Today, we will learn about the following things:
1. Modulation
2. Digital Modulation Schemes: ASK, FSK
3. InterSymbolInterference (ISI)
4. Pulse Shaping
5. Interpolation and Decimation
Q. What is Modulation?
Ans. Modulation is the process of varying one or more properties of a periodic waveform, called the carrier signal, with a modulating signal that typically contains information to be transmitted. It is nothing but, a carrier signal that varies in accordance with the message signal.
Modulation is of two main types: Analog and Digital Modulation
We'll be discussing Digital Modulation in detail here and Analog Modulation will be discussed in later posts.
Digital Modulation:
Three basic types of digital modulation techniques that we will be discussing are:
1. Amplitude Shift Keying
2. Frequency Shift Keying
3. Phase Shift Keying
All these techniques vary a parameter of a sinusoid to represent the information that we wish to send. The three main parameters, that can be varied are the:
Amplitude, Phase and Frequency.
Amplitude shift keying (ASK) is a simple and elementary form of digital modulation in which the amplitude of a carrier sinusoid is modified in a discrete manner depending on the value of a modulating symbol.
Let a group of ‘m’ bits make one symbol. Hence one can design M = 2m different baseband signals, dm(t), 0 ≤ m ≤ M and 0 ≤ t ≤ T. When one of these symbols modulates the carrier, say, c(t) = cosωct, the modulated waveform is:
This is a narrowband modulation scheme and we assume that a large number of carrier cycles are sent within a symbol interval,
All the main information is embedded only in the peak amplitude of the modulated signal.
The effect of multiplication by the carrier signal A*cos 2*π*fc*t,is simply to shift the spectrum of the modulating signal m(t) to fc as shown in the following figure.
The following figure shows the modulator and a possible implementation of the coherent demodulator for BASK signals.
Q. Why is Modulation done?
Ans. From electromagnetic theory, for efficient radiation of electrical energy from an antenna it must be at least in the order of magnitude of a wavelength in size; c = f*λ, where c is the velocity of light, f is the signal frequency and λ is the wavelength.
For a 1 kHz audio signal, the wavelength is 300 km. An antenna of this size is not practical for efficient transmission.
The low-frequency signal is thus, often frequency-translated to a higher frequency range for efficient transmission. The process is called modulation.
Advantage of using high frequency carrier signal in modulation: The use of a higher frequency range reduces antenna size.
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Q What is ISI? What are the reasons behind the cause of ISI ?
Ans. ISI stands for Inter Symbol Interference.
The following figure shows the data sequence 1,0,1,1,0 that we wish to send, which is in form of square pulses. But, the square pulses are hard to create in practice and also require far too much bandwidth.
Thus, shaping of the pulses in the form of dotted line (as shown in the figure) is done, which reduces the bandwidth requirement and can be easily created by the hardware.
The following figure shows, each of the symbol as it is received and it shows that the transmission medium creates a tail of energy that lasts much longer than intended. The energy from symbols 1 and 2 goes all the way upto 3 and hence each symbol interferes with one or more subsequent symbols.
This spreading and smearing of symbols such that the energy from one symbol effects the next ones in such a way that the received signal has a higher probability of being interpreted incorrectly is called Inter Symbol Interference.
Different reasons that can cause ISI are:
1. filtering effects from hardware
2. frequency selective fading
3. from non linearities and charging effects.
Q. How can ISI be improved ?
Ans.The two main ways to reduce ISI are:
1. By slowing down the signal and transmitting the next signal only when the received signal has damped down.
2. Pulse shaping
Slowing down a signal is not an option in today's world of trying to achieve higher and higher bit rates. So, the only other option that can be used is Pulse Shaping.
Q. What is Pulse shaping and how does it help reduce ISI ?
Ans. Pulse shaping is the process of changing the waveform of transmitted pulses. Its purpose is to make the transmitted signal better suited to its purpose or the communication channel, typically by limiting the effective bandwidth of the transmission.
By filtering the transmitted pulses this way, the inter symbol interference caused by the channel can be kept in control.
In RF communication, pulse shaping is essential for making the signal fit in its frequency band.
How can Pulse Shaping help in controlling ISI?
Secret lies in the demodulation process. When the timing pulse slices the signal to determine the value of the signal at that instant, it does not care what the signal looked like before or after it.
So, if there is some way we could keep the symbols from interfering in such a way that they don't affect the amplitude at the slicing instant, we can counter the ISI successfully.
