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SYSC 4405 - Digital Signal Processing
Marks (by last 3 digits of student number)
Discrete time signal and system representation: time domain, z-transform,
frequency domain. Sampling theorem. Digital filters: design, response,
implementation, computer-aided design. Spectral analysis: the discrete
Fourier transform and the FFT. Applications of digital signal processing.
Prerequisites
SYSC 2500 or SYSC 3500 or SYSC 3600.
Students who have not satisfied the perquisites for this course must either
a) withdraw from the course, or b) fill out a prerequisite waiver from
www.sce.carleton.ca/ughelp, or
c) may be deregistered from the course after
the last day to register for courses in the term.
Instructor
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Andy Adler
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Email: adler@sce.carleton.ca
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Note: Emails to the instructor must contain
a subject line "SYSC4405: your subject line"
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Office: Canal 6204
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Phone: +1-613-520-2600 x 8785
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Office Hours: Friday 1330−1500
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Teaching Assistants
Times and Locations
Fall 2011
(Sept. 8 − Dec. 5)
Google Calendar:
HTML
ICAL
| Section |
| Activity |
| Day |
| Time |
| Location |
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SYSC4405
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LEC
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Mon
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14:35−15:55
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TB 238
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LEC
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Wed
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14:35−15:55
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TB 238
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LAB 1
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Tues (even weeks)
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8:35−11:25
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AA 507A
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LAB 2
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Mon (odd weeks)
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11:35−14:25
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AA 507A
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LAB 3
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Thurs (odd weeks)
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11:35−14:25
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AA 507A
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Text
The text for this course will be the course slides. Links to
course slides are given on the corresponding schedule.
Recommended suplementary material.
Monson H. Hayes, Digital Signal Processing,
Schaum's Outlines, McGrawa-Hill
Steven W. Smith,
The Scientist and Engineer's Guide to Digital Signal Processing
California Technical Publishing
Additional Reference:
Course Notes (2006), Richard Dansereau
Marks
| Work |
| Value
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Quizzes (in Lab)
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15%
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Quizzes (in Class)
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10−15%
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Laboratories
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15%
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Midterm Exam
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10−15%
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Final Exam
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45
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Marks Policies
- Weighting of midterm and final will be optimized
within the range given to maximize student benefit.
- Late work Policy (without *excellent* excuse):
1) 20% if ≤ 7 days late,
2) 0 mark if > 7 days late.
- If you have a question about a mark you have received,
fill out, sign and submit
this form.
Students with Disabilities
Students with disabilities requiring academic accommodations in this
course are encouraged to contact a coordinator at the Paul Menton Centre
for Students with Disabilities to complete the necessary letters of
accommodation. After registering with the PMC, make an appointment
to meet and discuss yours needs with me at least two weeks prior to
the first in-class test or CUTV midterm exam. This is necessary in
order to ensure sufficient time to make the necessary arrangements.
Please note the following deadlines for submitting completed forms to
the Paul Menton Centre: Nov. 3 for Fall Term and Mar. 9 for the Winter Term.
Exams (Midterm and Final)
- Midterm exam is Oct. 24.
- Final exam date will be set by the university
- For all exams, you will be permitted a calculator and
one (1) 8.5"×11"
paper sheet containing any information you choose (double sided).
-
Previous Exams (for practice)
Final exam 2008,
Midterm exam 2008,
Midterm exam 2007 (with solutions − remove t in solution for Q#1),
Final exam 2007,
Practice exam 2007 (with solutions),
- Quiz solutions (2011):
Quiz#2,
Quiz#3,
Quiz#4,
Quiz#5A,
Quiz#5B,
Quiz Nov 14
Quiz Nov 28
Quizzes
Quizzes take place in the first 15 minutes of each
lab session. Each quiz will be one question from the
corresponding list below:
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| No. |
| Assignment |
| Due Date
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2
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- Characterize whether following systems are:
a) Linear,
b) Shift Invariant,
c) Memoryless,
d) LSI,
e) Causal,
f) Stable:
- y[n]= 8x[n] + 2
- y[n]= x[n]
+ x[n−2]
+ x[n−4]
+ x[n−6]
+ x[n−8]
+ …
- y[n]= x[n] + x[0]
- y[n]= 0
- y[n]= 2x[n²]
- y[n]= (x[n²])²
- Given the sequence, x[n]
x[n] = 2δ[n+3] +
(3−n)(u[n]−u[n−3])
sketch the following sequences:
- y1[n] =
x[2n−3]
- y2[n] =
x[|n|]
- y4[n] =
x[½(n)+2]
- An LSI system responds to a step input (u[n])
with output (g[n]).
Calculate the unit sample (impulse)
response as a function of g[n].
