Signals and Systems

Signals and systems

Course Introduction

Signal processing plays an extremely important and continually growing role in a wide variety of engineering systems. Furthermore, technology and algorithms for signal processing continue to develop rapidly. While only a short time ago signal processing systems were predominantly analog, integrated circuit technology has made digital signal processing often preferable and more cost-effective.

This course is an introduction to the basic concepts and theory of analog and digital signal processing. The background assumed is calculus, experience in manipulating complex numbers, and some exposure to differential equations. Prior exposure to the fundamentals of circuits for electrical engineers or fundamentals of dynamics for mechanical engineers is helpful but not essential.

Both for pedagogical reasons and as a reflection of the nature of modern signal processing systems, the concepts associated with continuous-time and with discrete-time signals and systems are treated together in a closely coordinated way. Among other things, this approach emphasizes both the similarities and the differences in the two classes of systems. Developing this video course has been an extremely enjoyable and rewarding experience. I hope that you also find it enjoyable, stimulating, and rewarding.

Course Format

The video course Signals and Systems has been designed to provide a thorough exposure to the topic with the opportunity for flexible scheduling. The course materials consist of four basic elements: the lecture videos, course notes, problems and solutions, and the textbook. These elements have been carefully integrated, with each having a particular and important role in the overall effectiveness of the course.

Lecture Videos

On each topic, the lecture provides the conceptual framework, perspective, and illustration of the ideas through examples and lecture demonstrations. Many of the details are avoided in the lectures since they are available in the textbook and are best studied and digested through individual textbook reading and problem solving.

Course Notes

The course notes provide a copy of all the slides and illustrations from the video lectures and are to be used in conjunction with viewing the lectures. They may also be helpful later as a detailed reminder of the content of each lecture.

Textbook

The videotaped lectures are designed to be closely integrated with the text:

Buy at Amazon Oppenheim, Alan V., and A. S. Willsky. Signals and Systems. Prentice Hall, 1982. ISBN: 9780138097318.

Problems and Solutions

There are recommended and optional problems and solutions to be worked after viewing the lecture and reading the text. While allowing for individual preferences and approaches to learning new material, I have made certain assumptions about the use of these materials. For each topic it is preferable to first view the tape in small groups (three to five) whenever possible. A significant advantage to a video course in contrast to a live lecture is that if a point is confusing, the video can be stopped to allow discussion among the viewers. Of course, where appropriate, portions can easily be replayed to help sort out confusing issues.

How to Approach This Course

I recommend that after viewing the lecture, each individual read carefully the appropriate section of the text given as Suggested Reading at the end of each lecture handout and in the Readings section. Finally, and perhaps most important, you should work through the problems in theAssignments section. It is hard to overemphasize the fact that this is the part of the course in which the learning really takes place and consequently is the most important. For each lecture there are recommended and optional problems. The recommended problems should really be thought of as “required,” at the very least in the sense that they are essential for a thorough understanding of the material. You should not proceed beyond any lecture until you feel comfortable with all of its recommended problems. The optional problems are generally more difficult and sometimes cover points that are either deeper or not essential.

Solutions are provided for all of the problems, but they should be used with caution. If you are having difficulty with a problem, it is far better to look for guidance from a colleague than from the solution provided. Furthermore, the solution given may approach the problem from a totally different perspective than you are using. It is generally best to use the solution provided to confirm your answer or as a last resort, when you are really about to give up and no other help is available.

 

tabs bg=”” border=”” color=””] [tab title=”Syllabus”]

Representation of continuous and discrete-time signals; shifting and scaling operations; linear, time-invariant and causal systems; Fourier series representation of continuous periodic signals; sampling theorem; Fourier, Laplace and Z transforms.

[/tab] [tab title=”Videos”]

Speech recognition technology is used more and more for telephone applications like travel booking and information, financial account information, customer service call routing, and directory assistance. Using constrained grammar recognition, such applications can achieve remarkably high accuracy. Research and development in speech recognition technology has continued to grow as the cost for implementing such voice-activated systems has dropped and the usefulness and efficacy of these systems has improved. For example, recognition systems optimized for telephone applications can often supply information about the confidence of a particular recognition, and if the confidence is low, it can trigger the application to prompt callers to confirm or repeat their request. Furthermore, speech recognition has enabled the automation of certain applications that are not automatable using push-button interactive voice response (IVR) systems, like directory assistance and systems that allow callers to “dial” by speaking names listed in an electronic phone book.

Speaker identity is correlated with the physiological and behavioral characteristics of the speaker. These characteristics exist both in the spectral envelope (vocal tract characteristics) and in the supra-segmental features (voice source characteristics and dynamic features spanning several segments). The most common short-term spectral measurements currently used are Linear Predictive Coding (LPC)-derived cepstral coefficients and their regression coefficients. A spectral envelope reconstructed from a truncated set of cepstral coefficients is much smoother than one reconstructed from LPC coefficients.

[/tab] [tab title=”Class Notes”]

Speech recognition technology is used more and more for telephone applications like travel booking and information, financial account information, customer service call routing, and directory assistance. Using constrained grammar recognition, such applications can achieve remarkably high accuracy. Research and development in speech recognition technology has continued to grow as the cost for implementing such voice-activated systems has dropped and the usefulness and efficacy of these systems has improved. For example, recognition systems optimized for telephone applications can often supply information about the confidence of a particular recognition, and if the confidence is low, it can trigger the application to prompt callers to confirm or repeat their request. Furthermore, speech recognition has enabled the automation of certain applications that are not automatable using push-button interactive voice response (IVR) systems, like directory assistance and systems that allow callers to “dial” by speaking names listed in an electronic phone book.

Speaker identity is correlated with the physiological and behavioral characteristics of the speaker. These characteristics exist both in the spectral envelope (vocal tract characteristics) and in the supra-segmental features (voice source characteristics and dynamic features spanning several segments). The most common short-term spectral measurements currently used are Linear Predictive Coding (LPC)-derived cepstral coefficients and their regression coefficients. A spectral envelope reconstructed from a truncated set of cepstral coefficients is much smoother than one reconstructed from LPC coefficients

[/tab] [tab title=”Reference Text Books”]

Speech recognition technology is used more and more for telephone applications like travel booking and information, financial account information, customer service call routing, and directory assistance. Using constrained grammar recognition, such applications can achieve remarkably high accuracy. Research and development in speech recognition technology has continued to grow as the cost for implementing such voice-activated systems has dropped and the usefulness and efficacy of these systems has improved. For example, recognition systems optimized for telephone applications can often supply information about the confidence of a particular recognition, and if the confidence is low, it can trigger the application to prompt callers to confirm or repeat their request. Furthermore, speech recognition has enabled the automation of certain applications that are not automatable using push-button interactive voice response (IVR) systems, like directory assistance and systems that allow callers to “dial” by speaking names listed in an electronic phone book.

Speaker identity is correlated with the physiological and behavioral characteristics of the speaker. These characteristics exist both in the spectral envelope (vocal tract characteristics) and in the supra-segmental features (voice source characteristics and dynamic features spanning several segments). The most common short-term spectral measurements currently used are Linear Predictive Coding (LPC)-derived cepstral coefficients and their regression coefficients. A spectral envelope reconstructed from a truncated set of cepstral coefficients is much smoother than one reconstructed from LPC coefficients

[/tab]

[/tabs]