Q. Define symbol time and symbol rate ?
Ans. Symbol Time, Ts represents the time period of the pulse, For example, in the following figure, which is the time domain representation of the square pulse. 1 second is the Symbol time.
Symbol rate, Rs is the inverse of symbol time. Rs is directly related to bandwidth such that larger the symbol rate, more bandwidth required.
Rs = 1/Ts
Here, symbol time is 1 second and the symbol rate is 1 symbol per second.
Q. Explain the use of the square pulses for pulse shaping purposes?
Ans. Let us consider the square pulse in the figure shown above.
The frequency response of the pulse is given by equation and is shown in the following figure
The symbol rate here is 1 second and the frequency response of the square pulse is in the shape of the sinc function.
As shown in the figures above, the low pass bandwidth is defined as the distance of the origin to the first zero crossing, which is equal to the symbol rate or 1Hz. The bandpass case is twice that.
Thus, for a square pulse, we have
The frequency response of the square pulse goes on forever, thus it is not usually used for the pulse shaping purposes.
Q. What are the disadvantages of using the square pulses for pulse shaping?
Ans. The square pulse has following disadvantages:
1. The square pulse is difficult to create in time domain because of the rise time and a decay time.
2. The frequency response of the square pulse goes on forever.
3. It is very sensitive to ISI.
Q. How do we measure bandwidth for each pulse?
Ans. Bandwidth is the measure on the positive half and is equal to its symbol rate.
Q. Explain the use of the sinc pulse for pulse shaping purposes?
Ans. Now, let us take sinc as the time domain pulse as shown by the red curve in the following figure.
Here, the frequency responce of a sinc pulse is now the square pulse, as shown by red curve in the following figure.
The major advantage of the sinc pulse as seen in the above figure is that the bandwidth requirement is cut to one-half as compared to the case of using square pulses.
Thus, for a sinc pulse, we have
Q. What are the disadvantages of using sinc pulses?
Ans. Following are the disadvantages of using sinc pulses:
1. In time domain, sinc pulse is of infinite length.
2. In reality, we can only design as approximation to the real sinc pulse of a finite length.
3. The pulse tail that falls in the adjacent symbols, decay at the rate of 1/x so, if there is some error in timing, this pulse is not very forgiving.
Q. What other type of pulses can be used for the pulse shaping ?
Ans. Raised Cosine Pulses which are the modification of the sinc pulse.
Advantage of RC pulses: The bandwidth of RC pulses is adjustable which can be varied from W to 2W if W is defined to be the bandwidth of the sinc pulse.
The factor α (roll of factor) relates the achieved bandwidth to the ideal bandwidth W as
where W is the Nyquist bandwidth and W0 is the utilized bandwidth.
The factor α known as the roll of factor, indicates how much bandwidth is being used over the ideal bandwidth.
Smaller the factor, more efficient is the scheme.
Typical roll off values used range from 0.2 to 0.4.
Raised cosine pulses are defined in time domain as follows:
The figure above shows the impulse response of the Raised Cosine filter using different values of roll off factor.
Source: http://complextoreal.com/wp-content/uploads/2013/01/isi.pdf
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Q. What is interpolation ?
Ans. Interpolation is the process to increase the sampling rate of a discrete-time signal.
The advantage of using interpolation is that the higher sampling rate preserves fidelity.
Q. What is decimation?
Ans. Decimation is the process which is used to reduce the sampling rate of a discrete-time signal The advantage of performing decimation is that the low sampling rate reduces storage and computation requirements.
Apply the filter H(ejω) to remove high frequencies and then decimate. The following figure shows the graphical view of Decimation for D=2.
1. Modulation
2. Digital Modulation Schemes: ASK, FSK
3. InterSymbolInterference (ISI)
4. Pulse Shaping
5. Interpolation and Decimation
Q. What is Modulation?
Ans. Modulation is the process of varying one or more properties of a periodic waveform, called the carrier signal, with a modulating signal that typically contains information to be transmitted. It is nothing but, a carrier signal that varies in accordance with the message signal.
Modulation is of two main types: Analog and Digital Modulation
Digital Modulation:
Three basic types of digital modulation techniques that we will be discussing are:
1. Amplitude Shift Keying
2. Frequency Shift Keying
3. Phase Shift Keying
All these techniques vary a parameter of a sinusoid to represent the information that we wish to send. The three main parameters, that can be varied are the:
Amplitude, Phase and Frequency.
Amplitude Shift Keying
These days, Low-frequency analog signals are often converted to digital format (PAM) before transmission.Amplitude shift keying (ASK) is a simple and elementary form of digital modulation in which the amplitude of a carrier sinusoid is modified in a discrete manner depending on the value of a modulating symbol.
