# Monthly Archives: January 2013

## AMAT 415 — Week 4 problems

P15) Finite, sampled signals and their discrete Fourier transforms both live in — a vector space. Show that the DFT respects basic vector space operations — addition and scalar multiplication. More precisely, show that (a) if and are signals in … Continue reading

## AMAT 415 — Matlab activity 3: Fourier series via FFT

This activity is meant to be instructive. I won’t ask you to submit your code or plots. Let be an -element vector. Its DFT is the vector defined by , where . (In class yesterday, we had a factor of … Continue reading

## AMAT 415 — Week 3 problems

P11) Compute the Fourier coefficients , where if and if . Use your answer to write down both the complex Fourier series of as well the real Fourier series of . P12) Same as P11), but with if and if . P13) … Continue reading

## AMAT 415 — Matlab activity 2: Plotting Fourier series

In this activity, we will plot some Fourier series and see how well they represent the functions that give rise to them. More precisely, if is a function, we will compare its graph to the graph of its Fourier series … Continue reading

## AMAT 415 — Assignment 1

For Assignment 1, please submit MATLAB activity 1 (worth 4 points) and the following problems: P1, P3 (a picture and brief explanation suffices here), P4, P7, P10 (worth 2 points each). Handwritten is fine, but it should be neat and … Continue reading

## AMAT 415 — M. Lamoureux’s notes

AMAT 415 has been taught many times by Michael Lamoureux. He has written up some very nice notes for the course material which he gave me permission to post: Complex analysis Digital signal processing

## AMAT 415 — Hints: Matlab activity 1

Describe the matrix A you get by typing the command A = [-10:10]’*ones(1,21). Describe A’, A+i*A’, and C=C=0.1*(A+i*A’). Type image(A+i*A’). Why does Matlab complain? Address Matlab’s complaint by entering image(abs(A+i*A’)) instead. Think about why the picture looks the way it … Continue reading

## AMAT 415 — Week 2 Problems

(You will be asked to submit a subset of these questions as part of Assignment 1.) P7) Find and . (Try to be clever and avoid duplication of effort.) P8) For a complex number , define the matrix . Show … Continue reading

## AMAT 415 — Matlab activity 1: My first fractal

If you haven’t used Matlab before, I recommend you spend half-an-hour going through the first few sections of the Matlab Primer to familiarize yourself with the basis syntax. In particular, you should learn how to enter and manipulate matrices (with … Continue reading

## AMAT 415 — Week 1 Summary

Topics discussed this week: Complex numbers — real and imaginary parts, modulus, conjugate, basic arithmetic, the complex plane and graphical representation of complex numbers, polar representation, computing -th roots of complex numbers using the polar representation Complex functions — polynomials … Continue reading