- Can a LSI system be characterized completely by its
reponse to one test input signal? However, in practice,
it is not a good idea to only use one test to characterize a
system. Briefly (<100 words) give two reasons
- A system is described by the LCCDE
y[n] − y[n−1]
+ y[n−2] =
x[n−3]
The input is x[n] =
n(u[n]−u[n−4]);
initial conditions are
y[−3] = 2 and
y[−4] = 1.
Show the response of the system from
n=−2 to n=+8.
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Sep. 26,
Oct. 4,
Sep. 29
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3
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Background: You're building a portable music recorder and playback system. The system has recorded a sample sound for playback.
The input, x(t), at the microphone is:
x(t)=
10 sin(600πt) +
5 sin(4100πt) mV
- Show the Fourier transform, X(Ω), as a phasor plot.
- Without using any type of anti-aliasing filter, the
signal is sampled at 1000 samples/s, giving a
sampled sequence x[n].
Calculate x[n] showing each
term in it's lowest frequency form.
- Calculate the Nyquist frequency for this sampling rate,
and calculate at what frequency the aliased representation of
sin(4100πt) will appear in the sampled signal.
Is this signal aliased?
- Calculate the value of x[n]
for n = 0 … 3 .
- Input x[n] is sent into two filters:
Filter 1: y = f1(x):
y1[n] = ½(
x[n] +
x[n−1] )
Filter 2: y = f2(y):
y2[n] = ½(
x[n] +
y[n−1] )
Show the block diagram for each filter.
Calculate
y1[n] and
y2[n]
for n = 0 … 3,
and x[n] = δ[n].
Assume initial conditions are zero.
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Calculate the impulse response
h1[n] and
h2[n], for each filter
- The filters f1 and
f2 are combined in
various ways. Calculate the impulse response of
the following combined filters
______ ______
i) x --->| f1 |-->| f2 | ---> y
______ ______
ii) x --->| f2 |-->| f1 | ---> y
______ __
iii)x -+->| f2 |-->|+| ---> y
|->| f1 |----^
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Oct. 13,
Oct. 18,
Oct. 24
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4
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Consider the signal, x(t),
x(t)=
5 sin(2π200t) +
4 sin(2π300t) +
3 sin(2π400t) +
2 sin(2π500t) mV
- Show the Fourier Transform phasor plot of
x(t)
- Initially we sample x(t) at 700Hz.
Calculate x[n].
Is the signal aliased?
- Show the Fourier Transform phasor plot
of x[n]. Label each
aliased component as "Folded" or "Non-folding".
- If we consider the aliased components to be noise,
What is the signal to noise ratio?
(power is proportional to the sum of Fourier Transform
phasor amplitude squared)?
- We wish to sample the signal with an ADC.
What is the maximum and minimum signal amplitude (give units)?
- We use a 10 bit ADC with Xmax = −Xmin = 1V.
What is Δ? What is the amplitude of quantization noise?
- Is the noise level due to aliasing greater than the noise
level due to quantization noise?
- Calculate the DTFT, X(ω), of:
x[n]= u[n](0.1)n
- Calculate the DTFT, X(ω), of:
x[n]= u[n](0.1)n cos( 0.1n )
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Oct. 27,
Nov. 1,
Nov. 7,
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5a
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- Calculate the DFT of the sequence
x[n]= {0,0,0,0,4,0,0,0}
- Calculate the IDFT of the sequence
X[k]= {8,0,0,0,8,0,0,0}
- We wish to calculate the convolution
( y[n]= h[n] * x[n] )
where
x[n]= {2,4,6,8,10,12,14,18}
h[n]= ½{1,1}
- Using linear convolution, calculate
y[0] to
y[5]
- Sketch the operation of the overlap-add method
using N=4, M=2, and L=3.
- Calculate
y[0] to
y[5]
using overlap-add with these parameters.
Implement circular convolution
using the DFT and IDFT of length N=4.
- Sketch the operation of the overlap-add method
using N=3, M=2, and L=2.
- Calculate
y[0] to
y[3]
using overlap-add with these parameters.
Implement circular convolution directly
for each step.
- Given a DSP system with Ts=1ms,
we need a high pass FIR filter,
hHP[n],
which will
1) Accept frequencies above 100Hz (to within 10%)
2) Reject frequencies below 60Hz (by at least 40 dB)
- Calculate the center frequency and sketch
the filter requirements
- Calculate the ideal filter hideal[n].
- Calculate a window w[n] to meet the requirements.
- What is the FIR filter hHP[n].
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Nov. 10,
Nov. 15
Nov. 21,
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5b
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We wish to implement a band-pass filter
to demodulate an AM radio station with
frequency content in the range
726−734kHz (content in this range
should be accepted ±1%). We need to reject
frequencies below 720kHz and above 740kHz
by at least 40dB. We use a DSP system
with a sampling frequency of 2MHz.