Let a group of ‘m’ bits make one symbol. Hence one can design M = 2m different baseband signals, dm(t), 0 ≤ m ≤ M and 0 ≤ t ≤ T. When one of these symbols modulates the carrier, say, c(t) = cosωct, the modulated waveform is:
sm(t) = dm(t).cosωct
This is a narrowband modulation scheme and we assume that a large number of carrier cycles are sent within a symbol interval,
All the main information is embedded only in the peak amplitude of the modulated signal.
In ASK, the bandwidth of the modulated signal will be the same as the bandwidth of the baseband signal. The baseband signal is a long and random sequence of pulses with discrete values.
Hence, ASK modulation is not bandwidth efficient.
It is implemented in practice when simplicity and low cost are principal requirements.
There are two main types of Amplitude shift keying as shown in the figure below:
Binary Amplitude Shift Keying
A binary amplitude-shift keying (BASK) signal can be defined by
s(t) = A*m(t)*cos 2*π*fc*t, 0 < t< T
where A is a constant, m(t) = 1 or 0, fc is the carrier frequency, and T is the bit duration.
If we take Φ1(t) as the orthonormal basis function, the applicable signal space or constellation diagram of the BASK signals is shown in following figure.
The following figure shows the BASK signal sequence generated by the binary sequence
0 1 0 1 0 0 1.
The amplitude of a carrier is switched or keyed by the binary signal m(t). This is sometimes called on-off keying (OOK).
 |
| a) Binary Modulating Signal b) BASK signal |
 | ||
|
The following figure shows the modulator and a possible implementation of the coherent demodulator for BASK signals.
 |
| (a) BASK modulator and (b) coherent demodulator. |
M-ary Amplitude Shift Keying
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Frequency Shift Keying
Q. What is Frequency Shift Keying?
Ans. Frequency Shift Keying (FSK) modulation is a popular form of digital modulation used in low-cost applications for transmitting data at moderate or low rate over wired as well as wireless channels.
Q. How many types of FSK?
Ans. FSK can also be of two types:
1. Binary Frequency Shift Keying ( BFSK ) 2. M-ary FSK
Q. Explain in detail Ninary Frequency Shift Keying (BFSK)?
Ans.Two carrier frequencies are used for binary frequency shift keying modulation.
One frequency is called the ‘mark’ frequency (f2) and the other as the space frequency ( f1)
By convention, the ‘mark’ frequency indicates the higher of the two carriers used
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Q. Why is Modulation done?
Ans. From electromagnetic theory, for efficient radiation of electrical energy from an antenna it must be at least in the order of magnitude of a wavelength in size; c = f*λ, where c is the velocity of light, f is the signal frequency and λ is the wavelength.
For a 1 kHz audio signal, the wavelength is 300 km. An antenna of this size is not practical for efficient transmission.
The low-frequency signal is thus, often frequency-translated to a higher frequency range for efficient transmission. The process is called modulation.
Advantage of using high frequency carrier signal in modulation: The use of a higher frequency range reduces antenna size.
--------------------------------------------------------------------------------------------------------------------------
Q What is ISI? What are the reasons behind the cause of ISI ?
Ans. ISI stands for Inter Symbol Interference.
The following figure shows the data sequence 1,0,1,1,0 that we wish to send, which is in form of square pulses. But, the square pulses are hard to create in practice and also require far too much bandwidth.
Thus, shaping of the pulses in the form of dotted line (as shown in the figure) is done, which reduces the bandwidth requirement and can be easily created by the hardware.
The following figure shows, each of the symbol as it is received and it shows that the transmission medium creates a tail of energy that lasts much longer than intended. The energy from symbols 1 and 2 goes all the way upto 3 and hence each symbol interferes with one or more subsequent symbols.
This spreading and smearing of symbols such that the energy from one symbol effects the next ones in such a way that the received signal has a higher probability of being interpreted incorrectly is called Inter Symbol Interference.
Different reasons that can cause ISI are:
1. filtering effects from hardware
2. frequency selective fading
3. from non linearities and charging effects.
Q. How can ISI be improved ?
Ans.The two main ways to reduce ISI are:
1. By slowing down the signal and transmitting the next signal only when the received signal has damped down.
2. Pulse shaping
Slowing down a signal is not an option in today's world of trying to achieve higher and higher bit rates. So, the only other option that can be used is Pulse Shaping.
