.

Third quadrant :

• For third quadrant operation, chopper CH1 is kept off, chopper CH2 is kept on and CH3  is operated.
• Polarity of load emf E must be reversed for this quadrant working.
• When chopper CH3 is on, the load gets connected to source Vs so that both V₀, I₀ are negative leading to third quadrant operation.
• When chopper CH3 is turn off, negative current freewheels through CH2, CH4. 
• In this manner V₀ and I₀ can be controlled in the third quadrant.
• Here chopper operates as a step-down, the chopper operates as a step down a chopper.

Fourth quadrant :

• And last here chopper CH4 is operated and also some other devices are kept off. Load emf E has its polarity and its as shown in figure for its operation in the fourth quadrant.
• With chopper CH4 on, positive current flows through chopper CH4, D2, L and E, inductance L stores energy during the time CH4 is on.
• When chopper CH4 is turn off current is fed back to the source through D2 and D3. 
• Here load voltages negative while load current is positive, leading to the chopper operation in the fourth quadrant. 
• Also, the power is fed back from the load to the source side. 
• Here  chopper operates as a step up chopper.

Type C chopper

As we know that a chopper is a static device that converts fixed dc input voltage to a variable dc output voltage directly. This characteristic of their operation in any four quadrants form the basis of their classification as class A, class B, class C, Class D, class E, etc.

This type of chopper is also called as two quadrants called type A chopper. This type of chopper is obtained by connecting type A and type B choppers in parallel as shown in the figure given below.

• The output voltage V₀ is always positive because of the presence of a freewheeling diode called FD across the load. 
• When chopper CH2  is on, or freewheeling diode conducts, output voltage V₀ = 0 and in case chopper CH1 is on or diode D2 conduct, the output voltage is equal to the voltage V₀ =  _Vs
• The load current called I₀ can, however, reverse its direction. 
• Current flows in the arrow direction marked in the figure.
• The load current is positive when CH1 is on or FD operate together as type A chopper in the first quadrant. 
• Likewise, CH2 and D2 operate together as type B chopper in the second quadrant.

• Average load voltage is always positive but the average load current may be positive or negative as explained above.
• Therefore, power flow may be from the source to load or from load to source.
• So in Chopper CH1 and chopper CH2 should not be on simultaneously as this would lead to a direct short circuit on the supply lines.
• This type of chopper configuration is used for motoring and regenerative braking of dc motors
• This type of operating region of this type of chopper is shown in figure second by the hatched area in the first and second quadrants.   

Type B chopper

As we know that a what chopper can operate in any of the four quadrants by an appropriate arrangement of semiconductor devices. This characteristic of their operation in any four quadrants form the basis of their classification as class A, class B, class C, Class D, class E, etc.

Power circuit for this type of chopper is shown in the figure. Note that load must contain a DC source of E, like a battery in this chopper circuit.

• When the chopper is in V₀ = 0 but load voltage E drives current through L and chopper 2. Inductance L store energy during Ton of a chopper. 
• When chopper is off mean  V₀ = ( E + L di/dt ) exceeds source voltage Vs.
• As result diode D2 is forward biased and also begins conditions, thus allowing power to flow to the source.
• The chopper may be ON or OFF, current I₀ flows out of the load, current I₀ is therefore treated as negative (-ve side). 
• Since voltage V₀ always positive and current I₀ is negative, power flow is always from load to source. 
• As load voltage V₀ = (E+L di/dt) is more than a source voltage of  Vs.
• Type B chopper is also called a step-up chopper.

• Both type A and type B chopper configuration have a common negative terminal between their input as well as output circuits.

Type A chopper

We all know that a chopper definition can operate in any of the four quadrants by an appropriate arrangement of semiconductor devices. This characteristic of their operation in any four quadrants form the basis of their classification as class A, class B, class C, Class D, class E, etc.

It is observed that the chopper circuit of the figure also types A chopper. 

• When the chopper is on V₀ = V_s and current i₀ flows from in the arrow direction shown. 
• When the chopper is in off  V₀=0 and i₀ in the load continues flowing in the same direction through freewheeling diode FD, shown in the figure. 
• It is thus seen that the average values of both load voltage and current  V₀ and I₀ are always positive.
• And this shown by the second figure by the hatched area in the first quadrant of  V₀ - I₀ plane in the figure.
• The power flow in type A chopper is always from the source side to load side. This chopper is also known as the step-down chopper as average output voltage V₀ is always less than the input dc voltage Vs.

Half adder and full adder difference

we all know that a half adder is a one types of combinational logic circuit with two input and also have two output wheres the full adder is add three one-bit binary numbers, two is operands and a carry bit but in output is to be two numbers, sum and carry bit, this is the main difference between them. This article gives information about the difference between the half adder and full adder to know more details about it.