Our DSP takes 1 clk cycle for addition and
5 clk cycles for multiplication (assume other
operations are zero cost). This DSP is available
in versions with clk speeds of:
1MHz, 2Mhz, 5Mhz,
10MHz, 20Mhz, 50Mhz,
100MHz, 200Mhz, 500Mhz,
1Ghz, 2GHz.
Faster DSPs are more expensive and use up
batteries faster.
- Sketch the filter specifications. What
are ωp,L, ωp,H and
ωs,L, ωs,H?
- Calculate ωc,
ω0 for the BPF.
Calculate the ideal BPF.
- Choose a windowing function and window length
for this filter.
- Calculate the expression for the FIR filter
to implement this specification.
- To implement this filter as an FIR convolution,
how many multiplies and additions are required
per output sample.
- What is the slowest clock speed DSP that
can be used for this application using FIR convolution?
- To implement this filter using FFT block processing,
calculate
how many multiplies and additions are required
per output sample:
- for N= 2048
- for N= 4096
- What is the slowest clock speed DSP that
can be used for this application using DSP block processing?
- What is the processing delay for the FIR?
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Nov. 24,
Nov. 29,
Dec. 5,
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Laboratories
Lab attendance is a compulsory component of this course. Laboratories will
be three hours alternate weeks as per the registration schedule.
Attendance is compulsory.
Labs will consist of programming in MATLABtm,
developing filter models
in SIMULINKtm, and using the TI TMS320C6713 DSP starter kit board.
Students must do labs in groups of two. Lab results must
be shown to T.A. before the end of the lab period.
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| No. |
| Laboratory |
| Lab Date |
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1
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Lab #1,
Filter model for lab.
(No assigned mark. Lab group #1, please do on own time)
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Sept. 15,
Sept. 20,
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2
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Lab #2,
Sheet music and mat file with notes for "Country Gardens"
Instructions to bypass speakers
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Sept. 26,
Sept. 29,
Oct. 4
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3
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Lab #3,
DSP Software
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Oct. 13,
Oct. 18,
Oct. 24
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4
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Lab #4
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Oct. 27,
Nov. 1,
Nov. 7
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5a
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Lab #5
You'll also need
this data file
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Nov. 10,
Nov. 15,
Nov. 21
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5b
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Continuation of lab 5a
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Nov. 24,
Nov. 29,
Dec. 5
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Course Outline
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Date
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Activity
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Sept. 12,
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Introduction to Digital Signal Processing
−
Slides #0,
Slides #1,
The Loudness War [Youtube]
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Sept. 14
Sept. 19,
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Signals and Systems
−
Slides #2,
Slides #3,
Slides #4
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Sept. 21
Sep. 26
Sep. 28
Oct. 1
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Fourier Analysis
− Slides #6,
Slides #7,
Slides #8,
Slides #9,
Matlab Programming for DSP:
Slides #5
DSP Examples:
Example #1,
Sound&Wave[Youtube],
Spectrogram View[Youtube],
Sonata Pathétique[Youtube]
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Oct. 3
Oct. 5
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Sampling
− Slides #10,
Slides #11,
Slides #12,
Slides #13,
Antialiasing fonts:
Sub-pixel rendering,
Anti-aliasing
DSP Examples:
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Oct. 10
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Class cancelled (Thanksgiving day)
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Oct. 12
Oct. 17
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Discrete Fourier Transform,
− Slides #14,
Slides #15,
Slides #16,
Slides #17,
Slides #18,
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Oct. 19
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Review:
Practice Midterm (F08),
Midterm (+ solutions),
Midterm exam 2008,
Midterm exam 2007 (with solutions − remove t in solution for Q#1),
Additional Office Hours:
A Adler: Thursday 13:30-17:30 (regular Friday 13:30-15:00)
B Wallace: Friday 9:30-11:30
Xiaosong Lu: Friday 11:30-13:30
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Oct. 24
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Midterm exam
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Oct. 26
Oct. 31
Nov. 2,
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FIR Filter Design
− Slides #19,
Slides #20,
Slides #21,
Slides #22,
Midterm Review
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Nov. 7,
Nov. 9,
Nov. 14,
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Spectrogram,
Fast Fourier Transform,
System Identification
− Slides #23,
Slides #24,
Slides #25,
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Nov. 16
Nov. 21
Nov. 23
Nov. 28
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Z-Transform and
Transform analysis of systems
− Slides #28,
Slides #29,
Slides #30,
Slides #31,
Slides #32,
Slides #33,
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Nov. 30
Dec. 5
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Review,
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Dec. 21
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Final Exam, 14:00−17:00
Additional Office Hours:
A Adler: Dec 20 (10:00-15:00),
B Wallace: Dec 19 (10:00-13:00),
Dec 20 (10:00-13:00)
Xiaosong Lu: Dec 19 (13:00-16:00),
Dec 20 (13:00-16:00)
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Last Updated:
$Date: 2012-02-16 16:32:43 -0500 (Thu, 16 Feb 2012) $
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Engineering