Show that: (a) The DCT of a length- (N) sequence (x(n)) corresponds to the Fourier transform of

Question:

Show that:

(a) The DCT of a length- $N$ sequence $x(n)$ corresponds to the Fourier transform of the length- $2 N$ sequence $\tilde{x}(n)$ consisting of $x(n)$ extended symmetrically; that is:

\[\tilde{x}(n)= \begin{cases}x(n), & \text { for } 0 \leq n \leq N-1 \\ x(2 N-n-1), & \text { for } N \leq n \leq 2 N-1 .\end{cases}\]

(b) The DCT of $x(n)$ can be computed from the DFT of $\tilde{x}(n)$.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Digital Signal Processing System Analysis And Design

ISBN: 9780521887755

2nd Edition

Authors: Paulo S. R. Diniz, Eduardo A. B. Da Silva , Sergio L. Netto

See More Books

Question Posted: Mar 27, 2024 02:00 AM

See More Questions

Define the contextual-equivalence relation ` M =ctx M0 : for pairs of PCF terms M, M0 , PCF types , and PCF type environments . [3 marks] (ii) For PCF terms M and N with respective typings ` M : and...
(a) Use the following text to derive distributions for rat and chased. Use a five-word window, including open- and closed- class words, ignore case, punctuation and sentence boundaries and weight...
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...
A regression analysis resulted in the following information regarding a dependent variable (y) and an independent variable (x). n = 10 x = 55 y = 55 x2 = 385 y2 = 385 xy = 220 Refer to Exhibit. The...
What appeal options do taxpayers have if they disagree with an audit decision?
How do we determine the attributes of value?
When goods available for salt- exceed sales, firms can manipulate income even when they use specific identification. Cypres, a discounter of consumer electronics, has 300 identical computers...
C&C Properties is an S corporation that owns two rental real estate undertakings: Carrot Plaza and Cantaloupe Place. Both properties produce an annual $10,000 operating loss. C&Cs Schedule K...
LST Company was the parent company, and BAG Company was a subsidiary. LST Company extended credit to BAG Company. The latter became insolvent, and the other creditors objected to LST's sharing...
Show that the discrete cosine transform of a length- $N$ sequence $x(n)$ can be computed from the length $N$ DFT of a sequence $\hat{x}(n)$ consisting of the following reordering of the even...
Compute, using an FFT algorithm, the linear convolution of the sequences (a) and (b) and then (b) and (c) in Exercise 3.13. Exercise 3.13. Compute and plot the magnitude and phase of the DFT of the...
Consider a hoop of mass 3.0 kg and radius 0.50 m that rolls without slipping down an incline. The hoop starts at rest from a height h = 2.5 m above the bottom of the incline and then rolls to the...
Systems thinking is all about solving problemsin organizations, world situations, and even our personal lives. But it is not just a procedure; it is a different way of approaching problems. Our...
How would I display the following 3 principles in an entertaining infographic? Be very specific . Principle 1: Employee Engagement and Motivation Drawing from the Human Relations Movement theory and...
Shown below is a cross section of tubular member which is subjected to a torque T= 5.5 kN-m. It has a length L-3.0-m and the material shear modulus G=27 GPa. Dimensions: b=150 mm, h= 100 mm and t= 8...
The hip roof shown in the below Figure 2 is constructed of 2x10 rafters spaced 16 inches on center. The hip rafters are 1 -inch-wide by 12-inch-high GLBs. The roof has a slope of 4:12. Prepare a list...
2. Estimate the populations of Fargo, ND and Bismarck, ND in years of 2040 and 2050. Select a single value of population that you would use for design purposes in each year. You need to specify and...
A single card is drawn at random from each of six well-shuffled decks of playing cards. Let A be the event that all six cards drawn are different. (a) Find P(A). (b) Find the probability that at...
Walker, Inc., is an all-equity firm. The cost of the company's equity is currently 11.4 percent and the risk-free.rate is 3.3 percent. The company is currently considering a project that will cost...
Question 24 Not yet answered Marked out of 1.00 P Flag question Muscat LLC's current assets and current liabilities are OMR 258,000 and OMR 192,000, respectively. In the year 2020, the company earned...
Question 24 Miami Company sold merchandise for which it received $710,400, including sales and excise taxes. All of the firms sales are subject to a 6% sales tax but only 50% of sales are subject to...
f the IRS intends to close a Taxpayer Assistance Center, they must notify the public at least _____ days in advance of the closure date. 14 30 60 90

Show that: (a) The DCT of a length- (N) sequence (x(n)) corresponds to the Fourier transform of

Question:

Step by Step Answer:

To show these properties lets consider the Discrete Cosine Transform DCT of a sequence xn Part a DCT Corresponds to the Fourier Transform of Extended ...View the full answer

Digital Signal Processing System Analysis And Design

Students also viewed these Computer science questions