ECSE304 Signals and Systems 2
ECSE 304
QUIZ 1
SIGNALS AND SYSTEMS II
ECSE304 Signals and Systems 2 Fall Semester 2011 Tutorial Section 2 McGill University Department of Electrical and Computer Engineering
QUIZ 2 Tuesday, November 8 NAME: _____________________________
STUDENT NUMBER: _______________________
Instructions: The Quiz consists of three problems. No notes or crib sheets are permitted during the quiz. You will be given 30 minutes to complete all the questions. Please show all your work on the pages provided. Problem 1: The system in the following block diagram is used for discrete time processing of a continuous time signal:
The box marked "C/D" is a continuous to discrete converter, or an ideal analog-to-digital converter. The box marked "D/C" is an ideal discrete to continuous converter. Suppose that is band-limited with continuous time Fourier transform for as shown in the figure below, Xa(j) 1
2 1000
2 1000
The discrete time system is an ideal low-pass filter with cutoff frequency . You are to find the continuous time Fourier transform of if the sampling frequencies for the C/D and D/C are and , respectively. a) Plot the Fourier transform of b) Plot the Fourier transform of c) Plot the Fourier transform of
ECSE 304
QUIZ 1
SIGNALS AND SYSTEMS II
ECSE 304
QUIZ 1
SIGNALS AND SYSTEMS II
Problem 2 : The discrete time signal x[n] was obtained by sampling a continuous time signal at a rate of 16KHz. However, to reduce the amount of disk space required for storing the signal, we would like to resample the signal at a rate of 12KHz. For performing this sampling rate conversion we use the setup shown in the following block diagram: x[n]
w[n]
v[n] H1
x[n] has discrete time Fourier transform
M
z[n] L
y[n] H2
where
discrete time frequency in this problem is represented by
Note that .
is the Fourier transform of
an ideal low-pass anti-aliasing filter which is labeled as H1 in the block diagram. Fourier transform of an ideal low-pass interpolating filter which is labeled as H2.
is the
a) Choose minimum integer values for L and M to realize the new sampling rate. b) Determine the cutoff frequencies and the gains of filters H1 and H2 so that no aliasing occurs and the sample rate changes successfully from 16KHz to 12KHz. c) Sketch the Fourier transform of signals v[n], w[n], z[n], and y[n]. Carefully label the important points on the frequency and amplitude axis.
ECSE 304
QUIZ 1
SIGNALS AND SYSTEMS II
ECSE 304
QUIZ 1
SIGNALS AND SYSTEMS II
Problem 3: Figure 1 shows the continuous time Fourier transform, signal in an amplitude modulation system.
, of a modulating
Figure 1
You are given the continuous time Fourier transforms of two amplitude modulated signals in Figures 2 and 3 below. Select the type of amplitude modulation used to generate the spectra in these figures from the following available options. Be sure and explain your answers. a) b) c) d)
Double Sideband (DSB) Amplitude Modulation Single-Sideband (SSB) Amplitude Modulation - Upper Sidebands Single-Sideband (SSB) Amplitude Modulation - Lower Sidebands Double Sideband (DSB) Amplitude Modulation with carrier
Figure 2
Figure 3
Figure 2: (3marks)______________________C________________________
Figure 3: (3marks)__________________A____________________________
ECSE 304
QUIZ 1
SIGNALS AND SYSTEMS II
QUIZ 1
SIGNALS AND SYSTEMS II
ECSE304 Signals and Systems 2 Fall Semester 2011 Tutorial Section 2 McGill University Department of Electrical and Computer Engineering
QUIZ 2 Tuesday, November 8 NAME: _____________________________
STUDENT NUMBER: _______________________
Instructions: The Quiz consists of three problems. No notes or crib sheets are permitted during the quiz. You will be given 30 minutes to complete all the questions. Please show all your work on the pages provided. Problem 1: The system in the following block diagram is used for discrete time processing of a continuous time signal:
The box marked "C/D" is a continuous to discrete converter, or an ideal analog-to-digital converter. The box marked "D/C" is an ideal discrete to continuous converter. Suppose that is band-limited with continuous time Fourier transform for as shown in the figure below, Xa(j) 1
2 1000
2 1000
The discrete time system is an ideal low-pass filter with cutoff frequency . You are to find the continuous time Fourier transform of if the sampling frequencies for the C/D and D/C are and , respectively. a) Plot the Fourier transform of b) Plot the Fourier transform of c) Plot the Fourier transform of
ECSE 304
QUIZ 1
SIGNALS AND SYSTEMS II
ECSE 304
QUIZ 1
SIGNALS AND SYSTEMS II
Problem 2 : The discrete time signal x[n] was obtained by sampling a continuous time signal at a rate of 16KHz. However, to reduce the amount of disk space required for storing the signal, we would like to resample the signal at a rate of 12KHz. For performing this sampling rate conversion we use the setup shown in the following block diagram: x[n]
w[n]
v[n] H1
x[n] has discrete time Fourier transform
M
z[n] L
y[n] H2
where
discrete time frequency in this problem is represented by
Note that .
is the Fourier transform of
an ideal low-pass anti-aliasing filter which is labeled as H1 in the block diagram. Fourier transform of an ideal low-pass interpolating filter which is labeled as H2.
is the
a) Choose minimum integer values for L and M to realize the new sampling rate. b) Determine the cutoff frequencies and the gains of filters H1 and H2 so that no aliasing occurs and the sample rate changes successfully from 16KHz to 12KHz. c) Sketch the Fourier transform of signals v[n], w[n], z[n], and y[n]. Carefully label the important points on the frequency and amplitude axis.
ECSE 304
QUIZ 1
SIGNALS AND SYSTEMS II
ECSE 304
QUIZ 1
SIGNALS AND SYSTEMS II
Problem 3: Figure 1 shows the continuous time Fourier transform, signal in an amplitude modulation system.
, of a modulating
Figure 1
You are given the continuous time Fourier transforms of two amplitude modulated signals in Figures 2 and 3 below. Select the type of amplitude modulation used to generate the spectra in these figures from the following available options. Be sure and explain your answers. a) b) c) d)
Double Sideband (DSB) Amplitude Modulation Single-Sideband (SSB) Amplitude Modulation - Upper Sidebands Single-Sideband (SSB) Amplitude Modulation - Lower Sidebands Double Sideband (DSB) Amplitude Modulation with carrier
Figure 2
Figure 3
Figure 2: (3marks)______________________C________________________
Figure 3: (3marks)__________________A____________________________
ECSE 304
QUIZ 1
SIGNALS AND SYSTEMS II