Definition :

• Half adder: Half adder is a combinational logic circuit which adds two 1 bit digits
• Full adder: Full adder is a combinational circuit which adds three 1 bit digits

Hardware :

• Half adder: It consists of one EX-OR gate and one AND gate 
• Full adder: It consists two EX-OR, two AND gate, and one OR gate

Carry addition :

• Half adder: Carry generated from a previous addition is not added in the next step
• Full adder: Carry generated from a previous addition in the next step

Application : 

• Half adder: Calculator, computers, digital measuring devices etc
• Full adder: Multiple bit addition, digital processor

Half adder block diagram

Half adder is a one types of combinational logic circuit with two input and  also have two output. It is basic building block for addition of two single bit  numbers.  This circuit has two outputs called as sum and carry.   

The half adder circuit designed to add two single bit binary numbers A and B. Hence the truth table of a half adder is shown in fig. 

       -          -
S = AB + AB

Using Karnaugh maps :

 

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Advantages and disadvantages of FIR and IIR filters

FIR stands for finite impulse response. Most of the FIR full form filter is that linear phase filter When the linear phase filter is desired an FIR filter is usually used. Here this article gives information about the advantages and disadvantages of FIR as well as IIR filters to know more details about it. 

Advantages of  FIR filters :

• FIR filter is always stable
• It is simple
• Design complexity generally linear
• FIR filter are having linear phase response
• It is easy to optimize
• Non causal
• Transient have a finite duration
• Quantization noise is not much as a problem
• Round of noise error is minimum
• Both filtering recursive, as well as nonrecursive filter, can be also designed using FIR designing techniques
• For designing of a filter having an arbitrary magnitude response; FIR filter designing techniques can be easily applied
• Good performance
• Robust
• The necessity of computational techniques for filter implementation
• A requirement of large storage
• Incapability of linear phase response

Disadvantages of FIR filters :

• Large storage requirements
• Can not simulate prototype analog filter
• For the implementation of FIR filter complex computational techniques are required to implement
• It is hard to implementation than IIR
• Expensive due to a large order
• Require more memory
• Time-consuming process

IIR stands for infinite impulse response. IIR Filter has a lower filter order then a corresponding FIR filter. Here this article also gives information about the advantages and disadvantages of  IIR filters to know more details about it.

Advantages of IIR filters :

• It has a stable design
• An IIR filter has a lesser number of side lobes in the stop band then FIR filter with the same number of parameters
• Implementation of an IIR filter involves fewer parameters 
• Less memory requirement
• Lower computational complexity
• Analog frequency and digital frequency are linearly related

Disadvantages of IIR filters :

• This filter is useful only when the analog filter is bandlimited
• They are harder to implement using fixed-point arithmetic, such as noise generated by calculations and also a limit cycles
• They are more susceptible to the problem of line finite length arithmetic
• They don't offer the computational advantages of FIR filter for the multi-rate application system

Explore more information:

1. Advantages and disadvantages of FIR filter
2. Advantages and disadvantages of IIR filter
3. Advantages and disadvantages of high pass filter
4. Advantages and disadvantages of digital filter
5. Advantages and disadvantages of  passive filter
6. Advantages and disadvantages of active filter

IIR filter example

IIR filter short form is for infinite impulse response. In IIR filter design that are following criteria should be satisfied by designing the digital filter in the analog domain and transforming into a digital domain.

The transfer function of analog filter is :

H(s) = 3 / (s+2) (s+3) with Ts = 0.1 sec

Design the digital IIR filter using BLT.

Answer :

H(s) = 3 / (s+2) (s+3)........................(1)

In BLT H(Z) is obtained by putting :

s = 2/Ts [ Z-1/Z+1] here Ts = 0.1 sec

s = 2/0.1 [ Z-1/Z+1]  

s = 20 [ Z-1/Z+1]  

Putting this value in equation (1) we get,

H(Z) = 3 / [ 20*(Z-1/Z+1)+2] [  20*(Z-1/Z+1)+3]

H(Z) = 3 / [(20Z-20/Z+1) + 2] [ (20Z-20/Z+1 ) + 3 ]

H(Z) = 3 (Z+1) (Z+1) / (20Z-20+2Z+2) (20Z-20+3Z+3) 

H(Z) = 3 (Z+1)² /  506Z²-374Z-414Z+306

-

H(Z) = 3  (Z²+ 2Z +1 )/  506Z²-788Z+306

H(Z) =  (Z²+ 2Z +1 )/  168.67Z²-262.67Z+102

This function required a function for digital IIR filter