Discrete Time Signal Processing Oppenheim 3rd Edition Pdf Solution Manual.zip

0 views

Skip to first unread message

Message has been deleted

Bok Mull

unread,

Jul 17, 2024, 6:35:41 AM7/17/24

to hyotennibet

Steve Eddins retired from MathWorks in 2024 after 30 years of service. He can now be found at MATLAB Central and at Matrix Values, where he continues to write about MATLAB and related topics. His MathWorks career included image processing, toolbox development, MATLAB development and design, development team management, and MATLAB design standards. He wrote the Steve on Image Processing blog for 18 years and is a co-author of Digital Image Processing Using MATLAB.

An amateur musician and French horn enthusiast, Steve is a member of Concord Orchestra and Melrose Symphony Orchestra, as well as a member of the board of directors for Cormont Music and the Kendall Betts Horn Camp. He blogs about music and French horn at Horn Journey.

discrete time signal processing oppenheim 3rd edition pdf solution manual.zip

Download File https://byltly.com/2yMTnq

My last meeting of the day ended just a little while ago, and I was starting to think seriously about figuring out a blog post for this week. What to write about? That's when I happened to see that Cleve posted just yesterday about the FFT. Ah ha! I'll write about that, too (in honor of National Blog About the FFT Week).

I have three little sort-of stories to tell, the first of which was inspired directly by Cleve's post. Cleve described a very compact, elegant implementation of the divide-and-conquer idea that's central to fast Fourier transform algorithms. Here's the key code fragment of Cleve's textbook function ffttx:

Like Cleve, I really love this little bit of code. But it makes me think back to all the FFT code that I saw back when I was first learning digital signal processing. (That would be the mid- to late-1980s.) Here's a typical textbook sample from the 1989 edition of Discrete-Time Signal Processing by Oppenheim and Schafer):

This code is typical for the time. The focus is on doing the computation in-place and using as few multiplies as possible. One thing you don't see here: explicit recursion! The function DITFFT does not call itself, either directly or indirectly. That was typical for the time. No one wanted to use the memory to make copies of the two half-length arrays, and no one wanted to incur the speed penalty of many recursive function calls. Another typical thing you see in this code is something charmingly called bit-reversed sorting, but that's a topic for another day (maybe).

Anyway, my point is that modern FFT implementations built for today's computer architectures often do make use of explicit recursion. The additional cost of dividing the input array into two or more smaller copies is more than offset by the gains of more cache-friendly execution as the divide-and-conquer problems get smaller and smaller.

Well, to make a little extra money for myself in grad school, I wrote a couple of chapters of the solutions manual for Discrete-Time Signal Processing. One of the chapters covered FFTs. This effort left me completely fed up with drawing butterfly diagrams and counting multiplies. One day I posted the following chart outside my cubicle:

About ten years ago, a tech support case was forwarded to me. A customer complained that MATLAB was very slow in computing the FFT of one specific vector. Other vectors of the same length would go really fast, but not this one.

So I loaded the customer's MAT-file containing the vector and started running FFTs on it. To my surprise, it really was slow! I scratched my head. Then I looked at the output values, and I was even more surprised to see that they were all NaNs! Strange! What was the point? And was this related to the speed issue?

Take a look again at that complicated butterfly diagram above. Notice that every output value depends on every input value. That's true in general for FFT computations of any length. With the way NaNs propagate through arithmetic operations, that implies that just one NaN in the input vector means that the output of fft will always be completely filled with NaNs.

That was related to the speed issue, as it turned out. NaN calculations often are executed in a less-well optimized part of the CPU, or even in software. Lots and lots of NaN calculations bogged down this particular customer's problem.

This class addresses the representation, analysis, and design of discrete time signals and systems. The major concepts covered include: Discrete-time processing of continuous-time signals; decimation, interpolation, and sampling rate conversion; flowgraph structures for DT systems; time-and frequency-domain design techniques for recursive (IIR) and non-recursive (FIR) filters; linear prediction; discrete Fourier transform, FFT algorithm; short-time Fourier analysis and filter banks; multirate techniques; Hilbert transforms; Cepstral analysis and various applications.

I would like to express my thanks to Thomas Baran, Myung Jin Choi, and Xiaomeng Shi for compiling the lecture notes on this site from my individual lectures and handouts and their class notes during the semesters that they were students in the course. These lecture notes, the text book and included problem sets and solutions will hopefully be helpful as you learn and explore the topic of Discrete-Time Signal Processing.