Q. What is Pulse shaping and how does it help reduce ISI ?
Ans. Pulse shaping is the process of changing the waveform of transmitted pulses. Its purpose is to make the transmitted signal better suited to its purpose or the communication channel, typically by limiting the effective bandwidth of the transmission.
By filtering the transmitted pulses this way, the inter symbol interference caused by the channel can be kept in control.
In RF communication, pulse shaping is essential for making the signal fit in its frequency band.
How can Pulse Shaping help in controlling ISI?
Secret lies in the demodulation process. When the timing pulse slices the signal to determine the value of the signal at that instant, it does not care what the signal looked like before or after it.
So, if there is some way we could keep the symbols from interfering in such a way that they don't affect the amplitude at the slicing instant, we can counter the ISI successfully.
Q. Define symbol time and symbol rate ?
Ans. Symbol Time, Ts represents the time period of the pulse, For example, in the following figure, which is the time domain representation of the square pulse. 1 second is the Symbol time.
Symbol rate, Rs is the inverse of symbol time. Rs is directly related to bandwidth such that larger the symbol rate, more bandwidth required.
Rs = 1/Ts
Q. Explain the use of the square pulses for pulse shaping purposes?
Ans. Let us consider the square pulse in the figure shown above.
The frequency response of the pulse is given by equation and is shown in the following figure
The symbol rate here is 1 second and the frequency response of the square pulse is in the shape of the sinc function.
As shown in the figures above, the low pass bandwidth is defined as the distance of the origin to the first zero crossing, which is equal to the symbol rate or 1Hz. The bandpass case is twice that.
Thus, for a square pulse, we have
Bandwidth of a square pulse = Rs (for low pass signals)
= 2 times Rs (for bandpass)
The frequency response of the square pulse goes on forever, thus it is not usually used for the pulse shaping purposes.
Q. What are the disadvantages of using the square pulses for pulse shaping?
Ans. The square pulse has following disadvantages:
1. The square pulse is difficult to create in time domain because of the rise time and a decay time.
2. The frequency response of the square pulse goes on forever.
3. It is very sensitive to ISI.
Q. How do we measure bandwidth for each pulse?
Ans. Bandwidth is the measure on the positive half and is equal to its symbol rate.
In the above figure, S1, S2 and S3 represent the bandwidth of the signal.
Q. Explain the use of the sinc pulse for pulse shaping purposes?
Ans. Now, let us take sinc as the time domain pulse as shown by the red curve in the following figure.
Thus, for a sinc pulse, we have
Bandwidth of a sinc pulse, W = Rs/2
The bandwidth here is called Nyquist bandwidth.
Q. What are the disadvantages of using sinc pulses?
Ans. Following are the disadvantages of using sinc pulses:
1. In time domain, sinc pulse is of infinite length.
2. In reality, we can only design as approximation to the real sinc pulse of a finite length.
3. The pulse tail that falls in the adjacent symbols, decay at the rate of 1/x so, if there is some error in timing, this pulse is not very forgiving.
Q. What other type of pulses can be used for the pulse shaping ?
Ans. Raised Cosine Pulses which are the modification of the sinc pulse.
Advantage of RC pulses: The bandwidth of RC pulses is adjustable which can be varied from W to 2W if W is defined to be the bandwidth of the sinc pulse.
The factor α (roll of factor) relates the achieved bandwidth to the ideal bandwidth W as
The factor α known as the roll of factor, indicates how much bandwidth is being used over the ideal bandwidth.
Smaller the factor, more efficient is the scheme.
Typical roll off values used range from 0.2 to 0.4.
Raised cosine pulses are defined in time domain as follows:
The first part is the sinc pulse and the second part is a cosine correction applied to the sinc pulse to make it behave better.
The figure above shows the impulse response of the Raised Cosine filter using different values of roll off factor.
Source: http://complextoreal.com/wp-content/uploads/2013/01/isi.pdf
--------------------------------------------------------------------------------------------------------------------------
Q. What is interpolation ?
Ans. Interpolation is the process to increase the sampling rate of a discrete-time signal.
The advantage of using interpolation is that the higher sampling rate preserves fidelity.
H(ejω) is the filter. Following figure shows the interpolation for L = 3
Q. What is decimation?
Ans. Decimation is the process which is used to reduce the sampling rate of a discrete-time signal The advantage of performing decimation is that the low sampling rate reduces storage and computation requirements.
Apply the filter H(ejω) to remove high frequencies and then decimate. The following figure shows the graphical view of Decimation for D=2.
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