Author Archives: mgreenbe
Here they are: pdf
Here they are: a3solns As usual, please report any errors, typos, etc.
50) Find the -transform of the sequence . (Give a closed-form expression.) 51) Let be as in the previous problem. Find two signals and such that . (You might consider letting be a -spike.) If , can you find a … Continue reading
Our previous MATLAB activities have dealt primarily with the study of periodic signals. The theory of Fourier series tells us that periodic signals can be represented as sums of the simplest kinds of periodic signals — sines and cosines. This … Continue reading
Please submit the following problems: 28, 33, 38, 42, 47. And: In MATLAB activity 6, you investigated the function graphically. Along which line segments is discontinuous? Explain why. Each problem is graded out of 2 points.
If is a real number, then is an unambiguously defined real number if . One reason for this is that is the inverse function of , an increasing and therefore one-to-one function. In the complex realm, is not well defined, … Continue reading
40) Find the first 5 terms of the Taylor series of around . 41) Find the Taylor series of around . (Suggestion: Use the identity .) 42) Find the first four nonzero terms in the Taylor series of around . … Continue reading
Here is the activity: pdf Rejoice! I couldn’t think come up with a worthwhile MATLAB-centric activity relevant to what we’ve been doing lately in class. But MAPLE or MATHEMATICA might come in handy…
Please report typos and errors by email. 28) Find all the solutions of . (Hint: Rewrite the equations in terms of exponentials and manipulate it into a quadratic equation in the variable .) 29) Suppose is analytic on . Let … Continue reading
(As usual, please report errors or typos by email.) Let’s plot the cosine wave of frequency 60 Hz, sampled 1000 times per second for 1 second: t = 0:0.001:1-0.001; x = cos(2*pi*60*t); plot(t,x); (Maximize your figure window if the graph … Continue reading