Lecture 1 Matlab Exercise
Lee-Kang Lester Liu
Problem M2.1
M2.1 : write a Matlab Program to generate the conjugate-symmetric and conjugate-anti-symmetric parts of a finite-length complex sequence.
Problem M2.1
What are conjugate-symmetric and conjugate-anti-symmetric ?
M2.1 : write a Matlab Program to generate the conjugate-symmetric and conjugate-anti-symmetric parts of a finite-length complex sequence.
Problem M2.1
π₯πβ [π ]=π₯π
β [βπ ]Conjugate-symmetric : Conjugate-anti-symmetric :
π₯πβ [π ]=βπ₯π
β [βπ ]
What are conjugate-symmetric and conjugate-anti-symmetric ?
Where * denotes complex conjugate.
M2.1 : write a Matlab Program to generate the conjugate-symmetric and conjugate-anti-symmetric parts of a finite-length complex sequence.
Problem M2.1
Any sequence can be expressed as a sum of conjugate-symmetric and conjugate-anti-symmetric sequences.
M2.1 : write a Matlab Program to generate the conjugate-symmetric and conjugate-anti-symmetric parts of a finite-length complex sequence.
Problem M2.1
Any sequence can be expressed as a sum of conjugate-symmetric and conjugate-anti-symmetric sequences.
π₯ [π ]=π₯πβ [π ]+π₯π
β [π ]
M2.1 : write a Matlab Program to generate the conjugate-symmetric and conjugate-anti-symmetric parts of a finite-length complex sequence.
Problem M2.1
Any sequence can be expressed as a sum of conjugate-symmetric and conjugate-anti-symmetric sequences.
π₯ [π ]=π₯πβ [π ]+π₯π
β [π ]Therefore π₯π
β [π ]=12
(π₯ [π ]+π₯β [βπ ] )=π₯πβ [βπ ] Conjugate-
symmetric
M2.1 : write a Matlab Program to generate the conjugate-symmetric and conjugate-anti-symmetric parts of a finite-length complex sequence.
Problem M2.1
Any sequence can be expressed as a sum of conjugate-symmetric and conjugate-anti-symmetric sequences.
π₯ [π ]=π₯πβ [π ]+π₯π
β [π ]Therefore π₯π
β [π ]=12
(π₯ [π ]+π₯β [βπ ] )=π₯πβ [βπ ]
π₯πβ [π ]=1
2(π₯ [π ]βπ₯β [βπ ] )=βπ₯π
β [βπ ] Conjugate-anti-symmetric
Conjugate-symmetric
M2.1 : write a Matlab Program to generate the conjugate-symmetric and conjugate-anti-symmetric parts of a finite-length complex sequence.
Problem M2.1
Matlab Exercise
Given x[n] =
M2.1 : write a Matlab Program to generate the conjugate-symmetric and conjugate-anti-symmetric parts of a finite-length complex sequence.
Question ?
Problem M2.2
M2.2 : (a) Using program 2_2, generate the sequence shown in Figure 2.23 and 2.24. (b) Generate and plot the complex exponential sequence for using program 2_2.
Problem M2.2(a)
M2.2 : (a) Using program 2_2, generate the sequence shown in Figure 2.23 and 2.24. (b) Generate and plot the complex exponential sequence for using program 2_2.
Problem M2.2(a)
M2.2 : (a) Using program 2_2, generate the sequence shown in Figure 2.23 and 2.24. (b) Generate and plot the complex exponential sequence for using program 2_2.
1. Index from 0 to 40
2. A sequence x[n] =
Problem M2.2(a)
M2.2 : (a) Using program 2_2, generate the sequence shown in Figure 2.23 and 2.24. (b) Generate and plot the complex exponential sequence for using program 2_2.
Problem M2.2(a)
M2.2 : (a) Using program 2_2, generate the sequence shown in Figure 2.23 and 2.24. (b) Generate and plot the complex exponential sequence for using program 2_2.
1. Index from 0 to 30
2.
3.
Problem M2.2(b)
M2.2 : (a) Using program 2_2, generate the sequence shown in Figure 2.23 and 2.24. (b) Generate and plot the complex exponential sequence for using program 2_2.
Question ?
Problem M2.5
M2.5 : Using Matlab to verify the result of Example 2.15.
Problem M2.5
M2.5 : Using Matlab to verify the result of Example 2.15.
Consider three sequence generated by uniformly sampling the three cosine functions of frequencies 3Hz, 7Hz, 13Hz, respectively:
with sampling rate , that is ,
Problem M2.5
M2.5 : Using Matlab to verify the result of Example 2.15.
Consider three sequence generated by uniformly sampling the three cosine functions of frequencies 3Hz, 7Hz, 13Hz, respectively:
with sampling rate , that is ,
Using Eq 2.63 and Eq 2.63
Problem M2.5
M2.5 : Using Matlab to verify the result of Example 2.15.
Consider three sequence generated by uniformly sampling the three cosine functions of frequencies 3Hz, 7Hz, 13Hz, respectively:
with sampling rate , that is ,
Using Eq 2.63 and Eq 2.63
Problem M2.5
M2.5 : Using Matlab to verify the result of Example 2.15.
Consider three sequence generated by uniformly sampling the three cosine functions of frequencies 3Hz, 7Hz, 13Hz, respectively:
with sampling rate , that is ,
Using Eq 2.63 and Eq 2.63 where where where
Question ?
Problem M3.1
M3.1 : Determine and plot the real and imaginary parts and the magnitude and phase spectra of the following DTFT for various value of and .
πΊ (π π π )= 1
1β2πΎ (πππ π )πβ π π+πΎ 2πβ2 π π0<πΎ<1
Problem M3.1
M3.1 : Determine and plot the real and imaginary parts and the magnitude and phase spectra of the following DTFT for various value of and .
πΊ (π π π )= 1
1β2πΎ (πππ π )πβ π π+πΎ 2πβ2 π π0<πΎ<1
In z-plane , what are those roots in denominator ?
πΊ (π§ )= 1
1β2πΎ (πππ π ) π§β1+πΎ 2π§β20<πΎ<1
Problem M3.1
M3.1 : Determine and plot the real and imaginary parts and the magnitude and phase spectra of the following DTFT for various value of and .
0<πΎ<1
Problem M3.1
M3.1 : Determine and plot the real and imaginary parts and the magnitude and phase spectra of the following DTFT for various value of and .
0<πΎ<1
Note : these roots are poles of the transfer function.
Question ?
Problem M3.3(b)
M3.1 : Determine and plot the real and imaginary parts and the magnitude and phase spectra of the following DTFT.
X
Problem M3.3(b)
M3.1 : Determine and plot the real and imaginary parts and the magnitude and phase spectra of the following DTFT.
X
Using Matlab roots function to check its zeros.!!
Question ?