ECE714/814 Fall 2009 Test #1 Study Guide
The first exam will be given in class on Wednesday, October 28. It will be given closed book and closed notes.
The exam will emphasize visualization and basic understanding rather than memorizing equations or performing
computations. However, a little computing (adding, subtracting, multiplying, dividing) will be necessary. You are
welcome to bring a simple calculator (but not a laptop computer), although I will try to choose numbers that can
be manipulated without one (e.g. 10/2 = ?).
The following items are intended to help you in preparing for the exam. This should give a good idea of what to
emphasize, although it is not guaranteed to be absolutely inclusive (since I haven’t made the test up yet). Also, I
can’t guarantee to ask about all of these things, given that the exam is only 50 minutes in duration.
Chapter 1 (and Assignment #1). Discrete Sequences and Systems
This chapter was very introductory, so there isn’t a lot to consider. However, you should definitely be
comfortable with:
1. The relationship between time-domain and frequency domain representations of discrete time signals,
as represented by figure 103.
2. The basic block diagram elements for representing discrete time LTI systems as represented in figure 1-
6.
3. What the “L” and the “TI” are all about when we refer to discrete time “LTI” systems (figures 1-7, 1-9, 1-
11.
Chapter 2 (and DTFT notes and Assignment #2). Periodic Sampling (and the DTFT)
This chapter appears to simply be about creating discrete time signals by sampling continuous time signals,
however, with the added class material on the DTFT, it addresses the most fundamental frequency domain
properties of discrete time signals, which impact absolutely everything that is done in DSP.
1. When we discuss discrete time signals in the time and frequency domain, we have the following
parameters (which we have used consistently in class and in the text): t, n, ts, f, fs, and w. You should
absolutely understand the meaning of these and the relationships between them.
2. You should understand the periodicity and the symmetry of the Fourier spectra of discrete time signals
as given by the DTFT. For example, given a partial representation of the Fourier spectrum of a signal (in
terms of either real/imaginary or magnitude/phase) over some frequency range, you should be able to
complete the representation based on the required periodicity and symmetry. Or, given a more
complete representation of the spectrum, you should be able to determine whether it satisfies the
periodicity and symmetry requirements.
3. You should understand the relationship between the Fourier spectrum of a continuous time low pass
(also called base band) signal and the Fourier spectrum of a discrete time signal created by sampling at a
specific sampling rate (figures 2-4, 2-5). I might, for example, show you a spectrum of a continuous time
signal similar to 2-4a, and ask you to sketch the resulting spectrum of a discrete time signal created by
sampling at a specific sampling rate (similar to 2-4b or 2-4c, depending on the sampling rate I specify).
4. In this context, you should understand the components of a basic low-pass sampling system (figure 2-6).
