Question: factorization (11) of a circulant matrix (9) with the n-vector a as its first column. In (11), W is the n n discrete Fourier transform

factorization (11) of a circulant matrix (9) with the n-vector a as its first column. In (11), W is the n n discrete Fourier transform matrix and diag(W a) is the diagonal matrix with the vector W a (the discrete Fourier transform of a) on its diagonal. (a) Suppose T (a) is nonsingular. Show that its inverse T (a)1 is a circulant matrix. Give a fast method for computing the vector b that satisfies T (b) = T (a)1. (b) Let a and b be two n-vectors. Show that the product T (a)T (b) is a circulant matrix. Give a fast method for computing the vector c that satisfies T (c) = T (a)T (b)

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

# 5: Fourier Interpolant and DFT 1 The Discrete Fourier Transform (DFT) of a periodic array fj , for j = 0, 1, . . . , N 1 (corresponding to data at equally spaced points, starting at the left end...

please help me with this asap do it carefully and clearly plz. # Import library import numpy as #(2 points) # Function register_Arun_3D # Input: Two 3x matrices of points to register: # fixed dataset...

Describe how to construct the function cpo ((D E), v) of two cpos (D, vD) and (E, vE). Prove that ((D E), v) is a cpo. (You may use facts about least upper bounds provided you state them clearly.)...

Make sense of the thoughts of static and dynamic chains, giving an illustration of a circumstance in which they contrast (for example reference to some unacceptable one would get to the wrong...

can someone solve this Modern workstations typically have memory systems that incorporate two or three levels of caching. Explain why they are designed like this. [4 marks] In order to investigate...

Hi I want to do these transformations but I couldn't. Can you tell the codes in cpp or c language? 1) Walsh transform 2) Fast Walsh transform 2.2 WALSH TRANSFORM We recommend the articles of...

ENSURE WORK IS ORIGINAL OR I REJECT AND REPORT YOU TON THE SUPPORT INSTANTLYThe end result does now not should be taken care of. You may additionally expect n 6 length(xs). [Hint: Function least is a...

Briefly describe ASCII and Unicode and draw attention to any relationship between them. [3 marks] (b) Briefly explain what a Reader is in the context of reading characters from data. [3 marks] A...

(a) How does the use of condition codes complicate the implementation of a superscalar processor that supports out-of-order execution? [4 marks] (b) A branch predictor with a high prediction accuracy...

Four Resistances P,Q,R,X formed a wheat stone bridge. The bridge is balanced when R=1002. If P and Q are inter changed the bridge balance for 1212 The value of x is 4. 1) 1002 2) 2002 3) 3002 4) 1102...

How will the investment in a private company be reported under IFRS 9, and how does this differ from IAS 39?

This is the set of financial statements that presents the governmental unit s infrastructure assets and long - term debt. At the present time, this body has the authority to prescribe generally...

Brave Company has the following inventory information. Accounting Transactions Assuming that a perpetual inventory system is used, what is the ending inventory on a LIFO basis? $6,423 $6,203 $6,654...