PHY408H
Matlab Tutorial Experiment
(Due on Jan 25, 11:59 pm)
Please submit your report in pdf format (with m-code pasted) to lren AT physics.utoronto.ca. Only
answers to Part 1 - 3 are required.
1 Warm-up Exercises
Try the following commands on your MATLA
Q Liu
Lab 3: Filter Design
Lab Three is due on Mar 25th, 11:59 pm. START EARLY!
1
A Notch Digital Filter
A notch lter is a lter that passes almost all frequencies with unit amplitude, except for a narrow
range of frequencies centered on the rejection freq
PHY 408H 2011
Time Series Analysis
Lecture/Lab Hours, TA (office hours)
Course webpage
http:/www.physics.utoronto.ca/~liuqy/courses/phy408h.html
Syllabus
Grading Schemes
Questionnaries
Signal and System
Signal: something conveys information, description o
Q Liu
Lab 4: Cross-correlation and Spectral Analysis
Due on Apr 6th, 11:59 pm. Oral exams are scheduled for Apr 7th
and 8th.
1
Cross-correlation
It has been shown that noise records at two seismic stations, when cross-correlated and stacked,
are very clos
Lab 2
PHY408H Lab 2
Due at 3:00 pm, March 9th before class.
1 Fourier transform of Gaussian Functions
Recall the Gaussian function we dened in lab 1:
g (t) =
1
2
e(t/tH )
tH
(1)
where tH is the half duration.
1. plot g (t) for tH = 10 and tH = 20 sec on
PHY308/408 - Topic 1 - LINEAR SYSTEMS
AND CONVOLUTION
R.C. Bailey, c 2005
January 12, 2006
1.1
Linear systems
Many objects of scientic interest can be described as linear systems. For
our purposes, a system is an object that engages in reproducible behavi
Q Liu
R. C. Bailey Notes Errata Sheet
1 Chapter One: Linear Systems and Convolution
1. Page 5, (1.15), g (t) should be g (t ).
2. Page 10, the end of question 2, < k 1 should be < k , and > k 1 should be
> k .
2 Chapter Two: Fourier Transform
1. Page 2,
Spectral Analysis of Stochastic Processes
Stationary and Non-stationary Signals
April 6, 2011
Cross-correlation
Cross-correlation of two signals f (t ) and g (t ) is dened as
Cfg ( ) =
f (t )g (t + )dt
(1)
1
2
3
4
shift g (t ) by with respect to f (t ), m
Digital Filters
Z-transform
March 23, 2011
LTI systems
1
Recall LTI systems which can be described by a weight function:
f (t ) w (t ) = g (t )
(1)
We sometimes need to design w (t ) based on given characteristics to
lter the input signal f (t ). These ch
Fourier Transform
DFT, sampling, truncation
March 2, 2011
Bucket Problem
Recall our bucket problem:
dy (t )
= p(t ) ky (t )
dt
1
2
For a sinusoid precipitation rate p(t ) = Po ei t (Po R or Po C),
suppose output y (t ) = Yo ei t .
LDE becomes algebraic eq
Linear System and Convolution
January 19, 2011
Linear system
1
2
signal a(t ): conveys information
e.g. a piece of music, temperature prole, seismogram
system: converts input a(t ) output A(t )
Linear system: if a(t ) A(t ), b(t ) B (t ), then
a(t ) + b(t
PHY308/408 Lab One
PHY408 Lab One: Convolution
Note: Due on Feb 8 11:59 pm. Please include your name on the cover page of your pdf report. Good
luck and have fun!
1 A Discrete Convolution Program
Write a discrete convolution function myConv that convolves
PHY308/408 - Topic 5 - DRAFT STOCHASTIC PROCESSES AND POWER
SPECTRA
R.C. Bailey, c 2005, 2006
October 8, 2008
4.1
Introduction
We have dealt so far with the processing of deterministic signals and systems.
Where we have wanted to design a lter, it has bee
PHY308/408 - Topic 4 - DIGITAL FILTERS
AND Z-TRANSFORMS
R.C. Bailey, c 2005,2006
February 28, 2007
4.1
Introduction
This Chapter deals with the ltering of functions of time in the form of
time series. Filtering here simply means passage of an input f thro
PHY308/408 - Topic 3 - DISCRETE
FOURIER TRANSFORMS
R.C. Bailey, c 2005
January 31, 2007
3.1
Introduction
The Fourier transform of the last chapter (aka the Fourier integral transform)
is the transform which actually applies to the laws of nature which gen
PHY308/408 - Topic 2 - FOURIER
TRANSFORMS
R.C. Bailey, c 2005
January 31, 2006
2.1
Sinusoidal solutions of linear systems
We solved the leaky bucket equation
dy
= p(t) k y (t)
dt
(2.1)
by using an integrating factor. The leaky bucket is a very simple line
Lab 0 - Computational Python
January 14, 2016
1
1.1
Python Tutorial
Warm-up Exercises
Try the following commands on your Python terminal and see what output they produce.
import numpy as np
import matplotlib.pyplot as plt
t = np.arange(10)
g = np.sin(t)
h