a. A signal is sampled with a sampling frequency of 44.1 KHz, A design engineer
ID: 2083778 • Letter: A
Question
a. A signal is sampled with a sampling frequency of 44.1 KHz, A design engineer claim that the sampled signal is perfectly reconstructed by low pass filter in each of the following cases: Whether his claim is correct? Give justifications. i The band limiting low pass filter frequency response is zero for all frequencies above 16 KHz. ii. The band limiting low pass filter frequency response is zero for all frequencies above 26 KHz. iii. The band limiting low pass filter frequency response is zero for all frequencies above 22.05 KHz. b. Compare Binary Phase shift Keying (BPSK) and Quadrature Phase Shift Keying (QPSK) in terms of error performance and data rate.Explanation / Answer
Sampling frequency =44.1KHz
i)
The band limiting low pass filter frequency response is zero for all frequencies above 16KHz.
Maximum frequency component fm= 16KHz. signal cam be completely represented in its samples and recovered back if the sampling frequency is fs>=2fm Reconstruction of a signal without distortion takes place when
fs>=2fm
fm = 16KHz
2fm = 2 * 16 KHz = 32KHz
fs > 2fm i.e 44.1KHz > 32KHz signal is perfectly reconstructed by LPF.
ii)
fm = 26KHz
2fm = 2 * 26KHz = 52KHz
fs < 2fm
44.1KHz < 52KHz
Signal cannot be reconstructed by LPF as fs < 2fm
iii)
fm = 22.05KHz
2fm = 2(22.05)KHz = 44.10KHz
Fs = 44.1KHz
As fs = 2fm signal is perfectly reconstructed by LPF.
iv)
BPSK
QPSK
1
Binary phase shift keying (BPSK) is the most simple method to encode data in the phase , it uses two phases +180° and -180°.
Quadrature phase shift keying encodes the data in four different phases, +45°, +135°, -45° and -135°.
2
BPSK represents binary input 1 and 0 w.r.t. change in carrier phase by 180 degree.
QPSK represents two bits using complex carrier symbol each having 90 degree shift with one another
3
BPSK is able to transmit one bit per symbol
QPSK transmits two bits per symbol. So QPSK can be used to double the data rate and still use the same bandwidth or to halve the bandwidth for the same data rate.
4
For the same energy per symbol it is more likely that a BPSK symbol is correctly decoded.
For the same energy per symbol it is more likely that a QPSK symbol is wrongly decoded .
5
In BPSK modulation the signal space is represented by a single basis function:
(t)=2Tbcos(2fct).
While in QPSK the signal space is represented by two basis function:
6
BPSK is considered to be robust modulation scheme compare to the QPSK as it is easy in the receiver to receive the original bits.
QPSK is difficult in the receiver to receive the original bits
7
BPSK signal when it is passed through channel and noise, BPSK demodulator require only two decision points.
QPSK signal when it is passed through channel and noise, QPSK demodulator require four decision points to retrieve the original binary information.
8
With BPSK, higher distance coverage can be achieved from the base station cellular cell or fixed station to the mobile subscribers compare to QPSK.
With QPSK, higher distance coverage can not be achieved from the base station cellular cell or fixed station to the mobile subscribers
9
BPSK data rate is less as one bit per carrier is used in this.
QPSK has advantages of having double data rate compare to BPSK. This is due to support of two bits per carrier in QPSK .
BPSK
QPSK
1
Binary phase shift keying (BPSK) is the most simple method to encode data in the phase , it uses two phases +180° and -180°.
Quadrature phase shift keying encodes the data in four different phases, +45°, +135°, -45° and -135°.
2
BPSK represents binary input 1 and 0 w.r.t. change in carrier phase by 180 degree.
QPSK represents two bits using complex carrier symbol each having 90 degree shift with one another
3
BPSK is able to transmit one bit per symbol
QPSK transmits two bits per symbol. So QPSK can be used to double the data rate and still use the same bandwidth or to halve the bandwidth for the same data rate.
4
For the same energy per symbol it is more likely that a BPSK symbol is correctly decoded.
For the same energy per symbol it is more likely that a QPSK symbol is wrongly decoded .
5
In BPSK modulation the signal space is represented by a single basis function:
(t)=2Tbcos(2fct).
While in QPSK the signal space is represented by two basis function:
- 1(t)=2Tbcos(2fct).1(t)=2Tbcos(2fct).
- 2(t)=2Tbsin(2fct).
6
BPSK is considered to be robust modulation scheme compare to the QPSK as it is easy in the receiver to receive the original bits.
QPSK is difficult in the receiver to receive the original bits
7
BPSK signal when it is passed through channel and noise, BPSK demodulator require only two decision points.
QPSK signal when it is passed through channel and noise, QPSK demodulator require four decision points to retrieve the original binary information.
8
With BPSK, higher distance coverage can be achieved from the base station cellular cell or fixed station to the mobile subscribers compare to QPSK.
With QPSK, higher distance coverage can not be achieved from the base station cellular cell or fixed station to the mobile subscribers
9
BPSK data rate is less as one bit per carrier is used in this.
QPSK has advantages of having double data rate compare to BPSK. This is due to support of two bits per carrier in QPSK .
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