A discrete-time periodic signal with fundamental period N0 = 6 has the values x[4] = 3, x[9] = –2, x[–1] = 1, x[14] = 5, x[24] = -3, and x[7] = 9.
Find the value of X[2].
The value of X[2] is of the form Aebj.
The value of A is...….and B is ……...
A discrete-time periodic signal with fundamental period N0 = 6 has the values x[4] = 3,...
A discrete-time signal xin] is periodic with period 8. One period of its Discrete Fourier Transform (DFT) harmonic function is (X[0], X[7]} = [3,4 + j5,-4 -j3,1+ j5,-4,1 j5,-4 + j3, 4 - j5). Solve the following: Average value of x[n] (i) [3 marks] Signal power ofx[n]. (ii) [5 marks] [n] even, odd or neither (iii) [3 marks]
A discrete-time signal xin] is periodic with period 8. One period of its Discrete Fourier Transform (DFT) harmonic function is (X[0], X[7]}...
O KT Question 11 Consider a periodic discrete-time signal with period No = 12. The fundamental frequency of this signal is 20 = • radians/sample radians/sample radians/sample 12 12 radians/sample radians/sample
Q4. For each signal, if it is periodic, find the fundamental period T. (in seconds) and the fundamental frequency (in rad/s). Otherwise prove that the signal is not periodic. [1 + 1 - 2 marks) a) X(t) = cos(5t) + sin(25t) b)x() = sin 91 + + sin(61 - 7) + cos(391)
Prob. 2 Discrete-Time Fourier Series (DTFs) (a) A periodic signal, rin] is shown below. Use the analysis equation to determine the discrete-time Fourier Series (DTFS) coefficients, a. Express the a in terms of cosines [72] -2 N= -3 (b) Sketch the spectrum, as vs. k for -5Sk s5. Please note each value. ak 2 5 Prob. 2 (cont.) -Discrete-Time Fourier Series (CTFS) (c) A periodic signal rafnl is given below. a2In] 2 1 E -3 what is the fundamental period...
Exercise 4 Given the periodic discrete signal with period No = 10, defined by: x(n) = si for - 25 ns +2 lo for + 3 sn s +7 Show that cx = + cos(k!) + cos(k), k = 0,1...,9. a) Clearly show how you get to this result! b) Given that cos(") = }(V5+1), cos(9= :(V5 - 1), cos(9) = -(V5 – 1) and cos(99) = -(V5+1), calculate Co. MacBook Pro
2: (a) Consider a discrete-time sequence x[n] = cos(n+3). Find the fundamental period(N). (b) Consider the sinusodal signal x(t) = 10 sin(21 Fot) with analog frequency F. Write an equa- tion for the discrete time signal n. (c) In part(b) if Fe = 400Hz and the sampling frequency F. = 4kHz, determine the fundamen- tal period of x[n].
A periodic discrete-time signal r[n] has the following samples over one period: Because l is periodic, it can be expressed as a Fourier series (DTPS) (a) What is the period N of the signal n)? (b) The value of ao is known to be a-0. Given this information, what is the value of 3]? Explain how you got this result. Answers without explanation receive 0 credit
Discrete-time signal. Question is regarding Signals and Systems. Find the fundamental period of each these functions. (a) g[n]=cos(27n/10) (b) g[n] = cos(in/10)= cos(2īn/20) (c) g[n] = cos(2n/5)+cos(2 ron /7) (d) g[n]=ej 2an/20 +ej27n/20 (e) g[n]=e+j27n/3 + ej27n/4 (f) g[n]=sin(1310n/8) –cos(97n/6)=sin(2x1310n/16) -cos (2x3mn/4) (8) g[n]=e367n/21 + cos(22n/36)– sin(11ăn/33)
Solution required in MATLAB
1. Convolution and Discrete-Time Fourier Series (DTFS) (a) Generate a periodic signal r2[n] with the fundamental period N ralla-sin(2nn/ İ0) + sin(2m, 2 ) + sin(2nn/30) for 0 < n < N-1 Find the fundamental frequency Ω0-2, N, with the fundamental period N. (b) Generate a periodic signal h2[n] with the fundamental period N haln] = (1/2)", for 0 < n < N-1 (e) Using the com ftuction n Matab, compute the compvolution (d) Using the...
4. (20 points) Consider the periodic signal r(t) shown in the Figure below: x(t) 3 2 N VAA 0 1 2 3 4 5 6 A . Determine the fundamental period T and the fundamental frequency wo. B. Compute the Fourier Series coefficients and simplify the expression to its simplest form.